text:
module ProcLang.EvaluatorSuite
( tests
) where

import           Data.List          (stripPrefix)
import           ProcLang.Data
import           ProcLang.Evaluator
import           ProcLang.Parser    (expression)
import           Test.HUnit
import           Text.Megaparsec

tests :: Test
tests = TestList
  [ testEq "Eval const" (ExprNum 3) "3"
  , testEq "Eval bounded var" (ExprNum 5) "v"
  , testNoBound "Eval no-bounded var" "y"
  , testEq "Eval binary num-to-num operator" (ExprNum 5) "-(10, 5)"
  , testEq "Eval binary num-to-bool operator (true case)"
           (ExprBool True) "greater?(4, 3)"
  , testEq "Eval binary num-to-bool operator (false case)"
           (ExprBool False) "less?(5,2)"
  , testEq "Eval minus" (ExprNum (-1)) "minus(1)"
  , testLet
  , testCond
  , testProc
  ]

testLet :: Test
testLet = TestList
  [ testEq "Eval let"
           (ExprNum 1)
           $ unlines
             [ "let x = 30"
             , "in let x = -(x,1)"
             , "       y = -(x,2)"
             , "   in -(x,y)"
             ]
  , testEq "Eval let*"
           (ExprNum 2)
           $ unlines
             [ "let x = 30"
             , "in let* x = -(x,1) y = -(x,2)"
             , "   in -(x,y)"
             ]
  ]

testCond :: Test
testCond = TestList
  [ testEq "Eval true branch of if expression"
           (ExprNum 3)
           "if zero? (0) then 3 else 4"
  , testEq "Eval false branch of if expression"
           (ExprNum 4)
           "if zero? (5) then 3 else 4"
  , testError "Empty condition expression should fail" "cond end"
  , testError "A condition expression with no true predicate should fail"
              "cond zero?(5) ==> 3 greater?(5, 10) ==> 4 end"
  , testEq "Match first condition"
           (ExprNum 1)
           "cond zero?(0) ==> 1 zero?(0) ==> 2 zero?(0) ==> 3 end"
  , testEq "Match third condition"
           (ExprNum 3)
           "cond zero?(1) ==> 1 zero?(2) ==> 2 zero?(0) ==> 3 end"
  ]

testProc :: Test
testProc = TestList
  [ testEq "Eval proc and call expression (no parameter)"
           (ExprNum 1)
           "(proc () 1)"
  , testEq "Eval proc and call expression (1 parameter)"
           (ExprNum 2)
           "(proc (x) + (x, x) 1)"
  , testEq "Eval proc and call expression (many parameters)"
           (ExprNum 7)
           "(proc (x, y, z) + (x, * (y, z)) 1 2 3)"
  , testEq "Eval named proc"
           (ExprNum 7)
           "let f = proc (x, y, z) + (x, * (y, z)) in (f 1 2 3)"
  , testError "Too many parameters" "(proc () 1 1)"
  , testError "Too many arguments" "(proc (x, y) +(x, y) 1)"
  ]

initEnv :: Environment
initEnv = initEnvironment [("i", ExprNum 1), ("v", ExprNum 5), ("x", ExprNum 10)]

testEq :: String -> ExpressedValue -> String -> Test
testEq msg expect input = TestCase $
  assertEqual msg (Right expect) evalRes
  where
    evalRes = case runParser expression "Test equal case" input of
      Right pRes  -> valueOf pRes initEnv
      Left pError -> Left $ show pError

testError :: String -> String -> Test
testError msg input = TestCase $
  assertBool msg evalRes
  where
    evalRes = case runParser expression "Test equal case" input of
      Right pRes  -> case valueOf pRes initEnv of
                       Left _  -> True
                       Right _ -> False
      Left _ -> False

testNoBound :: String -> String -> Test
testNoBound msg input = TestCase $
  assertEqual msg noBound True
  where
    noBound = case runParser expression "Test nobound case" input of
      Right pRes -> case valueOf pRes initEnv of
                      Left s -> case stripPrefix "Not in scope: " s of
                                  Nothing -> False
                                  _       -> True
                      _ -> False
      _ -> False


text:
\section{Introduction}
\label{intro}

The ongoing ultra-relativistic heavy-ion collision experiments at RHIC and LHC
enable us to study the quark-gluon plasma (QGP) which is a deconfined state of
hadronic matter generated at very high temperatures and/or densities.  Although
the quark-gluon plasma may be strongly coupled at low temperatures, at high
temperature there is evidence that resummed perturbation theory can be used to
understand the properties of the QGP.  To perturbatively study the QGP one needs
to have an in-depth understanding of the various collective modes.  These
collective modes can be roughly classified into three types which are associated
with different thermal scales, namely the energy (or hard) scale $T$, electric
scale $gT$, and magnetic scale $g^2T$, where $g$ is the strong coupling and $T$
is the temperature of the system.  The majority of studies in the literature
have focused on the hard and electric scales, since the magnetic scale is
related to the difficult non-perturbative physics of confinement.

 Based on the Hard-Thermal-Loop (HTL)
resummations~\cite{braaten1,braaten2,braaten3}, a reorganization of
finite-temperature perturbation theory called HTL perturbation theory (HTLpt)
was developed over a decade ago~\cite{andersen1}.  HTLpt deals with the
intrinsic energy scale $T$ as the hard scale and the electric scale $gT$ as the
soft scale and has been extensively used to calculate various physical
quantities associated with the deconfined state of matter.  These quantities
include: the thermodynamic potential and other relevant quantities associated
with
it~\cite{andersen1,andersen7,purnendu1,purnendu2,purnendu3,andersen8,andersen10,
andersen11,najmul1,andersen12,andersen13,
najmul2,andersen15,najmul4,mogliacci,najmul5,najmul6,najmul7,Strickland:2014zka,
Andersen:2014dua}, photon production rate~\cite{kapusta}, dilepton production
rate~\cite{yuan,griener}, single quark and quark anti-quark
potentials~\cite{mustafa1,mustafa3}, photon damping rate~\cite{markus,abada},
fermion damping rate~\cite{pisarski,peigne}, gluon damping
rate~\cite{pisarski1,pisarski2}, plasma
instabilities~\cite{mrowc,strickland1,strickland2}, jet energy
loss~\cite{markus1,markus2,markus3,strickland7,strickland8,mustafa5}, lepton
asymmetry during
 leptogenesis~\cite{kiessig1,kiessig2}, and thermal axion
production~\cite{graf}.

Although HTLpt seems to work well at a temperature of approximately 2 $T_c$ and
above, where $T_c \sim 160$ MeV is the pseudo-critical temperature for the QGP
phase transition, the time-averaged temperature of the QGP generated at RHIC and
LHC energies is quite close to $T_c$.  Near $T_c$, the running coupling $g$ is
large and the QGP could therefore be completely non-perturbative in this
vicinity of the phase diagram.  In order to make some progress at these
temperatures, it is necessary to consider the non-perturbative physics
associated with the QCD magnetic scale in order to assess its role.
Unfortunately, the magnetic scale is still a challenge for the theoreticians to
treat in a systematic manner since, although its inclusion eliminates infrared
divergences, the physics associated with the magnetic scale remains completely
non-perturbative~\cite{nadkarni}.  The fact that the $\mathcal{O}(g^2T)$
correction to the Debye mass receives non-perturbative contributions indicates
that the background physics is fundamentally
non-perturbative~\cite{arnold_yaffe}.  The physics in the magnetic sector is
described by a dimensionally reduced three-dimensional Yang-Mills theory and the
non-perturbative nature of the physics in this sector is related with the
confining properties of the theory.

Lattice QCD (LQCD) provides a first principles based method that can take into
account the non-perturbative effects of QCD.  Lattice QCD has been used to probe
the behavior of QCD in the vicinity of $T_c$, where matter undergoes a phase
transition from the hadronic phase to the deconfined QGP phase. At this point,
the QCD thermodynamic functions and some other relevant quantities associated
with the fluctuations of conserved charges at finite temperature and zero
chemical potential have been very reliably computed using LQCD (see
e.g.~\cite{borsanyi2,borsanyi3,bnlb1,bnlb2,milc,hotqcd1,hotqcd2,tifr}).  In
addition, quenched LQCD has also been used to study the structure of vector
meson correlation functions.  Such studies have provided critically needed
information about the thermal dilepton rate and various transport coefficients
at zero momentum~\cite{ding,kaczmarek1,arts2,laermann} and finite
momentum~\cite{arts5}.

Calculations in LQCD proceed by evaluating the Euclidean time correlation
function only for a discrete and finite set of Euclidean times. To obtain the
dilepton rate, one needs to perform an analytic continuation of the correlator
from discrete Euclidean times to reconstruct the vector spectral function in
continuous real time. However, this is an ill-posed problem.   To proceed, the
spectral function and hence the dilepton rate in continuous real time can be
obtained  from the correlator in discrete Euclidean times through a
probabilistic interpretation based on the maximum entropy method
(MEM)~\cite{mem1,mem2,mem3}, which requires an ansatz for the spectral
function.  Employing a free-field spectral function as an ansatz, the spectral
function in the quenched approximation of QCD was obtained earlier and found to
approach zero in the low-energy limit~\cite{laermann}.  In the same work, the
authors found that the lattice dilepton rate approached zero at low invariant
masses~\cite{laermann}.   In a more recent LQCD calculation with larger lattice
size, the authors used a Breit-Wigner (BW) form for low-energies plus a
free-field form for high-energies as their ansatz for the spectral
function~\cite{ding}.  The low-energy BW form of their ansatz gave a finite
low-energy spectral function and low-mass dilepton rate.  This indicates that
the computation of low-mass dilepton rate in LQCD is indeed a difficult task and
is also not very clear if there are structures in the low-mass dilepton rate
similar to those found in the HTLpt calculation~\cite{yuan}.

Given the uncertainty associated with lattice computation of dynamical
quantities, e.g. spectral functions,  dilepton rate, and transport coefficients,
it is desirable to have an alternative approach to include non-perturbative
effects that can be handled in a similar way as in resummed perturbation theory.
A few such approaches are available in the literature:  one approach is a
semi-empirical way to incorporate non-perturbative aspects by introducing a
gluon condensate\footnote{An important aspect of the phase structure of QCD is
to understand the effects of different condensates, which serve as order
parameters of the broken symmetry phase.  These condensates are non-perturbative
in nature and their connection with bulk properties of QCD matter is provided by
LQCD.  The gluon condensate has a potentially substantial impact on the bulk
properties, e.g., on the equation of state of QCD matter, compared to the quark
condensate.} in combination with the Green functions in momentum space, which
has been proposed in e.g. Refs.~\cite{schaefer1,schaefer2,peshier,pc1,pc2,pc3}.
In this approach, the effective $n$-point functions are related by
Slavnov-Taylor (ST) identities which contain gluon condensates in the deconfined
phase as hinted from lattice measurements in pure-glue QCD~\cite{boyd}.  The
dispersion relations with dimension-four gluon condensates in medium exhibits
two massive modes~\cite{schaefer1} (a normal quark mode and a plasmino mode)
similar to HTL quark dispersion relations.  This feature leads to sharp
structures (van Hove singularities, energy gap, etc.) in the dilepton production
rates~\cite{schaefer3,peshier} at zero momentum, qualitatively similar to the
HTLpt rate~\cite{yuan}.

Using quenched LQCD, Refs.~\cite{kitazawa1,kitazawa2} calculated the
Landau-gauge quark propagator and its corresponding spectral function by
employing a two pole ansatz corresponding to a normal quark and a plasmino mode
following the HTL dispersion relations~\cite{yuan}. In a very recent
approach~\cite{kim}, a Schwinger-Dyson (SD) equation
has been constructed with the aforementioned Landau-gauge propagator obtained
using quenched LQCD~\cite{kitazawa1,kitazawa2} and a vertex function related
through ST identity.  Using this setup the authors computed the dilepton rate
from the deconfined phase and found that it has the characteristic van-Hove
singularities
but does not have an energy gap.

In a very recent approach~\cite{nansu1} quark propagation in a deconfined medium
including both electric- and magnetic-mass effects has also been studied by
taking into account the non-perturbative magnetic screening scale by using the
Gribov-Zwanziger (GZ) action~\cite{Gribov1,zwanziger1}, which regulates the
magnetic IR behavior of QCD. Since the gluon propagator with the GZ action is IR
regulated, this mimics confinement, making the calculations more compatible with
results of LQCD and functional methods~\cite{mass}.  Interestingly, the
resulting HTL-GZ quark collective modes consist of two massive modes (a normal
quark mode and a plasmino mode) similar to the standard HTL dispersions along
with a \textit{new} massless spacelike excitation which is directly related to
the incorporation of the magnetic scale through the GZ action. This new quark
collective excitation results in a long range correlation in the system, which
may have important consequences for various physical quantities relevant for the
study of deconfined QCD matter. In light of this, we would like to compute the
dilepton production rate and the quark number susceptibility (QNS) associated
with the conserved number fluctuation from the deconfined QGP using the
non-perturbative GZ action.

This paper is organized as follows. In sec.~\ref{setup} we briefly outline the setup for quark propagation
in a deconfined medium using GZ action. In sec.~\ref{dilepton} we calculate the non-perturbative dilepton rate and
discuss the results.  Sec.~\ref{qns} describes the computation and results of non-perturbative QNS. In sec. 5 we
summarize and conclude.

\section{Setup}
\label{setup}

We know that gluons play an important role in confinement. In the GZ
action~\cite{Gribov1,zwanziger1} the issue of confinement is usually tackled
kinematically with the gluon propagator in covariant gauge taking the
form~\cite{Gribov1,zwanziger1}
\begin{eqnarray}
D^{\mu\nu}(P)=\left[\delta^{\mu\nu}-(1-\xi)\frac{P^\mu P^\nu}{P^2}\right]\frac{P^2}{P^4+\gamma_G^4}\, ,
\label{modified_gluon_prop}
\end{eqnarray}
where the four-momenta $P = (p_0, \vec p)$,  $\xi$ is the gauge parameter, and
$\gamma_G$ is called the {\em Gribov parameter}. Inclusion of the term involving
$\gamma_G$ in the denominator moves the poles of the gluon propagator off the
energy axis so that there are no asymptotic gluon modes.  Naturally, to maintain
the consistency of the theory, these unphysical poles should not be considered
in the exact correlation functions of gauge-invariant quantities.  This suggests
that the gluons are not physical excitations.  In practice, this means that the
inclusion of the Gribov parameter results in the effective confinement of
gluons.

In QCD, the Gribov ambiguity typically results in multiple gauge-equivalent
copies and, as a result, it renders perturbative QCD calculations ambiguous.
However, the dimensionful Gribov parameter appearing above can acquire a
well-defined meaning if the topological structure of the $SU(3)$ gauge group is
made to be consistent with the theory.  Very recently, this has been argued and
demonstrated by Kharzeev and Levin~\cite{kharzeev1} by taking into account the
periodicity of the $\theta$-vacuum~\cite{jackiw} of the theory due to the
compactness of the $SU(3)$ gauge group.  The recent work of Kharzeev and Levin
indicates that the Gribov term can be physically interpreted as the topological
susceptibility of pure Yang-Mills theory and that confinement is built into the
gluon propagator in Eq.~(\ref{modified_gluon_prop}), indicating non-propagation
of color charges at long distances and screening of color charges at long
distances in the running coupling.  This also reconciles the original view
Zwanziger had regarding $\gamma_G$ being a statistical parameter
\cite{zwanziger1}.  In practice, $\gamma_G$ can be self-consistently determined
using a one-loop gap equation and at asymptotically high temperatures it takes
the following form~\cite{nansu1,zwanziger2,nansu2}
\begin{eqnarray}
\gamma_G = \frac{D-1}{D}\frac{N_c}{4\sqrt{2}\pi}g^2T,  \label{Gribov_para}
\end{eqnarray}
where $D$ is the dimension of the theory and $N_c$ is the number of
colors.\footnote{Equation (\ref{Gribov_para}) is a one-loop result.  In the
vacuum, the two-loop result has been determined \cite{Gracey:2005cx} and the
Gribov propagator form (\ref{modified_gluon_prop}) is unmodified.  Only
$\gamma_G$ itself is modified to take into account the two-loop correction.  To
the best of our knowledge, this would hold also at finite temperature.} The
one-loop running strong coupling,
$g^2=4\pi\alpha_s$, is
\begin{eqnarray}
g^2(T)=\frac{48\pi^2}{(33-2N_f)\ln\left (\frac{Q^2_0}{\Lambda_0^2} \right )} , \label{alpha_s}
\end{eqnarray}
where $N_f$ is the number of quark flavors and $Q_0$ is the renormalization
scale, which is usually chosen to be $2\pi T$ unless specified.  We fix the
scale $\Lambda_0$ by requiring that $\alpha_s$(1.5 GeV) = 0.326, as obtained
from lattice measurements~\cite{alphas_lat}. For one-loop running, this
procedure gives $\Lambda_0 = 176$ MeV.

To study the properties of a hot QGP using (semi-)perturbative methods, the
effective quark propagator is an essential ingredient.  After resummation, the
quark propagator can be expressed as
\begin{eqnarray}
i S^{-1}(P) &=& \slashed{P}-\Sigma(P), \label{resum_prop}
\end{eqnarray}
where $\Sigma(P)$ is the quark self energy. One can calculate $\Sigma$ using the
modified gluon propagator
(\ref{modified_gluon_prop}) in the high-temperature limit to
obtain~\cite{nansu1}
\begin{eqnarray}
\Sigma(P) &=& (ig)^2C_F \sum\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\int\limits_{\;\;\;\;\;\;\;\;\;\;\;\;\{K\}} \!\! \gamma_\mu S_f(K) \gamma_\nu D^{\mu\nu}(P-K)
\approx -(ig)^2C_F\sum_\pm\int\limits_0^\infty \frac{dk}{2\pi^2}k^2\int \frac{d\Omega}{4\pi} \nonumber \\
&& \times \frac{\tilde{n}_\pm(k,\gamma_G)}{4E_\pm^0}\left[\frac{i\gamma_0+\hat{\bf{k}}\cdot\bf{\gamma}}{iP_0+k-E_\pm^0+
\frac{\bf{p}\cdot\bf{k}}{E_\pm^0}}
 +\frac{i\gamma_0-\hat{\bf{k}}\cdot\bf{\gamma}}{iP_0-k+E_\pm^0-\frac{\bf{p}\cdot\bf{k}}{E_\pm^0}}\right],
\label{modified_quark_self}
\end{eqnarray}
where $\Sigma_{\{K\}}\!\!\!\!\!\!\!\!\!\!\!\!\!\int\;\;\;\;\;\;$ is a fermionic sum-integral, $S_f(K)$ is the bare quark propagator, and
\begin{eqnarray}
\tilde{n}_\pm(k,\gamma_G)&\equiv& n_B\!\left(\sqrt{k^2 \pm i\gamma_G^2}\right)+n_F(k) \nonumber ,\\
E_\pm^0 &=& \sqrt{k^2 \pm i\gamma_G^2}\ , \label{freq}
\end{eqnarray}
where $n_B$ and $n_F$ are Bose-Einstein and Fermi-Dirac distribution functions, respectively.
The  modified  thermal quark  mass in presence  of the  Gribov term can also be obtained  as
\begin{eqnarray}
m_q^2(\gamma_G) = \frac{g^2C_F}{4\pi^2}\sum_\pm\int\limits_0^\infty dk \, \frac{k^2}{E_\pm^0} \, \tilde{n}_\pm(k,\gamma_G).
\label{tmass}
\end{eqnarray}
Using the modified quark self energy given in Eq.~(\ref{modified_quark_self}), it is now easy to write down
the modified effective quark propagator in presence of the Gribov term as
\begin{eqnarray}
i S^{-1}(P) &=& A_0\gamma_0 - A_s \gamma\cdot \hat{\bf{p}}, \label{propa0as}
\end{eqnarray}
where, keeping the structure typically used within the HTL approximation, $A_0$ and $A_s$ are defined as~\cite{nansu1}
\begin{eqnarray}
A_0(\omega,p) &=& \omega-\frac{2g^2C_F}{(2\pi)^2}\sum_\pm\int dk \, k \, \tilde{n}_\pm(k,\gamma_G)
\left[Q_0(\tilde{\omega}_1^\pm,p)+Q_0(\tilde{\omega}_2^\pm,p)\right]\nonumber , \\
A_s(\omega,p) &=& p+\frac{2g^2C_F}{(2\pi)^2}\sum_\pm\int dk \, k \, \tilde{n}_\pm(k,\gamma_G)
\left[Q_1(\tilde{\omega}_1^\pm,p)+Q_1(\tilde{\omega}_2^\pm,p)\right] . \label{a0as}
\end{eqnarray}
Here the modified frequencies are defined as $\tilde{\omega}_1^\pm \equiv E_\pm^0(\omega+k-E_\pm^0)/k$ and
$\tilde{\omega}_2^\pm \equiv E_\pm^0(\omega-k+E_\pm^0)/k$. The Legendre functions of
the second kind, $Q_0$ and $Q_1$, are
\begin{eqnarray}
Q_0(\omega,p) &\equiv& \frac{1}{2p}\ln \frac{\omega+p}{\omega-p} \\
Q_1(\omega,p) &\equiv& \frac{1}{p}(1-\omega Q_0(\omega,p)). \label{legd}
\end{eqnarray}
Using the {helicity representation, the modified effective fermion propagator can also be written as
\begin{eqnarray}
i S(P) &=& \frac{1}{2} \frac{(\gamma_0 - \gamma\cdot \hat{\bf{p}})}{D_+}
+ \frac{1}{2} \frac{(\gamma_0 + \gamma\cdot \hat{\bf{p}})}{D_-} , \label{hprop}
\end{eqnarray}
where $D_\pm$ are obtained as
\begin{eqnarray}
D_+(\omega,p,\gamma_G) &=& A_0(\omega,p) - A_s(\omega,p)\nonumber
= \omega - p - \frac{2g^2C_F}{(2\pi)^2}\sum_\pm\int dk k \tilde{n}_\pm(k,\gamma_G) \nonumber \\
&& \hspace{2cm} \times
\left[Q_0(\tilde{\omega}_1^\pm,p)+ Q_1(\tilde{\omega}_1^\pm,p)
+Q_0(\tilde{\omega}_2^\pm,p)+ Q_1(\tilde{\omega}_2^\pm,p)\right] ,\nonumber\\
D_-(\omega,p,\gamma_G) &=& A_0(\omega,p) + A_s(\omega,p)\nonumber
= \omega + p - \frac{2g^2C_F}{(2\pi)^2}\sum_\pm\int dk k \tilde{n}_\pm(k,\gamma_G) \nonumber \\
&& \hspace{2cm} \times
\left[Q_0(\tilde{\omega}_1^\pm,p)- Q_1(\tilde{\omega}_1^\pm,p)
+Q_0(\tilde{\omega}_2^\pm,p)- Q_1(\tilde{\omega}_2^\pm,p)\right]. \label{dpm}
\end{eqnarray}

\begin{figure}[t]
\begin{center}
\includegraphics[width=0.32\linewidth]{disp_rel_1.pdf}
\includegraphics[width=0.32\linewidth]{disp_rel_2.pdf}
\includegraphics[width=0.32\linewidth]{disp_rel_3.pdf}
\end{center}
\caption{Plot of the dispersion relations for different values of $\gamma_G$. In
the parenthesis, the first one represents a collective excitation mode whereas
the second one is the corresponding energy of that mode.}
\label{disp_rel}
\end{figure}

Solving for the zeros of $D_{\pm}^{-1}(P,\gamma_G)$ gives the dispersion
relations for the collective excitations in the medium.  In Fig.~\ref{disp_rel}
we show the resulting dispersion relations for three different values of the
Gribov parameter $\gamma_G$.  In absence of the Gribov term (\textit{i.e,}
$\gamma_G=0$), there are two massive modes corresponding to a normal quark mode
$q_+$ with energy $\omega_+$ and a long wavelength plasmino mode $q_-$ with
energy $\omega_-$ that quickly approaches free massless propagation in the
high-momentum limit. These two modes are similar to those found in the HTL
approximation~\cite{yuan}.  With the inclusion of the Gribov term, there is a
massless mode $q_G$ with energy $\omega_G$, in addition to the two massive
modes, $q_+$ and $q_-$~\cite{nansu1}. The extra mode $q_G$ is due to the
presence of the magnetic screening scale.
This new massless mode is lightlike at large momenta.\footnote{The slope of the
dispersion relation for this
extra  massless spacelike mode $q_G$ exceeds unity in some domain of momentum.
Thus, the group velocity, $d\omega_G/dp$, is superluminal for the spacelike
mode $q_G$ and approaches the light cone ($d\omega/dp=1$)  from above at high momentum.
Since the mode is spacelike, there is no causality problem.  Instead, this represents
anomalous dispersion in the presence of GZ action which converts Landau damping
into amplification of the spacelike dispersive mode.}  In this context, we note that in Ref.~\cite{pc3},
such an extra massive mode with significant spectral width was observed near
$T_c$ in presence of dimension-four gluon condensates~\cite{pc3} in addition to
the usual propagating quark and plasmino modes.  The existence of this extra
mode could affect lattice extractions of the dilepton rate since even the most
recent LQCD results~\cite{kitazawa1,kitazawa2} assumed that there were only two
poles (a quark mode and a plasmino mode) inspired by the HTL approximation.

In  HTL approximation ($\gamma_G=0$) the propagator contains a discontinuity in
complex plane stemming from the logarithmic terms in (\ref{dpm}) due to
spacelike momentum $\omega^2<p^2$.  Apart from two collective excitations
originating from the in-medium dispersion as discussed above, there is also a
Landau cut contribution in the spectral representation of the propagator due to
the discontinuity in spacelike momentum.  On the other hand, for $\gamma_G \neq
0$ the individual terms in (\ref{dpm}) possess  discontinuities at spacelike
momentum but canceled out when all terms are summed owing the fact that the
poles come in complex-conjugate pairs.  As a result, there is no discontinuity
in the complex plane.\footnote{Starting from the Euclidean expression
(\ref{modified_quark_self}), we have numerically checked for discontinuities and
found none.  We found some cusp-like structures at complex momenta, but $\Sigma$
was found to be $C^0$-continuous everywhere in the complex plane.}   This
results in disappearance of the Landau cut contribution in the spectral
representation of the propagator in spacelike domain. It appears as if the
Landau cut contribution in spacelike domain  for $\gamma_G=0$ is replaced by
massless spacelike dispersive mode in presence of  magnetic scale ($\gamma_G\ne
0$). So the spectral function corresponding to the propagator $D_{\pm}^{-1}$
for $\gamma_G \neq 0$ has only pole contributions.  As a result, one has

\begin{eqnarray}
\rho_\pm^G(\omega,p)= \frac{\omega^2-p^2}{2m_q^2(\gamma_G)}\left[\delta(\omega\mp\omega_+)+\delta(\omega\pm\omega_-)
+\delta(\omega\pm\omega_G)\right], \label{gspect}
\end{eqnarray}
where  $D_+$ has poles at $\omega_+$, $-\omega_-$, and $-\omega_G$
and $D_-$ has poles at $\omega_-$, $-\omega_+$, and $\omega_G$ with a prefactor,  $(\omega^2-p^2)/2m_q^2(\gamma_G)$,  as the residue.

At this point we would like to mention that the non-perturbative quark spectral
function obtained using the quark propagator analyzed in the quenched LQCD
calculations of Refs.~\cite{kitazawa1,kitazawa2,kim} and utilizing gluon
condensates in Refs.~\cite{schaefer1,schaefer2,schaefer3,peshier,pc3} also
forbids a Landau cut contribution since the effective quark propagators in these
calculations do not contain any discontinuities. This stems from the fact that
the quark self-energies in
Refs.~\cite{schaefer1,schaefer2,schaefer3,peshier,pc3}  do not have any
imaginary parts whereas in Refs.~\cite{kitazawa1,kitazawa2,kim} an ansatz of two
quasiparticles was employed for spectral function based on the LQCD quark
propagator analyzed in quenched approximation. The spectral function obtained
with the Gribov action (\ref{gspect}) also possesses only pole contributions but
no Landau cut.  As a result, this approach completely removes the
quasigluons responsible for the Landau cut that should be present in a high-temperature
quark-gluon plasma.  This is similar to findings in other nonperturbative approaches~\cite{kitazawa1,kitazawa2,kim,schaefer1,schaefer2,
schaefer3,peshier}. We will return to the consequences
of the absence of Landau cut in the results and conclusions sections.

Returning to the problem at hand, the spectral density in (\ref{gspect}) at
vanishing three momentum ($p \equiv |\vec{p}| =0$) contains three delta function
singularities corresponding to the two massive modes and one new massless Gribov
mode.  To proceed, one needs the vertex functions in presence of the Gribov
term.  These can be determined by explicitly computing the hard-loop limit of
the vertex function using the Gribov propagator.  One can verify, after the
fact, that the resulting effective quark-gluon vertex function satisfies the
necessary Slavnov-Taylor (ST) identity

\begin{eqnarray}
(P_1-P_2)_\mu\Gamma^\mu(P_1,P_2)= S^{-1}(P_1)-S^{-1}(P_2) \ .
\label{ward_id}
\end{eqnarray}
The temporal and spatial parts of the modified effective quark-gluon vertex can be written as
\begin{eqnarray}
\Gamma^0 &=& a_G ~\gamma^0 +b_G~\bf{\gamma} \cdot \hat{\bf{p}},\nonumber\\
\Gamma^i &=& c_G ~\gamma^i +b_G~\hat{p}^i\gamma_0+d_G~\hat{p}^i\left(\bf{\gamma} \cdot \hat{\bf{p}}\right), \label{vertex}
\end{eqnarray}
where the coefficients are given by
\begin{eqnarray}
a_G &=& 1-\frac{2g^2C_F}{(2\pi)^2}\sum_\pm\int dk \, k \, \tilde{n}_\pm(k,\gamma_G)\frac{1}{\omega_1-\omega_2}
\left[\delta Q_{01}^\pm+\delta Q_{02}^\pm\right],\nonumber\\
b_G &=& -\frac{2g^2C_F}{(2\pi)^2}\sum_\pm\int dk \, k \, \tilde{n}_\pm(k,\gamma_G)\frac{1}{\omega_1-\omega_2}
\left[\delta Q_{11}^\pm+\delta Q_{12}^\pm\right],\nonumber\\
c_G &=& 1+\frac{2g^2C_F}{(2\pi)^2}\sum_\pm\int dk \, k \, \tilde{n}_\pm(k,\gamma_G)\frac{1}{3(\omega_1-\omega_2)}
\left[\delta Q_{01}^\pm+\delta Q_{02}^\pm-\delta Q_{21}^\pm-\delta Q_{22}^\pm\right],\nonumber\\
d_G &=& \frac{2g^2C_F}{(2\pi)^2}\sum_\pm\int dk \, k \, \tilde{n}_\pm(k,\gamma_G)\frac{1}{\omega_1-\omega_2}
\left[\delta Q_{21}^\pm+\delta Q_{22}^\pm\right],\nonumber
\end{eqnarray}
with
\begin{eqnarray}
\delta Q_{n1}^\pm &=& Q_n(\tilde{\omega}_{11}^\pm,p)- Q_n(\tilde{\omega}_{21}^\pm,p){\rm{~for~}} n=0,1,2 \, \, ,\nonumber\\
\omega_{m1}^\pm &=& E_\pm^0(\omega_m+k-E_\pm^0)/k {\rm{~for~}} m=1,2\, \, , \nonumber\\
\omega_{m2}^\pm &=& E_\pm^0(\omega_m-k+E_\pm^0)/k {\rm{~for~}} m=1,2\,\, .\nonumber
\end{eqnarray}
Similarly, the four-point function can be obtained by computing the necessary
diagrams in the hard-loop limit and it satisfies the following generalized ST
identity
\begin{eqnarray}
P_\mu\Gamma^{\mu\nu}(-P_1,P_1;-P_2,P_2) = \Gamma^{\nu}(P_1-P_2,-P_1;P_2)-\Gamma^{\nu}(-P_1-P_2,P_1;P_2) \ . \label{wi_4pt}
\end{eqnarray}

\section{One-loop dilepton production with the Gribov action}
\label{dilepton}

The dilepton production rate for a dilepton with energy $\omega$ and
three-momentum ${\vec q}$ is related to the discontinuity of the photon self
energy $\Pi^{\mu\nu}(Q)$ as~\cite{larry}
\begin{eqnarray}
\frac{dR}{d\omega d^3q}=\frac{\alpha}{12\pi^3Q^2}\frac{1}{e^{\beta\omega}-1}\frac{1}{2\pi i} \, \textmd{Disc} \, \Pi_\mu^\mu(Q).
\label{dilep_def}
\end{eqnarray}
At one-loop order, the dilepton production rate is related to the two diagrams shown in Fig.~\ref{feyn_diag}, which can be written as
\begin{eqnarray}
\Pi_\mu^\mu(Q)&=&\frac{5}{3}e^2\sum_{p_0}\int\frac{d^3p}{(2\pi)^3} \biggl\{\textmd{Tr}\biggl[S(P)
~\Gamma_\mu(K,Q,-P)~S(K)~\Gamma_\mu(-K,-Q,P)\biggr]\label{se_tr} \nonumber \\
&& \hspace{5cm} + \; \textmd{Tr}\biggl[S(P)~\Gamma_\mu^\mu(-P,P;-Q,Q)\biggr]\biggr\}, \label{dilep_tr}
\end{eqnarray}
where $K=P-Q$.  The second term in (\ref{dilep_tr}) is due to the tadpole
diagram shown in Fig.~\ref{feyn_diag} which, in the end, does not contribute
since $\Gamma_\mu^\mu=0$. However, the tadpole diagram is essential to satisfy
the transversality condition, $Q_\mu\Pi^{\mu\nu}(Q)=0$ and thus gauge invariance
and charge conservation in the system.

\begin{figure}[t]
\begin{center}
\includegraphics[width=0.35\linewidth]{oneloop_self_energy_photon}
\hspace{5mm}
\includegraphics[width=0.3\linewidth]{oneloop_quark_photon}
\end{center}
\caption{The self-energy (left) and  tadpole (right) diagrams in one loop order.}
\label{feyn_diag}
\end{figure}

Using the $n$-point functions computed in sec.~\ref{setup} and performing traces, one obtains
\begin{eqnarray}
\Pi_\mu^\mu(\vec{q}=0)&=&\frac{10}{3}e^2T\sum_{p_0}\int\frac{d^3p}{(2\pi)^3}  \nonumber \\
&& \times \Biggl[\left\{\frac{(a_G+b_G)^2}{D_+(\omega_1,p,\gamma_G)D_-(\omega_2,p,\gamma_G)}+
\frac{(a_G-b_G)^2}{D_-(\omega_1,p,\gamma_G)D_+(\omega_2,p,\gamma_G)}\right\}\nonumber\\
&& - \left\{\frac{(c_G+b_G+d_G)^2}{D_+(\omega_1,p,\gamma_G)D_-(\omega_2,p,\gamma_G)}+
\frac{(c_G-b_G+d_G)^2}{D_-(\omega_1,p,\gamma_G)D_+(\omega_2,p,\gamma_G)}\right\}\nonumber\\
&& -2c_G^2\left\{\frac{1}{D_+(\omega_1,p,\gamma_G)D_+(\omega_2,p,\gamma_G)}+\frac{1}{D_-(\omega_1,p,\gamma_G)D_-(\omega_2,p,\gamma_G)}\right\}\Biggr].
\label{dlep_trace_se}
\end{eqnarray}

The discontinuity can be obtained by Braaten-Pisarski-Yuan (BPY) prescription~\cite{yuan}
\begin{eqnarray}
\textmd{Disc~}T\sum_{p_0}f_1(p_0)f_2(q_0-p_0)&=& 2\pi i (1-e^{\beta \omega})\int d\omega_1 \int d\omega_2~n_F(\omega_1)
n_F(\omega_2)\nonumber \\
&& \times \ \delta(\omega-\omega_1-\omega_2) \ \rho_1(\omega_1)\rho_2(\omega_2), \label{bpy_pres}
\end{eqnarray}
which, after some work, allows one to determine the dilepton rate at zero three momentum
\begin{eqnarray}
\frac{dR}{d\omega d^3q}({\vec q}=0)&=&\frac{10\alpha^2}{9\pi^4}\frac{1}{\omega^2}\int\limits_0^\infty p^2dp
\int\limits_{-\infty}^\infty d\omega_1 \int\limits_{-\infty}^\infty d\omega_2 n_F(\omega_1) n_F(\omega_2)
\delta(\omega-\omega_1-\omega_2)\nonumber\\
&&\Bigg[4\left(1-\frac{\omega_1^2-\omega_2^2}{2p\,\omega}\right)^2 \rho_+^G(\omega_1,p) \rho_-^G(\omega_2,p)\nonumber\\
&&+\left(1+\frac{\omega_1^2+\omega_2^2-2p^2-2m_q^2(\gamma_G)}{2p\,\omega}\right)^2\rho_+^G(\omega_1,p) \rho_+^G(\omega_2,p)\nonumber\\
&&+\left(1-\frac{\omega_1^2+\omega_2^2-2p^2-2m_q^2(\gamma_G)}{2p\,\omega}\right)^2\rho_-^G(\omega_1,p) \rho_-^G(\omega_2,p)\Bigg]
.\label{dilep_spec}
\end{eqnarray}

Using (\ref{gspect}) and considering all physically allowed processes by the in-medium dispersion,
the total contribution can be expressed as
\begin{eqnarray}
\frac{dR}{d\omega d^3q}\Big\vert^{pp}({\vec q}=0)&=&\frac{10\alpha^2}{9\pi^4}\frac{1}{\omega^2}
\int\limits_0^\infty p^2\, dp \times \nonumber \\
&& \Biggl [\delta(\omega-2\omega_+)\ n_F^2(\omega_+)\left(\frac{\omega_+^2-p^2}{2m_q^2(\gamma_G)}\right)^2
\left\{1+\frac{\omega_+^2-p^2-m_q^2(\gamma_G)}{p~\omega}\right\}^2\nonumber\\
&&+~\delta(\omega-2\omega_-)\ n_F^2(\omega_-)\left(\frac{\omega_-^2-p^2}{2m_q^2(\gamma_G)}\right)^2
\left\{1-\frac{\omega_-^2-p^2-m_q^2(\gamma_G)}{p~\omega}\right\}^2\nonumber\\
&&+~\delta(\omega-2\omega_G)\ n_F^2(\omega_G)\left(\frac{\omega_G^2-p^2}{2m_q^2(\gamma_G)}\right)^2
\left\{1-\frac{\omega_G^2-p^2-m_q^2(\gamma_G)}{p~\omega}\right\}^2 \nonumber \\
&& +4 \ \delta(\omega-\omega_+-\omega_-) \ n_F(\omega_+) \ n_F(\omega_-)
\left(\frac{\omega_+^2-p^2}{2m_q^2(\gamma_G)}\right)
\left(\frac{\omega_-^2-p^2}{2m_q^2(\gamma_G)}\right) \nonumber \\
&& \times \left\{1-\frac{\omega_+^2-\omega_-^2}{2p\,\omega}\right\}^2 \nonumber \\
&& +\delta(\omega-\omega_++\omega_-) \ n_F(\omega_+)n_F(-\omega_-)
\left(\frac{\omega_+^2-p^2}{2m_q^2(\gamma_G)}\right)\left(\frac{\omega_-^2-p^2}{2m_q^2(\gamma_G)}\right) \nonumber \\
&& \times \left\{1+\frac{\omega_+^2+\omega_-^2-2p^2-2m_q^2(\gamma_G)}{2p\,\omega}\right\}^2
~\Biggr]. \label{dilep_pp}
\end{eqnarray}
Inspecting the arguments of the various energy conserving $\delta$-functions in
(\ref{dilep_pp}) one can understand the physical processes originating from the
poles of the propagator.   The first three terms in (\ref{dilep_pp}) correspond
to the annihilation processes of $q_+{\bar q}_+\rightarrow \gamma^*$, $q_-{\bar
q}_-\rightarrow \gamma^*$, and $q_G{\bar q}_G\rightarrow \gamma^*$,
respectively.  The fourth term corresponds to the annihilation of $q_+{\bar
q}_-\rightarrow \gamma^*$.  On the other hand, the fifth term corresponds to a
process, $q_+\rightarrow q_-\gamma*$, where a $q_+$ mode makes a transition to a
$q_-$ mode along with a virtual photon.  These processes involve soft quark
modes ($q_+, \, q_-$, and $q_G$ and their antiparticles) which originate by
cutting the self-energy diagram in Fig.~\ref{feyn_diag} through the internal
lines without a ``blob''.  The virtual photon, $\gamma^*$, in all these five
processes decays to lepton pair and can be visualized from the dispersion plot
as displayed in the Fig.~\ref{dilepton_processes}.  The momentum integration in
Eq.~(\ref{dilep_pp}) can be performed using the standard delta function
identity
\begin{eqnarray}
\delta(f(x))&=& \sum_i \frac{\delta(x-x_i)}{\mid \! f'(x) \!\mid_{x=x_i}}, \label{delta-prop}
\end{eqnarray}
where $x_i$ are the solutions of $f(x_i)=0$.

\begin{figure}[t]
\begin{center}
\includegraphics[width=0.5\linewidth]{processes.pdf}
\end{center}
\caption{Various dilepton processes which originate from the in-medium dispersion with the Gribov term.}
\label{dilepton_processes}
\end{figure}

\begin{figure}[t]
\begin{center}
\includegraphics[width=0.75\linewidth]{dilepton_processes.pdf}
\end{center}
\caption{The dilepton production rates corresponding to quasiparticle processes in Fig.~\ref{dilepton_processes}.}
\label{dilepton_pp}
\end{figure}

\begin{figure}[t]
\begin{center}
\includegraphics[width=0.75\linewidth]{dilepton_rate_comparison.pdf}
\end{center}
\caption{Comparison of dilepton production rates involving various quasiparticle modes with and without inclusion of $\gamma_G$.}
\label{dilepton_comparison}
\end{figure}

The contribution of various individual processes to  the dilepton production
rate in presence of the Gribov term are displayed in the
Fig.~\ref{dilepton_pp}.  Note that in this figure and in subsequent figures
showing the dilepton rate, the vertical axis shows the dimensional late dilepton
rate $dR/d^4p = dN/d^4xd^4p$ and the horizontal axis is scaled by the thermal
quark mass as to make it dimensionless. In Fig.~\ref{dilepton_pp} we see that
the transition process, $q_+\rightarrow q_-\gamma*$, begins at the energy
$\omega=0$ and ends up with a van-Hove peak\,\footnote{A van-Hove
peak~\cite{van_Hove,van_Hove1} appears where the density of states diverges as
$f'(x)|_{x=x_0}=0$ since the density of states is inversely proportional to
$f'(x)$.} where all of the transitions from $q_+$ branch are directed towards
the minimum of the $q_-$ branch. The annihilation process involving the massless
spacelike Gribov modes, $q_G{\bar q}_G\rightarrow \gamma^*$, also starts at
$\omega=0$ and falls-off very quickly.  The annihilation of the two plasmino
modes, $q_-{\bar q}_-\rightarrow \gamma^*$, opens up with again a van-Hove peak
at $\omega=2 \times $ the minimum energy of the plasmino mode. The contribution
of this process decreases exponentially.  At $\omega=2m_q(\gamma_G)$, the
annihilation processes involving usual quark modes, $q_+{\bar q}_+\rightarrow
\gamma^*$, and that of a quark and a plasmino mode, $q_+{\bar q}_-\rightarrow
\gamma^*$, begin.  However, the former one ($q_+{\bar q}_+\rightarrow \gamma^*$)
grows with the energy and would converge to the usual Born rate (leading order
perturbative rate)~\cite{born} at high mass whereas the later one ($q_+{\bar
q}_-\rightarrow \gamma^*$) initially grows at a very fast rate, but then
decreases slowly and finally drops very quickly. The behavior of the latter
process can easily be understood from the dispersion properties of quark and
plasmino mode. Summing up, the total contribution of all theses five processes
is displayed in Fig.~\ref{dilepton_comparison}. This is compared with the
similar dispersive contribution
when $\gamma_G=0$~\cite{yuan}, comprising processes $q_+\rightarrow q_-\gamma*$,
$q_+{\bar q}_+\rightarrow \gamma^*$, $q_-{\bar q}_-\rightarrow \gamma^*$ and
$q_+{\bar q}_-\rightarrow \gamma^*$. We note that when $\gamma_G=0$, the
dilepton rate contains both van-Hove peaks and an energy gap~\cite{yuan}. In
presence of the Gribov term ($\gamma_G\ne 0$),
the van-Hove peaks remain, but the energy gap disappears due to the annihilation
of new massless Gribov modes, $q_G{\bar q}_G\rightarrow \gamma^*$.

\begin{figure}[t]
\begin{center}
\includegraphics[width=0.75\linewidth]{dilepton_rate_comparison_all.pdf}
\end{center}
\caption{Comparison of various dilepton production  rates from  the deconfined matter.}
\label{dilepton_all}
\end{figure}

In Fig.~\ref{dilepton_all} we compare the rates obtained using various
approximations:  leading-order perturbative (Born) rate~\cite{born}, quenched
LQCD rate~\cite{ding,laermann}, and with and without the Gribov term.  The
non-perturbative rate with the Gribov term shows important structures compared
to the Born rate at low energies.  But when compared to the total HTLpt
rate~\footnote{Since HTL spectral function (i.e, $\gamma_G=0$) has both pole and
Landau cut contribution, so the HTLpt rate~\cite{yuan} contains an additional
{\textit {higher order}} contribution due to the Landau cut stemming from
spacelike momenta.} it is suppressed  in the low mass region due to the absence
of Landau cut contribution for $\gamma_G \neq 0$.  It seems as if the higher
order Landau cut contribution due to spacelike momenta for $\gamma_G=0$ is
replaced by the soft process involving spacelike Gribov modes in the collective
excitations for $\gamma_G\neq 0$. We also note that the dilepton rate~\cite{kim}
using the spectral function constructed with two pole ansatz by analyzing LQCD
propagator in quenched approximation~\cite{kitazawa1,kitazawa2} shows similar
structure  as found here for $\gamma_G\ne0$. On the other hand, such structure
at low mass is also expected in the direct computation of dilepton rate from
LQCD in quenched approximation~\cite{ding,laermann}. However, a smooth variation
of the rate was found at low mass. The computation of dilepton rate in LQCD
involves
various intricacies and uncertainties.  This is because, as noted in
sec.~\ref{intro}, the spectral function in continuous time is obtained from the
correlator in finite set of discrete Euclidean time using a probabilistic MEM
method~\cite{mem1,mem2,mem3} with a somewhat ad hoc continuous ansatz for the
spectral function at low energy and also fundamental difficulties in performing
the necessary analytic continuation in LQCD. Until LQCD overcomes the
uncertainties and difficulties in the computation of the vector spectral
function, one needs to depend, at this juncture, on the prediction of the
effective approaches for dilepton rate at low mass in particular. We further
note that at high-energies the rate for both  $\gamma_G=0$ and $\gamma_G\ne 0$
is higher than the lattice data and Born rate.  This is a consequence of using
the HTL self-energy also at high-energies/momentum where the soft-scale
approximation breaks down. Nevertheless, the low mass rate obtained here by
employing the non-perturbative magnetic scale ($\gamma_G\ne 0$) in addition to
the electric scale allows for a model-based inclusion of the effect of
confinement and the result has a somewhat rich structure at low energy compared
to that obtained using only the electric scale ($\gamma_G = 0$) as well in
LQCD.

We make some general comments concerning the dilepton rate below.
 If one looks at the dispersion plots in Fig.~\ref{disp_rel} for  $\gamma_G=0$,
then one finds that $\omega_-$  falls off  exponentially  and approaches light
cone, whereas $\omega_+$ does not follow fall off exponentially to light cone, but
instead behaves as $[p+m^2_q(T)/p]$ for large $p$. On the other hand,  in
the presence of  $\gamma_G \ne 0$ both  $\omega_-$  and $\omega_G$ approach the light
cone very quickly, but again $\omega_+$ has a similar asymptotic behavior as
before.
This feature of $\omega_+$  makes the dilepton rate at large $\omega$ in
Fig.~\ref{dilepton_all} saturate for both $\gamma_G=0$ and $\gamma_G \ne 0$,
because the dominant contribution comes from the annihilation of two $\omega_+$
as discussed in Fig.~\ref{dilepton_pp}. In general, the total dilepton rate in
Fig.~\ref{dilepton_all}, behaves as  $\sim \exp(-\omega/T)$ for
$\gamma_G(T) = 0$  due to the Landau damping contribution coming from
the quasigluons in a hot and dense medium. As the Landau cut contribution is
missing in the $\gamma_G(T) \neq 0$ case, one finds a leveling off at low $\omega$.
In other words, since the Landau damping contribution is absent for
$\gamma_G(T) \ne 0$, the rate approaches that of the pole-pole
contribution for $\gamma_G=0$ as shown in Fig.~\ref{dilepton_comparison},
except in the mass gap region.  We further note that the LQCD
rate~\cite{ding} matches with Born rate at large $\omega$  simply because a free spectral function
has been assumed for large $\omega$. On the other hand the LQCD
spectral function~\cite{ding} at low $\omega$ is sensitive to the prior
assumptions and, in such a case, the spectral function extracted using
a MEM~\cite{mem1,mem2,mem3} analyses should be interpreted carefully with a proper
error analysis~\cite{mem1}. Since the MEM analyses is sensitive to the prior
assumption, but is not very sensitive to the structure of the spectral function
at small $\omega$, the error is expected to be significant at small
$\omega$. The existence of fine structure such as van Hove singularities at
small $\omega$ cannot be excluded based on the LQCD rate~\cite{ding} at this moment in time.

\section{One-loop quark number susceptibility with the Gribov action}
\label{qns}

We now turn to the computation of the quark number susceptibility (QNS)
including the Gribov term.  The QNS can be interpreted as the response of the
conserved quark number density, $n$ with infinitesimal variation in the quark
chemical potentials $\mu+\delta\mu$. In QCD thermodynamics it is defined as the
second order derivative of pressure ${\cal P}$ with respect to quark chemical
potential, $\mu$. But again, using the fluctuation-dissipation (FD) theorem, the
QNS for a given quark flavor can also be defined from the time-time component of
the current-current correlator in the
vector channel~\cite{purnendu1,purnendu3,forster,kunihiro}. The QNS is in general expressed as
\begin{eqnarray}
\chi_q(T)&=& \! \! \left. \frac{\partial n}{\partial\mu}\right|_{\mu\rightarrow 0}
\!\!\! = \!\!\!\left. \frac{\partial^2 {\cal P}}{\partial^2\mu}\right|_{\mu\rightarrow 0}
\!\!\! =\int d^4x\langle J_0(0,{\vec x})J_0(0,{\vec 0})\rangle \nonumber \\
&=&
\beta\int\limits_{-\infty}^{\infty}\frac{d\omega}{2\pi}\frac{-2}{1-e^{-\beta\omega}}
~\textmd{Im}~\Pi_{00}(\omega, {\vec 0}), \label{def_qns}
\end{eqnarray}
where $J_0$ is the temporal component of the vector current and $\Pi_{00}$ is the time-time component of the vector
correlator or self-energy with external four-momenta $Q \equiv (\omega, \vec q)$. The above relation in
(\ref{def_qns}) is known as the  thermodynamic sum rule~\cite{forster,kunihiro} where the thermodynamic derivative
with respect to the external source, $\mu$ is related to the time-time
component of static correlation function in the vector channel.

In order to compute the QNS we need to calculate the imaginary part of the temporal component of the
two one-loop diagrams given in Fig.~\ref{feyn_diag}. The contribution of the self energy diagram is
\begin{eqnarray}
\Pi^s_{00}(Q)&=&N_fN_cT\sum_{p_0}\int\frac{d^3p}{(2\pi)^3} \textmd{Tr}\left[S(P)~\Gamma^0(K,Q,-P)~S(K)
~\Gamma^0(-K,-Q,P)\right],
\end{eqnarray}
where $K=P-Q$. After performing the traces of the self energy diagram, one obtains
\begin{eqnarray}
\Pi^s_{00}(\vec{q}=0)&=& 2N_fN_cT\sum_{p_0}\int \!\!\!\frac{d^3p}{(2\pi)^3}
\left[\frac{(a_G+b_G)^2}{D_+(\omega_1,p,\gamma_G)D_-(\omega_2,p,\gamma_G)}\right.\nonumber\\
&&\hspace{3.3cm}+\left.\frac{(a_G-b_G)^2}{D_-(\omega_1,p,\gamma_G)D_+(\omega_2,p,\gamma_G)}\right] , \label{se}
\end{eqnarray}
where
\begin{eqnarray}
a_G + b_G &=& 1-\frac{2g^2C_F}{(2\pi)^2}\sum_\pm\int dk k \tilde{n}_\pm(k,\gamma_G)\frac{1}{\omega}\nonumber\\
&& \times \Bigl[Q_0(\tilde{\omega}_{11}^\pm,p) + Q_1(\tilde{\omega}_{11}^\pm,p)+Q_0(\tilde{\omega}_{21}^\pm,p)
- Q_1(\tilde{\omega}_{21}^\pm,p)\nonumber\\
&&+Q_0(\tilde{\omega}_{12}^\pm,p) + Q_1(\tilde{\omega}_{12}^\pm,p)+Q_0(\tilde{\omega}_{22}^\pm,p)- Q_1(\tilde{\omega}_{22}^\pm,p)\Bigr]\nonumber\\
&=& 1+\frac{1}{\omega}\left[D_+(\omega_1,p,\gamma_G)+D_-(\omega_2,p,\gamma_G)-\omega_1-\omega_2\right]\nonumber\\
&=& 1- \frac{\omega_1+\omega_2}{\omega} + \frac{D_+(\omega_1,p,\gamma_G)+D_-(\omega_2,p,\gamma_G)}{\omega}, \label{coeffsa}
\end{eqnarray}
and
\begin{eqnarray}
a_G - b_G &=& 1-\frac{2g^2C_F}{(2\pi)^2}\sum_\pm\int dk k \tilde{n}_\pm(k,\gamma_G)\frac{1}{\omega}\nonumber\\
&& \times \Bigl[Q_0(\tilde{\omega}_{11}^\pm,p)- Q_1(\tilde{\omega}_{11}^\pm,p)+Q_0(\tilde{\omega}_{21}^\pm,p)
+ Q_1(\tilde{\omega}_{21}^\pm,p)\nonumber\\
&&+Q_0(\tilde{\omega}_{12}^\pm,p) - Q_1(\tilde{\omega}_{12}^\pm,p)+Q_0(\tilde{\omega}_{22}^\pm,p) + Q_1(\tilde{\omega}_{22}^\pm,p)\Bigr]\nonumber\\
&=& 1+\frac{1}{\omega}\left[D_-(\omega_1,p,\gamma_G)+D_+(\omega_2,p,\gamma_G)-\omega_1-\omega_2\right]\nonumber\\
&=& 1- \frac{\omega_1+\omega_2}{\omega} + \frac{D_-(\omega_1,p,\gamma_G)+D_+(\omega_2,p,\gamma_G)}{\omega}, \label{coeffsb}
\end{eqnarray}
where $D_\mp(\omega,p,\gamma_G)$ were defined in Eq.~(\ref{dpm}). We write only those terms of Eq.~(\ref{se}) which contain discontinuities
\begin{eqnarray}
\frac{(a_G+b_G)^2}{D_+(\omega_1,p,\gamma_G)D_-(\omega_2,p,\gamma_G)} &=& \frac{(1- \frac{\omega_1+\omega_2}{\omega})^2}
{D_+(\omega_1,p,\gamma_G)D_-(\omega_2,p,\gamma_G)}\nonumber\\
&& \hspace{5mm} + \frac{1}{\omega^2}\left\{\frac{D_+(\omega_1,p,\gamma_G)}{D_-(\omega_2,p,\gamma_G)}+\frac{D_-(\omega_2,p,\gamma_G)}
{D_+(\omega_1,p,\gamma_G)}\right\}, \nonumber\\
\frac{(a_G-b_G)^2}{D_-(\omega_1,p,\gamma_G)D_+(\omega_2,p,\gamma_G)} &=& \frac{(1- \frac{\omega_1+\omega_2}{\omega})^2}
{D_-(\omega_1,p,\gamma_G)D_+(\omega_2,p,\gamma_G)}\nonumber\\
&& \hspace{5mm} + \frac{1}{\omega^2}\left\{\frac{D_-(\omega_1,p,\gamma_G)}{D_+(\omega_2,p,\gamma_G)}+\frac{D_+(\omega_2,p,\gamma_G)}
{D_-(\omega_1,p,\gamma_G)}\right\}.\label{coeffs1}
\end{eqnarray}
Calculating the discontinuity using the BPY prescription given in Eq.~(\ref{bpy_pres}), one can write the imaginary part of Eq.~(\ref{se}) as
\begin{eqnarray}
\textmd{Im}~\Pi^s_{00} &=& 4N_cN_f\pi(1-e^{\beta\omega})\int\frac{d^3p}{(2\pi)^3}\int d\omega_1
\int d\omega_2 ~\delta(\omega-\omega_1-\omega_2)
n_F(\omega_1)n_F(\omega_2)\nonumber\\
&& \times \Bigl[\left(1- \frac{\omega_1+\omega_2}{\omega}\right)^2 \rho_+^G(\omega_1,p)\rho_-^G(\omega_2,p)+
\frac{C_1\rho_+^G(\omega_2,p)+C_2\rho_-^G(\omega_2,p)}{\omega^2}\Bigr], \label{im_se}
\end{eqnarray}
with
\begin{eqnarray}
C_1 &=& \textmd{Im}~D_-(\omega_1,p)=0, \nonumber\\
C_2 &=& \textmd{Im}~D_+(\omega_1,p)=0. \label{c1c2}
\end{eqnarray}
The tadpole part of Fig.~\ref{feyn_diag} can now be written as
\begin{eqnarray}
\Pi^t_{00}(Q)&=&N_fN_cT\sum_{p_0}\int\frac{d^3p}{(2\pi)^3}
 \textmd{Tr}\biggl[S(P)~\Gamma_{00}(-P,P;-Q,Q)\biggr]. \label{qns_tad}
\end{eqnarray}
The four-point function $\Gamma_{00}$ at zero three-momentum can be obtained using Eq.~(\ref{wi_4pt}) giving
\begin{eqnarray}
\Gamma^{00}&=& -(e_G\gamma^0+f_G~ \hat{p}\cdot\vec{\gamma}),\label{4pt}\\
e_G &=& \frac{2g^2c_F}{(2\pi)^2}\sum_\pm\int dk k \tilde{n}_\pm(k,\gamma_G)\frac{1}{(\omega_1-\omega_2)}\left[\delta Q_{01}^\pm+\delta Q_{02}^\pm+\delta Q_{01}^{\pm\prime}+\delta Q_{02}^{\pm\prime}\right],\nonumber\\
f_G &=& \frac{2g^2c_F}{(2\pi)^2}\sum_\pm\int dk k \tilde{n}_\pm(k,\gamma_G)\frac{1}{(\omega_1-\omega_2)}\left[\delta Q_{11}^\pm+\delta Q_{12}^\pm+\delta Q_{11}^{\pm\prime}+\delta Q_{12}^{\pm\prime}\right],\nonumber
\end{eqnarray}
where
\begin{eqnarray}
\delta Q_{n1}^{\pm\prime} &=& Q_n(\tilde{\omega}_{11}^\pm,p)- Q_n(\tilde{\omega}_{21}^{\pm\prime},p){\rm{~for~}} n=0,1,2 \, \, , \nonumber\\
\tilde{\omega}_{21}^{\pm\prime}&=& E_\pm^0(\omega_2^\prime +k-E_\pm^0)/k  \, , \nonumber\\
\tilde{\omega}_{22}^{\pm\prime}&=& E_\pm^0(\omega_2^\prime -k+E_\pm^0)/k  \, , \nonumber\\
\omega_2^\prime &=& \omega_1 + \omega. \nonumber
\end{eqnarray}

Proceeding in a similar way as the self-energy diagram, the contribution from the tadpole diagram is
\begin{eqnarray}
\textmd{Im}~\Pi_{00}^t &=& -4N_cN_f\pi(1-e^{\beta\omega})\int\frac{d^3p}{(2\pi)^3}\int d\omega_1 \int d\omega_2
~ \delta(\omega-\omega_1-\omega_2)\frac{n_F(\omega_1)n_F(\omega_2)}{\omega^2}\nonumber\\
&&\times \Bigl[C_1\rho_+^G(\omega_2,p)+C_2\rho_-^G(\omega_2,p)\Bigr]=0. \label{tad_im}
\end{eqnarray}
The total imaginary contribution of the temporal part shown in Fig.~\ref{feyn_diag} can now be written as
\begin{eqnarray}
\textmd{Im}~\Pi_{00} &=&  \textmd{Im}~\Pi^s_{00} + \textmd{Im}~\Pi^t_{00} \nonumber \\
&=& 4N_cN_f\pi(1-e^{\beta\omega})\int\frac{d^3p}{(2\pi)^3}\int d\omega_1 \int d\omega_2 ~\delta(\omega-\omega_1-\omega_2)
n_F(\omega_1)n_F(\omega_2)\nonumber\\
&& \times \Bigl[\left(1- \frac{\omega_1+\omega_2}{\omega}\right)^2 \rho_+^G(\omega_1,p)\rho_-^G(\omega_2,p)\Bigr]. \label{tot_im}
\end{eqnarray}
It is clear from (\ref{im_se}) and (\ref{tad_im}) that the tadpole contribution
in (\ref{tad_im}) exactly cancels with the second term of (\ref{im_se}) even if
$C_1$ and $C_2$ are finite, e.g., for the HTL
case ($\gamma_G=0$) \cite{purnendu1,purnendu3}. At finite $\gamma_G$, the form
of the sum of self-energy and tadpole diagrams remains the same, even though the
individual contribution are modified.

Putting this in the expression for the QNS in Eq.~(\ref{def_qns}), we obtain
\begin{eqnarray}
\chi_q(T)&=&4N_cN_f\beta\int\frac{d^3p}{(2\pi)^3}\int\limits_{-\infty}^{\infty}d\omega\int d\omega_1
\int d\omega_2 ~\delta(\omega-\omega_1-\omega_2)n_F(\omega_1)n_F(\omega_2) \nonumber \\
&&\hspace{1cm} \times \Big[\left(1- \frac{\omega_1+\omega_2}{\omega}\right)^2
\rho_+^G(\omega_1,p)\rho_-^G(\omega_2,p)\Big] \nonumber \\
&=& 4N_cN_f\beta\int\frac{d^3p}{(2\pi)^3}\Bigl[
\left(\frac{\omega_+^2-p^2}{2m_q^2(\gamma_G)}\right)^2n_F(\omega_+)n_F(-\omega_+) \nonumber\\
&+&\left(\frac{\omega_-^2-p^2}{2m_q^2(\gamma_G)}\right)^2n_F(\omega_-)n_F(-\omega_-)+\left(\frac{\omega_G^2-p^2}{2m_q^2(\gamma_G)}\right)^2n_F(\omega_G)n_F(-\omega_G)
\Bigr] \nonumber \\
&=& \chi_q^{\rm{pp}}(T).\label{qns_pp}
\end{eqnarray}
where we represent the total $\chi_q(T)$ as $\chi^{\rm {pp}}_q(T)$ since there
is only the pole-pole contribution for $\gamma_G\ne 0$. However for $\gamma_G=0$
there will be pole-cut ($\chi^{\rm {pc}}_q(T)$) and cut-cut
($\chi^{\rm{cc}}_q(T))$ contribution in addition to pole-pole contribution
because the spectral
function contains  pole part + Landau cut contribution of the quark propagator.

\begin{figure}[t]
\begin{center}
\includegraphics[width=0.48\linewidth]{plot_qns_pp_resub2.pdf}
\hspace{2mm}
\includegraphics[width=0.48\linewidth]{plot_qns_pc_resub2.pdf}\\
\vspace{5mm}
\includegraphics[width=0.48\linewidth]{plot_qns_cc_resub2.pdf}
\hspace{2mm}
\includegraphics[width=0.48\linewidth]{plot_qns_with_lattice_resub2.pdf}
\end{center}
\caption{ QNS scaled with free values are compared with and without the
inclusion of $\gamma_G$. In each case a band appears due to the choice of the
two renormalization scales as $2\pi T$ and $4\pi T $.  The various symbols
correspond to LQCD data from various groups labeled as  WB~\cite{borsanyi2},
BNL-BI(B) and BNL-BI(u)~\cite{bnlb1,bnlb2}, and TIFR~\cite{tifr}.}

\label{qns_Gribov}
\end{figure}

In Fig.~\ref{qns_Gribov} we have presented the different contribution of QNS
scaled with the corresponding free values with and without the Gribov term.
We, at first, note that the running
coupling in (\ref{alpha_s}) is a smooth function of $T$ around and below
$T_c$.  We have extended to low temperatures as an extrapolation of our
high-temperature result even though our treatment is strictly not valid below $T_c$.
Now from the first panel of Fig.~\ref{qns_Gribov}, the pole-pole contribution
to the QNS with the Gribov action is increased at low $T$, compared to that in
absence of the Gribov term. This improvement at low $T$ is solely due to the
presence of the non-perturbative Gribov mode in the collective excitations.
However, at high $T$ both contributions become almost same as the Gribov mode
disappears.  There are no pole-cut (pc) or cut-cut (cc) contribution for
$\gamma_G(T)\ne 0$, compared to that for $\gamma_G = 0$. The pc and cc
contributions in absence of magnetic scale are displayed in second and third
panels. As a result, we find that the QNS in presence of magnetic scale contains
only the pp-contribution due to collective excitations originating from the
in-medium dispersion whereas, in absence of magnetic scale, the QNS is enhanced
due to additional higher order Landau cut (i.e., pole-cut + cut-cut)
contribution as shown in the fourth panel. When compared with LQCD data from
various groups~\cite{borsanyi2,bnlb1,bnlb2,tifr}, the QNS in presence of
magnetic scale lies around $(10-15)\%$ below the LQCD results whereas that in
absence of magnetic scale is very close to LQCD data. This is expected due to
the {\textit{additional higher-order Landau cut}} contribution  in absence of
magnetic scale as discussed earlier. This also suggests that it is necessary to
include higher loop orders in QNS in presence of the   magnetic scale, which is
beyond scope of this paper. However, we hope to carry out this non-trivial task
in near future.

\section{Conclusions and outlook}
\label{conclusions}

In this paper we considered the effect of inclusion of magnetic screening in the
context of the Gribov-Zwanziger picture of confinement.  In covariant gauge,
this was accomplished by adding a masslike parameter, the Gribov parameter, to
the bare gluon propagator resulting in the non-propagation of gluonic modes.
Following Ref.~\cite{nansu1} we obtained the resummed quark propagator taking
into account the Gribov parameter.  A new key feature of the resulting resummed
quark propagator is that it contains no discontinuities.  In the standard
perturbative hard-thermal loop approach there are discontinuities at spacelike
momentum associated with Landau damping which seem to be absent in the GZ-HTL
approach.  Using the resulting quark propagator, we evaluated the spectral
function, finding that it only contains poles for $\gamma_G \neq 0$.  We then
used these results to compute (1) the dilepton production rate at vanishing
three-momentum and (2) the quark number susceptibility.  For the dilepton
production rate, we found that, due to the absence of Landau damping for
$\gamma_G \neq 0$, the rate contains sharp structures, e.g. Van Hove
singularities, which don't seem to be present in the lattice data.  That being
said, since the lattice calculations used a perturbative ansatz for the spectral
function when performing their MEM analysis\cite{mem1} of the spectral
function, it is unclear how changing the underlying prior assumptions about the
spectral function would affect the final lattice results.
Moreover, the error analsis for spectral function with MEM
prescription~\cite{mem2} has to be done carefully than it was done in LQCD
calculation~\cite{ding}. Since the result is sensitive to the prior
assumptions, the error seems to become large and as a result no conclusion
can be drawn for fine structures at low mass dileptons from the LQCD result.
For the quark number susceptibilities, we found that, again due to the absence
of Landau damping for $\gamma_G \neq 0$, the results do not agree well with
available lattice data.  This can be contrasted with a standard HTLpt
calculation, which seems to describe the lattice data quite well with no free
parameters. It is possible that higher-order loop calculations could improve
the agreement between the Gribov-scenario results and the lattice data;
however, the
success of HTLpt compared to lattice data as well as nonperturbative model
calculations suggests that at \mbox{$T\gtrsim$ 200 MeV} the electric sector
alone provides an accurate description of QGP thermodynamics.
Nevertheless, the present HTLpt results poses a serious
challenge to the Gribov scenario for only inclusion of magnetic mass effects in
the QGP.
The absence of quasigluons responsible for the Landau cut makes
the results for both dilepton production and quark number susceptibility
dramatically different from those in perturbative approaches. We conclude that
the results with present GZ action is in conflict with those in perturbative
approaches due to the absence of the Landau cut contribution in the non-perturbative
quark propagator.

\acknowledgments{
We would like to thank N. Su, K. Tywoniuk, W. Florkowski, and P. Petreczky for useful
conversations.  A.~Bandyopadhyay and M.G.~Mustafa were supported by the Indian
Department of Atomic Energy.  N.~Haque was supported the Indian Department of
Atomic Energy and an award from the Kent State University Office of Research and
Sponsored Programs.  M.~Strickland was supported by the U.S. Department of
Energy under Award No.~DE-SC0013470.

}

redpajama_set_name: RedPajamaArXiv


History can be better appreciated when it is seen and touched, when it is experienced. I didn't appreciate history – or those ideas until I was an adult living in Wuerzburg, Germany for almost six years. At that point I fell in love with the city of Wuerzburg, the history of Wuerzburg, and history in general!
My first book was written during that six year visit – An American Looks at Wuerzburg, Germany. And my love affair with history was born. Years later, I wrote my first three short stories – all about different places/times in World History.


A Boeing 737 MAX 8 airplane being built for Spain-based Air Europa rolls toward takeoff before a test flight, Wednesday, April 10, 2019, at Boeing Field in Seattle.
In a March 13, 2019 file photo, an American Airlines Boeing 737 MAX 8 sits at a boarding gate at LaGuardia Airport in New York.
In this March 23, 2019 file photo a Southwest Airlines Boeing 737 Max aircraft lands at the Southern California Logistics Airport in the high desert town of Victorville, Calif.


As a finish and condiment, high quality Extra Virgin Olive Oils are poured over everything from rice, potatoes, vegetables and beans to meats, poultry and fish or even ice-cream.
Olive oil is a versatile ingredient that has been used in cooking for thousands of years. It has broken down a lot of boundaries in recent times, becoming a staple in kitchens well beyond the area of its Mediterranean roots. Not only can you cook just about anything with olive oil.
For the most health benefit and taste quality, you should add the oil after cooking.
You marinate fish, meat , chicken or vegetables in extra virgin olive oil and your desired spices, cover with a lid or plastic, put it in the fridge for a 1/2 to 1 hour. The oil and spices had the time to enter the flesh and is now ready to use for frying stirring or cooking. Do not add more oil to your pan or pot, there is oil enough to roast. This is the best and most healthy way of cooking with Extra Virgin Olive Oil. It will not burn because the oil has already entered in the meat, fish or vegetables.
Extra virgin olive oil does lose its great taste and healthy benefits when it's heated to a point, so you might want to choose a more economical grade when you cook above a low/medium heat. Use blended extra virgin olive oil combined with sunflower oil for all of your cooking 30/70. See the recipes section for more ideas for cooking with olive oil.
Join our IGADI Oil Club here for access to recipes and other information.


text:
About Solidarity
Founding Statement (1986)
Basis of Political Agreement
Gendered Violence Process
What is Solidarity?
Labour Party Pakistan statement on assassination of Benazir Bhutto
Labour Party Pakistan mourns Benazir's tragic death
It's a murder of democracy. Musharraf should resign: A tragedy wrought by combination of dictatorship, fundamentalism, imperialism
Lahore (PR): The Labour Party Pakistan (LPP) strongly condemns the tragic murder of Benazir Bhutto, former prime minister and chairperson Pakistan Peoples Party
(PPP).
In a joint statement issued here on Friday, LPP spokesperson Farooq Tariq and National Secretary Nisar Shah said: "It is not mere a murder of an individual but murder of democracy and political culture in Pakistan." They said it was the duty of the regime to provide Benazir Bhutto with a fool-proof security. "This is a failure on the part of the regime hence exposing country to an unprecedented danger and chaos. Therefore, we demand an immediate resignation of Pervez Musharraf and his cabinet," they added.
They said the tragedy that struck Pakistan yesterday was yet another expression of the instability created in the region owing to the US presence in the region. "Her brutal murder is a tragedy jointly wrought by religious fundamentalists, military dictatorships in Pakistan and the USA," they commented.
They said Al-Qaida had taken upon itself the responsibility for this horrendous crime according to media reports. "But the Frankenstein of Al-Qaida would not have been ruling the roost in Pakistan had it not been created by the USA and pampered by military dictatorships in Pakistan," they said. Urging the PPP workers restraint, they said LPP workers were with them in that hour of grief.
"We must turn this anger on the culprits who plotted this dastardly murder", they said. They appreciated Pakistan Muslim League (N)'s decision to boycott the elections due on January 8 and APDM decision to suspend the campaign recently launched for the boycott of elections.
An exchange over Electoral Politics from Solidarity's Pre-Convention Discussion A convergence of crises, dominated by the covid-19 pandemic

redpajama_set_name: RedPajamaCommonCrawl


text:
JOIN RTLET
RIGHT TO LIFE OF EAST TEXAS
Teaching respect for life from conception till natural death
Can YOU help save lives by donating to Right to Life of East Texas? Your donation is appreciated!
100% of your donation will be used to help in efforts to preserve life.
Right to Life of East Texas, Inc. is a 501(c)(3) non-profit organization.
NEED HELP WITH YOUR PREGNANCY? GO TO OUR HELP PAGE.
A note from Fr. Frank Pavone Sanctuary Cities Update 12/31/21 Cemetery of the Innocents 2022
Right to Life of East Texas is registered with amazonsmile, and by choosing RTLET
as your charity of choice when making purchases from amazon,
a percentage of the sale is automatically donated! It costs you NOTHING! For details, click HERE
LEARN THE FACTS ABOUT THE PRO-LIFE MOVEMENT
NATIONAL RIGHT TO LIFE - The mission of National Right to Life is to protect and defend the most fundamental right of humankind, the right to life of every innocent human being from the beginning of life to natural death.
ABORTION FACTS - We believe that true cultural change happens when we intentionally participate in the public square to create cultural goods that will winsomely and artfully tug on the heart strings of the populace so that they begin to feel the pain and consequences of abortion. True change happens when someone reads a book that makes them see the world in a new way. True change happens when someone sympathizes with a character in a TV show or movie and begins to slowly acclimate to a different viewpoint.
TEXAS RIGHT TO LIFE - Texas Right to Life legally, peacefully and prayerfully protects the God-given Right to Life of innocent human beings from fertilization to natural death.
MARCH FOR LIFE - We march because we envision a future world where the beauty and dignity of every human life are valued and protected. We promote the beauty and dignity of every human life by working to end abortion—uniting, educating, and mobilizing pro-life people in the public square.
PROLIFE AMERICA - a variety of resources and informative articles on abortion and the fight to end it in America.
LIFENEWS.COM - LifeNews.com is an independent news agency devoted to reporting news that affects the pro-life community. With a team of experienced journalists and bloggers, LifeNews.com reaches more than 750,000 pro-life advocates each week via our web site, email news reports, social networking outreach and weekday radio program. LifeNews.com also acts as a service provider to furnish news content to media that share the pro-life perspective. The topics covered by LifeNews.com include abortion, assisted suicide and euthanasia, bioethics issues such as human cloning and stem cell research, campaigns and elections, and cultural legal and legislative issues as they affect the pro-life community.
HUMAN LIFE INTERNATIONAL - The HLI vision is a world where the incalculable value of every human life is respected, protected, loved, and served, and the family is ordered in accordance with God's design. Their mission is to defend life and family around the world.
PRIESTS FOR LIFE - Priests for Life has come to signify two distinct but related movements within the wider pro-life movement. On one level, as described below, Priests for Life refers to a very specific effort to galvanize the clergy to preach, teach, and mobilize their people more effectively in the effort to end abortion and euthanasia. On another level, Priests for Life represents a family of ministries that reach and enrich every aspect of the pro-life movement, for clergy and laity alike, in a wide variety of activities. This has come to pass precisely because priests are not ordained for themselves, but for the people. So in activating clergy, we are activating all the segments of the Church, the pro-life movement, and the wider society in the defense of life.
The RTLET Directors are dedicated to educating the East Texas area about the sanctity of life, from abortion of our newly-created individuals to euthanasia applied to our vulnerable elderly.
THE RTLET LOGO
The RTLET logo is colored black, red, and white: black for the evil of abortion and euthanasia, red for the blood that is spilled, and white for the innocence of those whose lives are taken.
Longview TX 75608-9294
903-576-1407 (leave message)
or email rtletx@gmail.com
Please, before you end an innocent life, contact us.
THERE IS HOPE.
Right to Life of East Texas, PO Box 9294, Longview TX 75608-9294
email: rtletx@gmail.com
Right to Life of East Texas, Inc. is a 501(c)(3) non-profit organization. RTLET depends entirely on donations.
To see a copy of our bylaws, click here.


text:
<!DOCTYPE html>

  <meta charset="utf-8">
  <meta http-equiv="X-UA-Compatible" content="IE=edge">
  <title>piMAT | Settings</title>

  <meta content="width=device-width, initial-scale=1, maximum-scale=1, user-scalable=no" name="viewport">

  <link rel="stylesheet" href="/static/bower_components/bootstrap/dist/css/bootstrap.min.css">

  <link rel="stylesheet" href="/static/bower_components/font-awesome/css/font-awesome.min.css">

  <link rel="stylesheet" href="/static/plugins/timepicker/bootstrap-timepicker.min.css">

  <link rel="stylesheet" href="/static/dist/css/AdminLTE.min.css">
  <link rel="stylesheet" href="/static/dist/css/skins/skin-blue.css">

  <link rel="stylesheet"
        href="https://fonts.googleapis.com/css?family=Source+Sans+Pro:300,400,600,700,300italic,400italic,600italic">

  {% include "header.html" %}

MAIN MENU

 Dashboard

            Statistics

Sensors

Monitoring

            Monitoring

            {% for client in clients %}

{{ client }}

            {% endfor %}

 Cameras

 Logs

 Documentation

Settings

 Home

Settings

      {% with messages = get_flashed_messages() %}
        {% if messages %}

            {% for category, message in get_flashed_messages(with_categories=true) %}

                <button type="button" class="close" data-dismiss="alert" aria-hidden="true">×</button>
                {{ message | safe }}

            {% endfor %}

        {% endif %}
      {% endwith %}

Update Settings

        <form action="/settings" method="post">
          <input type="hidden" name="csrf_token" value="{{ csrf_token() }}"/>

Pimat

                    Pimat URL

                      <input type="text" class="form-control" id="server_ip" name="server_ip"
                             value="{{ config['pimat']['server_ip'] }}" placeholder="URL or IP address" required>

                    Relay Config file

                      <input type="text" class="form-control" id="relay_config" name="relay_config"
                             value="{{ config['pimat']['relay_config'] }}" placeholder="Path to config file" required>

                    Pimat Log

                      <input type="text" class="form-control" id="log" name="log"
                             value="{{ config['pimat']['log'] }}" placeholder="Path to log file" required>

                    Avatar's Folder

                      <input type="text" class="form-control" id="upload_folder" name="upload_folder"
                             value="{{ config['pimat']['upload_folder'] }}" placeholder="Path to users avatar folder" required>

                    Recaptcha Pub. Key

                      <input type="password" class="form-control" id="recaptcha_public_key" name="recaptcha_public_key"
                             value="{{ config['pimat']['recaptcha_public_key'] }}" placeholder="Recaptcha Public Key">

                    Recaptcha Priv. Key

                      <input type="password" class="form-control" id="recaptcha_private_key" name="recaptcha_private_key"
                             value="{{ config['pimat']['recaptcha_private_key'] }}" placeholder="Recaptcha Private Key">

                    Pimat Secret Key

                      <input type="password" class="form-control" id="secret_key" name="secret_key"
                             value="{{ config['pimat']['secret_key'] }}" placeholder="Pimat Secret Key">

                        Debug

                              {% if config['pimat']['debug'] == 'True' %}
                                <input class="form-check-input" value="True" name="debug" type="checkbox" checked>
                              {% else %}
                                <input class="form-check-input" value="True" name="debug" type="checkbox">
                              {% endif %}

                        Recaptcha

                               {% if config['pimat']['recaptcha'] == 'True' %}
                                <input class="form-check-input" value="True" name="recaptcha" type="checkbox" checked>
                              {% else %}
                                <input class="form-check-input" value="True" name="recaptcha" type="checkbox">
                              {% endif %}

                        CSRF

                               {% if config['pimat']['csrf_enabled'] == 'True' %}
                                <input class="form-check-input" value="True" name="csrf_enabled" type="checkbox" checked>
                              {% else %}
                                <input class="form-check-input" value="True" name="csrf_enabled" type="checkbox">
                              {% endif %}

Pins

                    Temp. Sensor Pin

                      <input type="number" class="form-control" id="temp_sensor" name="temp_sensor"
                             value="{{ config['pins']['temp_sensor'] }}" placeholder="Pin">

                    LDR Sensor Pin

                      <input type="number" class="form-control" id="ldr_sensor" name="ldr_sensor"
                             value="{{ config['pins']['ldr_sensor'] }}" placeholder="Pin">

                    Rf433 Receptor Pin

                      <input type="number" class="form-control" id="rf433_rcpt_pin" placeholder="Pin">

                    Rf433 Emitter Pin

                      <input type="number" class="form-control" id="rf433_emit_pin" placeholder="Pin">

Dashboard

                    Dashboard Graph Source
                    <select class="custom-select mb-2 mr-sm-2 mb-sm-0" id="dashboard_graph" name="dashboard_graph"  required>
                      {% if config['dashboard']['graph'] == 'sensors' %}
                        <option value="sensors" selected>Sensors</option>
                      {% else %}
                         <option value="sensors">Sensors</option>
                      {% endif %}
                      {% if config['dashboard']['graph'] == 'monitoring' %}
                        <option value="monitoring" selected>Monitoring</option>
                      {% else %}
                         <option value="monitoring">Monitoring</option>
                      {% endif %}
                    </select>

                    Dashboard Graph Client
                    <select class="custom-select mb-2 mr-sm-2 mb-sm-0" id="dashboard_client" name="dashboard_client"  required>
                      {% for client in clients %}
                        {% if config['dashboard']['client'] == client %}
                          <option value="{{ client }}" selected>{{ client }}</option>
                        {% else %}
                         <option value="{{ client }}">{{ client }}</option>
                        {% endif %}
                      {% endfor %}
                    </select>

                    Dashboard Relays Client
                    <select class="custom-select mb-2 mr-sm-2 mb-sm-0" id="dashboard_relays_client" name="dashboard_client"  required>
                      {% for client in clients %}
                        {% if config['dashboard']['relay_client'] == client %}
                          <option value="{{ client }}" selected>{{ client }}</option>
                        {% else %}
                         <option value="{{ client }}">{{ client }}</option>
                        {% endif %}
                      {% endfor %}
                    </select>

                    Number of Relays
                    <select class="custom-select mb-2 mr-sm-2 mb-sm-0" id="number_relays" name="number_relays"  required>
                      <option value="4" selected>4</option>
                      <option value="8">8</option>
                      <option value="8">16</option>
                    </select>

                        Relays

                              {% if config['dashboard']['relays'] == 'True' %}
                                <input class="form-check-input" value="True" name="dashboard_relays" type="checkbox" checked>
                              {% else %}
                                <input class="form-check-input" value="True" name="dashboard_relays" type="checkbox">
                              {% endif %}

                        Schedules

                               {% if config['dashboard']['schedules'] == 'True' %}
                                <input class="form-check-input" value="True" name="dashboard_schedules" type="checkbox" checked>
                              {% else %}
                                <input class="form-check-input" value="True" name="dashboard_schedules" type="checkbox">
                              {% endif %}

                        Sensors

                               {% if config['dashboard']['sensors'] == 'True' %}
                                <input class="form-check-input" value="True" name="dashboard_sensors" type="checkbox" checked>
                              {% else %}
                                <input class="form-check-input" value="True" name="dashboard_sensors" type="checkbox">
                              {% endif %}

                        Statistics

                               {% if config['dashboard']['stats'] == 'True' %}
                                <input class="form-check-input" value="True" name="dashboard_stats" type="checkbox" checked>
                              {% else %}
                                <input class="form-check-input" value="True" name="dashboard_stats" type="checkbox">
                              {% endif %}

Database

                    Database Type
                    <select class="custom-select mb-2 mr-sm-2 mb-sm-0" id="db_type" name="db_type"  required>
                      {% if config['database']['db_type'] == 'mysql' %}
                        <option value="mysql" selected>MySQL</option>
                      {% else %}
                         <option value="mysql">MySQL</option>
                      {% endif %}
                      {% if config['pimat']['db_type'] == 'sqlite' %}
                        <option value="sqlite" selected>SQLite</option>
                      {% else %}
                         <option value="sqlite">SQLite</option>
                      {% endif %}
                      {% if config['pimat']['db_type'] == 'pgsql' %}
                        <option value="pgsql" selected>PgSQL</option>
                      {% else %}
                         <option value="pgsql">PgSQL</option>
                      {% endif %}
                    </select>

                     Server

                      <input type="text" class="form-control" id="db_server" name="db_server"
                             value="{{ config['database']['db_server'] }}"
                             placeholder="Server URL or IP for SQLite use path to db file" required>

                     Port

                      <input type="number" class="form-control" id="db_port" name="db_port"
                             value="{{ config['database']['db_port'] }}" placeholder="Server port">

                     Username

                      <input type="text" class="form-control" id="db_username" name="db_username"
                             value="{{ config['database']['db_user'] }}" placeholder="Database user">

                     Password

                      <input type="password" class="form-control" id="db_password" name="db_password"
                             value="{{ config['database']['db_password'] }}" placeholder="Password">

                     Database

                      <input type="text" class="form-control" id="db_name" name="db_name"
                             value="{{ config['database']['db_name'] }}" placeholder="Database name">

Email

                    Enabled

                          {% if config['email']['enabled'] == 'True' %}
                            <input class="form-check-input" value="True" name="mail_enabled" type="checkbox" checked>
                          {% else %}
                            <input class="form-check-input" value="True" name="mail_enabled" type="checkbox">
                          {% endif %}

                     Server

                      <input type="text" class="form-control" id="mail_server" name="mail_server"
                             value="{{ config['email']['mail_server'] }}" placeholder="Email server">

                     Port

                      <input type="number" class="form-control" id="mail_port" name="mail_port"
                             value="{{ config['email']['mail_port'] }}" placeholder="Server Port">

                     Username

                      <input type="text" class="form-control" id="mail_username" name="mail_username"
                             value="{{ config['email']['mail_username'] }}" placeholder="Email server username">

                     Sender

                      <input type="text" class="form-control" id="mail_default_sender" name="mail_default_sender"
                             value="{{ config['email']['mail_default_sender'] }}" placeholder="Default mail sender ">

                     Password

                      <input type="password" class="form-control" id="mail_password" name="mail_password"
                             value="{{ config['email']['mail_password'] }}" placeholder="Password">

                        SSL

                              {% if config['email']['mail_use_ssl'] == 'True' %}
                                <input class="form-check-input" value="True" name="mail_use_ssl" type="checkbox" checked>
                              {% else %}
                                <input class="form-check-input" value="True" name="mail_use_ssl" type="checkbox">
                              {% endif %}

                        TLS

                              {% if config['email']['mail_use_tls'] == 'True' %}
                                <input class="form-check-input" value="True" name="mail_use_tls" type="checkbox" checked>
                              {% else %}
                                <input class="form-check-input" value="True" name="mail_use_tls" type="checkbox">
                              {% endif %}

Clients

                        Hostname
                        IP or FQDN
                        Sensors
                        Relays
                        Monitoring

                      {% for client in clients %}

                          {{ client }}
                          {{ clients[client] }}
                          Yes
                          yes
                          yes
                          Delete

                      {% endfor %}

                  <button type="button" data-record-title="NEw"
                          data-toggle="modal" data-target="#edit-client"class="btn btn-primary pull-right">Add new</button>

Cameras

                        Camera
                        IP or FQDN

                      {% for camera in cameras %}

                          {{ camera }}
                          {{ cameras[camera] }}
                          Delete

                      {% endfor %}

                    <input type="text" class="form-control mb-2 mr-sm-2 mb-sm-0" id="camera_name" name="camera_name" placeholder="Camera Name">

URL

                      <input type="text" class="form-control" id="camera_ip" name="camera_ip" placeholder="Camera IP or FQDN">

                    <button type="submit" class="btn btn-primary">Add</button>

           <button type="submit" class="btn btn-primary pull-right">Submit</button>

        </form>

  {% include "footer.html" %}

                  <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button>

Confirm Delete

You are about to delete  this procedure is irreversible.

Do you want to proceed?

                  <button type="button" class="btn btn-default" data-dismiss="modal">Cancel</button>
                  <button type="button" class="btn btn-danger btn-ok">Delete</button>

        <form action="/settings" method="post">

            <button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button>

Edit Client -

            <input type="hidden" name="csrf_token" value="{{ csrf_token() }}"/>

              New IP or URL
              <input type="password" id="inputPassword4" class="form-control mx-sm-3" aria-describedby="passwordHelpInline">

                <input class="form-check-input" type="checkbox" id="inlineCheckbox10" value="option1"> Sensors

                <input class="form-check-input" type="checkbox" id="inlineCheckbox11" value="option2"> Relays

                <input class="form-check-input" type="checkbox" id="inlineCheckbox12" value="option3"> Monitoring

            <button type="button" class="btn btn-default" data-dismiss="modal">Cancel</button>
            <button type="submit" class="btn btn-success btn-ok">Edit</button>

        </form>

redpajama_set_name: RedPajamaGithub


text:
A user generated interactive environment
The Bible Now space acts as both a receiver and a transmitter for real-time information that shows the impact of the Bible. These user-generated media workstations allow visitors to generate and transmit their own creations out into the surrounding panorama.
Visualizing the Space
As the interactive space is a real-time experience, we were inspired by the energy of Times Square — the bustling sight of streaming information coming live from the web, from people, and from Biblical places and organizations.
Rendering of Immersive Space
One of the interactive workstations is a data-driven interactive which works with YouVersion, a Bible App that has over 9 million downloads around the world. This was an interesting piece to work on, as the narrative was told through real data, rather than curating it.
There were interesting insights found in the data. For example, the first most searched keyword around the world is love. In Sweden, most people were searching for 'children'; in India a quarter of the population was searching for 'woman'. In countries where there is no internet access, such as North Korea, there were 0 returns in data. With this knowledge, we created an algorithm that breaks down the data such that it is decipherable.
Animating User Interaction
We had to think of ways to visualize the data in such a way that it is engaging to the user. Datagraphics sometimes appear dull in the form of charts and numbers, so we thought of ways to simplify the data that it is easily digestible in a galaxy of moving cards.
The Final Product
Agency— C&G Partners
Role— User Interaction and Motion Design
Explore More Projects
The Bamberger Group
Bamberger strives to help residents understand the local community at Murray Hill, and to leave their homes in good hands if it's time to move away.
Shanghai Planetarium
Crime in Manhattan
Our privacy and offline behavior are at threat by our buzzing online activity, as we ambiguously delve into the depths of the internet and upload our lives at the click of our mouse.
My name is Ping and I'm an Experience Design Lead at Gensler.
My career began in 2009 as an art director in advertising. I was awarded the DesignSingapore and Parsons Presidential scholarship to pursue my passion for creating interactive spaces in New York. I taught design for MFA Design + Technology at Parsons The New School of Design, where I discovered my love for teaching.
Along the way, I've been humbled to collaborate with talented individuals, and was recently honoured by Tatler as a young leader driving change. Some of my work has been featured on Mashable and DesignBoom.
When I'm not behind a computer, you can find me documenting my personal journey during the COVID pandemic.
SAY HELLO HERE
hi.handson@gmail.com
SAY HELLO THERE
twitter medium vimeo instagram behance linkedin
© Handson Registered 2013 — 2021


text:
Pastry Dedication: Cafe Breizh's Bakers Keep It Authentic
Las Vegas Weekly/ August 3rd, 2017/ Brittany Brussel
What goes into crafting badass baked goods? For Pierre Gatel, pastry chef and partner at Café Breizh, the foundation lies in sugar-inspired stints at Wynn and Encore and with French culinary legends Alain Ducasse and François Payard. But it's respect that really moves macaron mountains.
"We don't reinvent products, we make them right," Gatel says.
This command over ingredients is evident as three different types of dough are created for the cinnamon roll, apple turnover and croissant—each has its own recipe, number of folds and rest time. The five-day process of producing turnovers unites Isigny Sainte-Mère butter-infused puff pastry with sweet heaps of Fuji apples. Only fresh blueberries and hand-chopped, high-quality chocolate stud the insides of muffins and cookies. Gatel also produces savory items he knows well, including Niçoise salad and a lunch staple, the Waldorf chicken salad sandwich.
A similar artisanal approach is employed by his fellow chef (and Breizh, France native) Jerome Marchand for regional standards like crêpes—from the caramel butter variation to cream citron—and genuine galettes using Treblec buckwheat flour and land- and sea-inspired fillings.
These childhood friends-turned-café owners take care not to overwhelm themselves, keeping a small team and slowly unveiling more options like bike basket-worthy baguettes. While everything from the brioche to the brownies deserves the spotlight, it's the authenticity that's truly on display.
https://lasvegasweekly.com/dining/2017/aug/03/pastry-dedication-cafe-breizhs-bakers-authentic/
Breton Salted-Caramel
Vegas Seven / Dish & Tell / June 21, 2017 / Marisa Finetti
There's no shortage of salted caramel iterations. The exotic indulgence became a culinary obsession at restaurants, which offered their renditions in cakes, sauces and ice creams. While the trend has subsided in the U.S., it was never a passing fancy in Brittany, France, because the salty, sweet and buttery wrapped candies (caramels au beurre salé) originated in this historic coastal region and have been part of its heritage for as long as one can remember. During the 1500s, Brittany was the only part of France to be exempt from a salt tax. As a result, salt was liberally sprinkled in the local cuisine. Then, a creative pastry chef decided to use salted butter to make caramel, and a beautiful union was born. To enjoy the true flavors of salted caramel is to have it at Café Breizh(3555 S. Fort Apache Rd., cafebreizh.com), here in Las Vegas. The region of Bretagne (Brittany) is also called Breizh (the local dialect), which is where owners Pierre Gatel and Jerome Marchand were born and raised. You can bet that the two take their local specialties quite seriously. Try the Breizh crepes with salted caramel and baked apple, salted caramel macarons and salted caramel Macchiato for a trip to their hometown.
Marisa savors with all five senses. Read more at vegasseven.com/dishandtell or visit her blog, loveandrelish.com.
http://vegasseven.com/2017/06/21/waterfront-dining-breton-salted-caramel-and-a-dessert-only-spot-you-can-bank-on/
Las Vegas' New French Café
VEGAS SEVEN / Marisa Finetti, DISH AND TELL Thursday, December 8 3:34pm
If you adore galettes, you'll be thrilled to know that a new French café, Café Breizh (3555 S. Fort Apache Rd., cafebreizh.com), opened last week in Summerlin. The casual dining spot with its outdoor patio garden is the perfect setting for La Colombe coffee, French-inspired sandwiches, pastries and galettes. Cafe Breizh makes its galettes using flour imported directly from Breizh, France (also called Brittany, or Bretagne in the native dialect), from which the folded square buckwheat crepe delicacy hails. Try the traditional galette, which features egg, ham and cheese. Owners Pierre Gatel and Jerome Marchand were both born and raised in the historic region of Bretagne, and became friends during an apprenticeship early in their culinary education. Also a must-try is the apple turnover—an inverted puff pastry that holds a mixture of Fuji apples, fresh and compote—and the baked chicken and Gouda quiche. C'est magnifique!
Source + full story located here: http://vegasseven.com/2016/12/08/dining-dark-summerlins-new-french-cafe-chefly-holiday-gifts/
Chef Pierre Gatel to Debut Cafe Breizh This Week!
An authentic taste of Brittany is almost here.
VEGAS EATER / Bradley Martin Nov 28, 2016, 12:30pm PST
A new bakery will debut in Spring Valley this week featuring some high-caliber chef credentials behind the scenes. Cafe Breizh will debut its 2,308-square-foot space at the Apache Center on Dec. 1, close to the intersection of Spring Mountain and Fort Apache toads.
Partners in the venture are Jerome Marchand and Chef Pierre Gatel, who spent 11 years at the Wynn and Encore resorts rising to the position of Executive Pastry Chef. His earlier career includes time spent working in New York with Francois Payard and Alain Ducasse.
The partners were both born in Brittany, or Breizh as it is known in the local Breton language. Marchand's specialty addition to the project will be authentic Bretagne galettes.
Already recommended by the team, Salad Nicosie, Croque Monsieur, chicken and Gouda quiche, crepes with apple and salted caramel and Paris–Brest.
The cafe will be open daily from 7 a.m. to 7 p.m and an outdoor patio is also on the way.
Source: http://vegas.eater.com/2016/11/28/13768342/chef-pierre-gatel-to-debut-cafe-breizh-this-week


text:
rambling reflections of a middle aged Columbian grad
California Dreams (Part III)
November 3, 2017 November 2, 2017 Earthly Moments
Day 3 started with a visit to the General Grant Tree. With a base circumference of 107.6 ft (32.8 m), it is the second largest tree in the world after the General Sherman Tree.
What was more impressive for me was Cristina, whom we met at the entrance to the General Grant Grove. She was also looking for the General Grant Tree and gave us a lift from the roadside to the parking lot. Originally from Chile, she lived in New York City for 30+ years before retiring about five years ago. She then embarked on what she calls a second career as a "world traveler". After exploring different countries for a couple years, she turned her sights on experiencing the beauties of her adopted homeland. With that mission in mind, she traveled down to Florida, bought a used 2003 RV, drove it back to New York for registration and then started her journey westward. This as a year ago. Friends and family would join her for short weekend stints or week-long trips. For the rest of the time, she was by herself with just a map and an vague idea of where she wanted to head to next.
At the entrance of the General Grant Tree Trail rests the Fallen Monarch. No one knows exactly when this giant sequoia fell, but the tree had been hollowed out by fires and so when it did collapse, its outer shell formed a natural room-like structure. Native Americans used it as shelter, and from 1868 to 1870, it even served as a hotel and saloon for weary travelers. From 1870 to 1872, the Gamlin brothers used the fallen tree as a temporary house as they built their cabin nearby. Then later, in 1876, the US Cavalry used it as a stable for 32 horses.
Giant sequoias possess high amounts of tannin in their wood – giving them their characteristic red tint. As a result also, the giant sequoia is practically immune to fatal attack by either fungous diseases or insects and becomes very much resistant against decay. Comparing a photo of the Fallen Monarch taken today with one taken in 1911, you can barely discern the differences a century has had on this felled tree.
imaged obtained from Library of Congress online
As its name indicates, Kings Canyon National Park revolves primarily around Kings Canyon, a rugged glacier-carved valley more than a mile deep. Road access is only open during the summer months and it is about a two-hour round-trip drive along a curving road that slowly winds its way from the canyon overlook unto the valley basin following more or less the path of the Kings River. Outlook points have been strategically positioned along the route to provide visitors with awe-inspiring panoramas.
More than anything, I was struck by the warm deep golden hue of the encompassing mountains and jutting rocks.
Even when standing in the shadows, the gold would break through, casting a halo-effect upon the mountain-tops.
All this, while the bright blue-green river waters raged below.
Within Kings Canyon, there are also hikes of varying lengths leading to hidden treasures, the most famous of which is the Zumwalt Meadow Loop.
The trail starts innocently enough tracing the banks of the river, providing peeks along the way to the mountains afar.
The denouement though is fully unexpected. As you walk through the trees, you suddenly find in front of you a stunning expanse of grassy meadow encircled by granite mountains. All I wanted to do was to run through the tall grass with my arms open and feel the each blade glide under my fingertips. But alas, that was prohibited by park rules, and probably dangerous too given this was a wetland.
Nature never ceases to inspire.
I'll leave you though on a note of whimsy – a whale in the sand that I chanced upon during the hike around the loop trail. Time runs along a spectrum. At one point this entire expanse was covered in glaciers. Who knows, perhaps in another hundred million years, the ocean will consume this land and it'll become a home for the whales.
Tagged Kings Canyon, National Park, nature, Sierra Nevada, travel
Previous postCalifornia Dreams (Part II)
Next postCalifornia Dreams (Part IV)
Adirondack Adirondacks ALF animals appetizer architecture art autumn beer Bell Pepper California Canada celebration Chicago Chicken Chihuly Chinese conservation Corn Culture design dessert DIY earrings eStore flower flowers food Frank Lloyd Wright fruits gardens Gilded Age green tea Grill hiking historic buildings history home decor homemade incense jewelry Labor Day lake mansion matcha military National Park nature Newport New York City Onion origami park pendant red bean reflections Roosevelt rose Sausage scenery shop spring Squash Taconic TCM technology towel art Traditional Chinese Medicine travel tulips Vegetables waterfalls wine woodpecker workday