text:
\section{Introduction}

Since pioneering work~\cite{Isgur} in the field, the standard approach for baryon spectroscopy is the
constituent quark model. The Hamiltonian typically contains a spin independent
part formed of the kinetic plus the confinement energies and a
spin dependent part given by a hyperfine interaction. The quark model results are \textit{de facto} model
dependent; it is therefore very important to develop model independent methods that
can help in alternatively understanding baryon spectroscopy and support
(or not) quark model assumptions. Apart from promising lattice QCD
calculations~\cite{lattice}, large $N_c$ QCD, or alternatively the $1/N_c$
expansion, offers such a method.
In 1974 't Hooft generalized QCD from SU(3) to an arbitrary number of colors SU($N_c$) \cite{HOOFT} and suggested a perturbative
expansion
in $1/N_c$, applicable to all QCD regimes. Witten has then applied
the approach to baryons \cite{WITTEN} and this
has led to a systematic and predictive $1/N_c$ expansion method to study static
properties
of baryons. The method is based on the discovery that, in the limit
$N_c \rightarrow \infty$, QCD possesses an exact contracted
SU(2$N_f$) symmetry \cite{Gervais:1983wq} where $N_f$ is the number
of flavors. This symmetry is approximate for finite $N_c$ so that corrections have to be added
in powers of $1/N_c$. Notice that a baryon is a bound state of $N_c$ quarks in the large $N_c$ formalism.

The $1/N_c$ expansion has successfully been
applied
to ground state baryons, either light \cite{DJM94,Jenkins:1998wy} or heavy~\cite{Jenkins:1996de,Jenkins:2007dm}.
Its applicability to excited states is a subject of current
investigations. The classification scheme used in the $1/N_c$ expansion for excited states is based on the standard SU(6) classification as in a constituent quark model. Baryons are grouped into excitation bands $N= 0$, 1, 2,\dots,
each band containing at least one SU(6) multiplet, the band number $N$
being the total number of excitation quanta  in a harmonic oscillator picture.

The purpose of the present paper is to show that there is
a compatibility between the quark model and the $1/N_c$ expansion methods.
It is organized as follows. We first give a summary of the $1/N_c$ expansion
method in Sec.~\ref{barlnc}. Then we present a relativistic quark model in
Sec.~\ref{barqm} and derive analytic mass formulas from its Hamiltonian
in Sec.~\ref{massfor}. The comparison between the quark model and the
$1/N_c$ mass formulas is discussed in Sec.~\ref{compar} and conclusions
are drawn in Sec.~\ref{conclu}. We point out that the results summarized
hereafter have been previously presented in Refs.~\cite{us1,us2} for the
light baryons and \cite{us3} for the heavy baryons. This work aims at
being a pedagogical overview of these last three references.

\section{Baryons in large $N_c$ QCD}\label{barlnc}
\subsection{Light nonstrange quarks}
We begin with a summary of the $1/N_c$ expansion in the case $N_f = 2$,
but the arguments are similar for any $N_f$. The contracted SU(2$N_f$) symmetry
is here the group SU(4) which has 15 generators: The spin and isospin subgroup
generators $S_i$ and $T_a$ and operators acting on both spin and isospin
degrees of freedom denoted by $G_{ia}$ ($i,a = 1,2,3$).

The SU(4) algebra is
\begin{equation*}
[S_i,T_a] = 0, \quad [S_i,G_{ja}]  =  i \varepsilon_{ijk} G_{ka},\quad [T_a,G_{ib}]  =  i \varepsilon_{abc} G_{ic},
\end{equation*}
\begin{equation}\label{ALGEBRASU4}
[S_i,S_j]  =  i \varepsilon_{ijk} S_k,\quad [T_a,T_b]  =  i \varepsilon_{abc} T_c,\quad [G_{ia},G_{jb}] = \frac{i}{4} \delta_{ij} \varepsilon_{abc} T_c
+\frac{i}{4} \delta_{ab}\varepsilon_{ijk}S_k.
\end{equation}
In the limit $N_c \rightarrow \infty$ one has  $[G_{ia},G_{jb}]
\rightarrow 0$
which implies the existence of a contracted algebra. These SU(4) generators
form the building blocks of the mass operator, at least in the ground state
band ($N=0$). For orbitally excited states the generators $\ell^i$ of SO(3),
as well as the tensor operator $\ell^{(2)ij}$ also appear since the
symmetry under consideration is extended to SU(4) $\otimes$ SO(3).

In the $1/N_c$ expansion the mass operator $M$  has general form
\begin{equation}
\label{massoperator}
M = \sum_{i} c_i O_i,
\end{equation}
where the coefficients $c_i$
encode the QCD dynamics and have to be determined from a fit to the existing
data, and where the operators $O_i$ are SU(4) $\otimes$ SO(3) scalars of the form
\begin{equation}\label{OLFS}
O_i = \frac{1}{N^{n-1}_c} O^{(k)}_{\ell} \cdot O^{(k)}_{SF}.
\end{equation}
Here $O^{(k)}_{\ell}$ is a $k$-rank tensor in SO(3) and $O^{(k)}_{SF}$
a $k$-rank tensor in SU(2)-spin,
but invariant in SU(2)-flavor.
The lower index $i$ in the left hand side represents a specific
combination.
Each $n$-body operator is multiplied by an explicit factor of
$1/N^{n-1}_c$ resulting from the power counting rules \cite{WITTEN}, where $n$
represents the minimum of gluon exchanges to generate the operator.
For the ground state, one has $k$ = 0. For excited states the $k = 2$
tensor is important. In practical applications, it is customary to include terms
up to $1/N_c$ and drop higher order corrections of order $1/N_c^2$.

As an example, we show the operators
used in the calculation of the masses of the $[{\bf 70},1^-]$ multiplet
up to
order $1/N_c$ included \cite{Matagne:2006dj} (the sum over repeated indices is implicit)
\begin{eqnarray}\label{example}
O_1 = N_c \, {\bm 1} \negthinspace \negthinspace\negthinspace
\negthinspace\negthinspace&, &
~O_2  =  \frac{1}{N_c}\ell^i S^i,
~~~O_3 = \frac{1}{N_c} T^aT^a,
~~~O_4 = \frac{1}{N_c} S^iS^i,\nonumber\\
& O_5 & =  \frac{15}{N_c^2}\ell^{(2)ij}G^{ia}G^{ja},
~~~O_6 =  \frac{3}{N_c^2}\ell^iT^aG^{ia}.
\end{eqnarray}
Note that although $O_5$ and $O_6$ carry a factor of $1/N_c^2$ their matrix elements are
of order $1/N_c$ because they contain the coherent operator $G^{ia}$
which brings an extra factor $N_c$. $O_1 = N_c \, {\bm 1} $ is the trivial operator, proportional
to
$N_c$ and the only one surviving when $N_c \rightarrow \infty$
\cite{WITTEN}. The operators $O_2$ (spin-orbit), $O_5$ and $O_6$ are relevant for orbitally excited
states only. All the SU(4) quadratic invariants
$S^iS^i$, $T^aT^a$ and $G^{ia} G^{ia}$ should enter the mass
formula but they are
related to each other by the operator identity~\cite{Jenkins:1998wy}
\begin{equation}
\label{CASIMIR}
 \left\{S^i,S^i\right\} + \left\{T^a,T^a\right\} + 4  \left\{G^{ia},
 G^{ia}\right\} = \frac{1}{2} N_c (3N_c + 4),
\end{equation}
so one can express $G^{ia} G^{ia}$ in terms of $S^iS^i$ and $T^aT^a$.

Assuming an exact SU(2)-flavor symmetry, the mass formula for the ground state band up to order $1/N_c$ takes the following simple form~\cite{Jenkins:1998wy}
\begin{equation}\label{GS}
 M = c_1 N_c + c_4\frac{1}{N_c}S^2 + \mathcal{O}\left(\frac{1}{N_c^3}
 \right),
\end{equation}
which means that
for $N = 0$ only the operators $O_1$ and $O_4$ (spin-spin) contribute to the
mass.

Among the excited states, those belonging to the $N = 1$ band,
or equivalently to the $[{\bf 70},1^-]$ multiplet,
have been most extensively studied,
either for $N_f = 2$ (see \textit{e.g.} Refs.~\cite{CGKM,Goity,PY1,CCGL,cohen1})
or for $N_f = 3$ \cite{SGS}. The $N = 2$ band contains the $[{\bf 56'},0^+]$, $[{\bf 56},2^+]$,
$[{\bf 70},\ell^+]$ ($\ell$ = 0, 2), and $[{\bf 20}, 1^+]$ multiplets.
There are no physical resonances associated to $[{\bf 20}, 1^+]$.
The few studies related to the $N = 2$ band concern the
$[{\bf 56'},0^+]$ for $N_f$ = 2 \cite{CC00}, $[{\bf 56},2^+]$
for $N_f = 3$ \cite{GSS}, and $[{\bf 70},\ell^+]$ for
$N_f = 2$ \cite{MS2}, later extended to $N_f = 3$
\cite{Matagne:2006zf}. The method has also been applied \cite{Matagne:2004pm}
to highly excited non-strange and strange
baryons belonging to $[{\bf 56},4^+]$,
the lowest multiplet of the $N = 4$ band \cite{SS94}.

The group theoretical similarity of excited symmetric states
and the ground state makes the analysis of these states simple
\cite{GSS,Matagne:2004pm}. For mixed symmetric states, the situation
is more complex.
There is a standard procedure which reduces the study of mixed
symmetric states to that of symmetric states.
This is achieved by the decoupling of the baryon into an excited
quark and a symmetric core of $N_c - 1$ quarks.
This procedure has been applied to the $[{\bf 70},1^-]$ multiplet
\cite{CGKM,Goity,PY1,CCGL,cohen1,SGS}
and to the $[{\bf 70},\ell^+]$ ($\ell$ = 0, 2) multiplets
\cite{MS2,Matagne:2006zf}. But it has recently been shown that
the decoupling is not necessary \cite{Matagne:2006dj}, provided
one knows the matrix elements of the SU(2$N_f$) generators
between mixed symmetric states.
The derivation of these matrix elements is not trivial. For SU(4) they
have been derived by Hecht and Pang \cite{HP} in the context of nuclear
physics and adapted to quark physics in Ref. \cite{Matagne:2006dj},
where it has been shown that the isospin-isospin term becomes as dominant
in $\Delta$ as the spin-spin term in $N$ resonances.

The derivation of SU(6) matrix elements between mixed symmetric states
$[N_c-1,1]$ is underway \cite{MSnew}.

A detailed description of the problems raised by the standard procedure
\cite{CCGL} of
the separation of a system of mixed spin-flavour symmetry $[N_c-1,1]$
into a symmetric core of $N_c-1$ quarks and an excited quark
has been given in Refs. \cite{Matagne:2008fw,Matagne:2008zn}.

\subsection{Inclusion of strangeness}
For light strange baryons ($N_f=3$) the mass operator in the
$1/N_c$ expansion has the general form
\begin{equation}
\label{massoperator2}
M = \sum_{i=1} c_i O_i + \sum_{i=1} d_i B_i,
\end{equation}
where the operators $O_i$ are invariants under SU(6) transformations
and the operators $B_i$ explicitly break SU(3)-flavor symmetry.
In the case
of nonstrange baryons, only the operators $O_i$ contribute, see Eq. (\ref{massoperator}). Therefore
$B_i$ are defined such as their expectation values are zero
for nonstrange baryons. The coefficients
$d_i$ are determined from the experimental data including strange
baryons.
In Eq.~(\ref{massoperator2}) the sum over $i$ is finite and in practice
it containes the most dominant operators. Examples of $O_i$ and $B_i$ can be
found in
Refs.~\cite{GSS,Matagne:2006zf,Matagne:2004pm}.

Assuming that each strange quark brings
the same contribution $\Delta M_s$ to the SU(3)-flavor breaking
terms in the mass formula, we define the total contribution of strange quarks
as \cite{us2}
\begin{equation}\label{break}
n_s ~\Delta M_s = \sum_{i=1} d_i B_i,
\end{equation}
where $n_s=-{\cal S}$ is the number of strange quarks in a baryon,
${\cal S}$ being its strangeness.

\subsection{Heavy quarks}

The approximate spin-flavor symmetry for large $N_c$ baryons
containing light $q = \{u, d, s\}$ and heavy $Q =\{ c, b\}$ quarks
is SU(6)$\times$ SU(2)$_c$ $\times$  SU(2)$_b$,
\emph{i.e.} there is a separate spin symmetry for each heavy flavor.
Over a decade ago the $1/N_c$ expansion has been
generalized to include an expansion
in $1/m_Q$ and light quark flavor
symmetry breaking \cite{Jenkins:1996de}. The majority of the currently
available experimental data concerning heavy baryons is related to ground
state baryons made of one heavy and two light quarks~\cite{PDG}.
Such heavy baryons, denoted as $qqQ$ baryons, have been recently reanalyzed
within the combined $1/N_c$ and $1/m_Q$ expansion \cite{Jenkins:2007dm},
and masses in good agreement with experiment have been obtained. A first
attempt to extend this framework to excited heavy baryons can be found
in Refs.~\cite{lee} but much work remains to be done in this field.
That is why we focus here on the $N=0$ band for $qqQ$ baryons only.

Let us first consider that SU(3)-flavor symmetry is exact. In
this case the mass operator $M^{(1)}$ is a flavor singlet and in the
combined $1/m_Q$ and $1/N_c$ expansion to order $1/m_Q^2$
it takes the following
form
\begin{equation}\label{mlnc}
M^{(1)}=m_Q {\bm 1}
+\Lambda_{qq}+\lambda_Q+\lambda_{qqQ}.
\end{equation}
The leading order term
is $m_Q$ at all orders in the $1/N_c$ expansion. Next we have
\begin{equation}
\Lambda_{qq}=c_0\, N_c\, {\bm 1}+\frac{c_2}{N_c}\, J^2_{qq}, \quad {\rm and} \quad\lambda_Q=N_Q \frac{1}{2 m_Q} \left(c^{'}_0\,
{\bm 1}+\frac{c^{'}_2}{ N^2_c}J^2_{qq}\right),
\end{equation}
where $\vec J_{qq}$ is identical to the total spin  $\vec S_{qq}$
of the light quark pair when one deals with the $N=0$ band. Note that
$\Lambda_{qq}$ contains the dynamical contribution of the light
quarks and is independent of $m_Q$ while $\lambda_Q$ gives $1/m_Q$ corrections.
The last term, $\lambda_{qqQ}$, contains the
heavy-quark spin-symmetry violating operator which reads
\begin{equation}
\lambda_{qqQ}=2 \frac{c^{''}_2}{N_c m_Q}\vec J_{qq}\cdot \vec J_Q,
\end{equation}
where $\vec J_Q$ is identical to the spin $\vec S_Q$ of the heavy quark.

The unknown coefficients $c_0$, $c_2$, $c^{'}_0$, $c^{'}_2$, and  $c^{''}_2$
are functions of $1/N_c$ and of a QCD scale parameter $\Lambda$.
Each coefficient has an expansion in $1/N_c$ where the leading term
(in dimensionless units) is
of order unity and does not depend on $1/m_Q$. Thus,
without loss of generality, by including dimensions,
one can set $c_0 \equiv \Lambda$.  The quantity $\Lambda$, as well as the other
coefficients, have to be fitted to the available experimental data. In agreement with Ref.~\cite{Jenkins:1996de}, we take
\begin{align}
\label{largenpar}
c_0 =  \Lambda, \quad c_2 \sim \Lambda,\quad\quad c^{'}_0  \sim   c^{'}_2\sim c^{''}_2  \sim  {\Lambda}^2.
\end{align}

The inclusion of SU(3)-flavor breaking leads to an
expansion of the mass operator in the SU(3)-violating parameter $\epsilon$ which contains
the singlet $M^{(1)}$, an octet $M^{(8)}$, and a 27-plet $M^{(27)}$.
The last term brings contributions proportional to $\epsilon^2$
and we neglect it. For $M^{(8)}$ we retain its dominant contribution
$T^{8}$ to order $N^0_c$. Then the mass formula becomes
\begin{equation}
\label{breaksim}
M = M^{(1)} + \epsilon T^{8}.
\end{equation}
The flavor breaking parameter $\epsilon$ is governed by the mass
difference $m_s - m$ (where $m$ is the average of the $m_u$ and $m_d$ masses)
and therefore is $\epsilon \sim 0.2$-0.3. It is measured in units of
the chiral symmetry breaking scale parameter $\Lambda_{\chi} \sim 1$ GeV.

\section{Quark model for baryons}\label{barqm}
\subsection{Main Hamiltonian}
The quark model used here to describe baryons aims at capturing the main
physical features of a three-quark system while keeping the formalism as
simple as possible in order to get analytical mass formulas.
It contains: Relativistic kinetic energy for the quarks, $Y$-junction
confining potential, one-gluon exchange potential and quark
self-energy contribution added as perturbative terms. Let us now shortly
describe all these ingredients.

A baryon, seen as a bound state of three valence quarks, can
be described, at the dominant order, by the spinless Salpeter Hamiltonian
$H=\sum^3_{i=1}\sqrt{\vec p^{\, 2}_i+m^2_i}+V_Y$,
where $m_i$ is the bare mass of the quark $i$ and where $V_Y$ is the
confining interaction potential. We use the bare mass of the quarks in
the relativistic kinetic energy term as suggested by the field correlator
method~\cite{simo}, but other approaches, like Coulomb gauge QCD,
rather favor a running constituent quark mass~\cite{cgqcd}. Although very
interesting conceptually, the influence of this choice on the mass spectra
should not be so dramatic than it could have been expected at the first
glance: First, the bare and constituent heavy quark masses are nearly
identical. Second, the constituent light quark masses quickly decrease
at large momentum and become similar to the bare masses; a common limit
is reached for the excited states. The situation is thus mainly different
for low-lying $nnn$ baryons ($u$ and $d$ quarks are commonly denoted as $n$),
where the bare mass $m_n$ can be set equal to 0, but where the constituent
mass is about 300~MeV~\cite{cgqcd}. However, the strength of additional
interactions like one-gluon exchange (see next section) can be tuned in
both cases and lead to final mass spectra which are quite similar.

Both the flux tube model \cite{CKP} and lattice
QCD \cite{Koma} support the Y-junction picture for the confining
potential: A flux tube
starts from each quark and the three tubes meet at the Torricelli
(or Steiner or Fermat) point of the
triangle formed by the three quarks, let us say the $ABC$ triangle.
This point $T$, located at $\vec x_{T}$, minimizes the sum
of the flux tube lengths and leads to the following confining potential $V_Y=a \sum^{3}_{i=1} \left|\vec{x}_{i}-\vec{x}_{T}\right|$, where the position of quark $i$ is denoted by $\vec x_i$ and where $a$ is the energy
density of the flux tubes. If all the angles of $ABC$ are less than 120$^{\rm o}$, then the Toricelli point is such that the angles $\widehat{ATB}$, $\widehat{BTC}$, and  $\widehat{ATC}$ are
all equal to 120$^{\rm o}$. If the angle corresponding to an apex is greater
than 120$^{\rm o}$, the Toricelli point is precisely at this apex.

As $\vec x_T$ is a complicated three-body function,
it is interesting to approximate the confining potential by a more tractable
form. In the following, we shall use
\begin{align}
\label{ssh2}
H_R&=\sum^3_{i=1}\sqrt{\vec p^{\, 2}_i+m^2_i}+V_R, \\
\label{pot1}
V_R&=k\,a \sum^{3}_{i=1}\left|\vec{x}_{i}-\vec{R}\right|,
\end{align}
where $\vec{R}$ is the position of the center of mass and  $k$
is a corrective factor \cite{Bsb04}. The accuracy of the
replacement~(\ref{pot1}) has been checked to be very satisfactory
(better than 5\%) in this last reference provided that the appropriate
scaling factor is used: $k_0=0.952$ for $qqq$ baryons and $k_1=0.930$ for
$qqQ$ baryons. For highly excited states, the contribution of the
configurations in which the Toricelli point is located on one of the quarks
becomes more and more important, and one could think that the center of mass
approximation~(\ref{pot1}) is then wrong. But in such cases the angle made
by the Toricelli point and the other two quarks is larger than $120^{\rm o}$
and the center of mass is consequently still close to the true Toricelli point.
The approximation~(\ref{pot1}), although being less accurate for highly
excited states, remains however relevant.

\subsection{Perturbative terms}

Besides the Hamiltonian (\ref{ssh2}),
other contributions are necessary to reproduce the baryon masses. We
shall add them as perturbations to the dominant Hamiltonian~(\ref{ssh2}).
The most widespread correction is a Coulomb interaction term of the form
\begin{equation}
\Delta H_{oge}=-\frac{2}{3}\sum_{i<j}\frac{\alpha_{S,ij}}{|
\vec x_i-\vec x_j|},
\end{equation}
arising from one-gluon exchange processes, where $\alpha_{S,ij}$ is the
strong coupling constant between the quarks $i$ and $j$. Actually, one should deal
with a running form $\alpha_S(r)$, but it would considerably increase the
difficulty of the computations. Typically, we need two values:
$\alpha_0=\alpha_{S,qq}$ for a $qq$ pair and $\alpha_1=\alpha_{S,qQ}$ for a
$qQ$ pair, in the spirit of what has been done in a previous study describing
mesons in the relativistic flux tube model \cite{tf_Semay}. There it was found that $\alpha_1/\alpha_0 \approx 0.7$ describes rather well the
experimental data of $q\bar q$ and $Q\bar q$ mesons.

Another perturbative contribution to the
 mass is the quark self-energy. This is
due to the color magnetic moment of a quark propagating through the QCD vacuum. It adds a negative contribution to the hadron masses \cite{qse}. The quark self-energy contribution for a baryon is given by
\begin{equation}
\label{qsedef}
\Delta H_{qse}=-\frac{fa}{2\pi}\sum_i\frac{\eta(m_i/\delta)}{\mu_i},
\end{equation}
where $\mu_i$ is the kinetic energy of the quark $i$, that is $\mu_i=\left\langle \sqrt{\vec p^{\, 2}_i+m^2_i}\right\rangle$,
the average being computed with the wave function of the unperturbed spinless
Salpeter Hamiltonian~(\ref{ssh2}). The factors $f$ and $\delta$ have been computed in quenched and unquenched
lattice QCD studies; it seems well established that
$3 \leq f\leq 4$ and ($1.0 \leq \delta \leq 1.3$)~GeV \cite{qse2}.
The function $\eta(\epsilon)$ is analytically known; we refer the reader to
Ref.~\cite{qse} for an explicit formula. It can accurately be fitted by
\begin{alignat}{3}
\label{etaap}
\eta(\epsilon)&\approx 1-\beta \epsilon^2 && \quad\textrm{with} \quad \beta=2.85
&& \quad\textrm{for} \quad 0 \le \epsilon \leq 0.3,\nonumber \\
&\approx \frac{\gamma}{\epsilon^2} && \quad\textrm{with} \quad \gamma=0.79
&& \quad\textrm{for} \quad 1.0 \leq \epsilon \leq 6.0.
\end{alignat}
Let us note that the corrections depending on the parameter $\gamma$ appear at order $1/m_Q^3$ in the mass formula, so they are not considered in this work.

We finally point out that the quark model we developed in this section is spin
independent. This neglect of the fermionic nature of the quarks is the reason
why such a model is often called ``semirelativistic": The implicit covariance
is preserved, but spin effects are absent. Spin dependent contributions
(spin-spin, spin-orbit, etc.) typically come from relativistic corrections
to the one-gluon exchange potential. It is useful to mention that in our
formalism such potential terms between the quarks $i$ and $j$ should be of
the form~\cite{simo}
\begin{equation}\label{Vsd}
	V_{ij}\propto(\mu_i\mu_j)^{-1}.
\end{equation}

\section{Mass formulas}\label{massfor}

\subsection{The auxiliary field method}
The comparison between the quark model and large $N_c$ mass formulas would be
more straightforward if we could obtain analytical expressions. To this aim,
the auxiliary field method is used in order to transform the Hamiltonian~(\ref{ssh2}) into an analytically solvable one \cite{Sem03}. With $\lambda=k\, a$, we obtain
\begin{eqnarray}\label{ham3b}
H(\mu_i,\nu_j)=\sum^3_{j=1}\left[\frac{\vec{p}^{\, 2}_j+m
^2_j}{2\mu_j}+\frac{\mu_j}{2}\right]+\sum^3_{j=1}\left[\frac{ \lambda^2 (\vec{x}_j-\vec{R})^2}{2\nu_j}+
\frac{\nu_j}{2}\right].
\end{eqnarray}
The auxiliary fields, denoted as $\mu_i$ and $\nu_j$, are operators, and
$H(\mu_i,\nu_j)$ is equivalent to $H$ up to their elimination thanks to the
constraints
\begin{align}
\label{elim}
\left.\delta_{\mu_i}H(\mu_i,\nu_j)\right|_{\mu_i=\hat\mu_i}&=0\ \Rightarrow\ \hat\mu_{i}=
\sqrt{\vec{p}^{\, 2}_i+m^2_i}, \nonumber \\
\left.\delta_{\nu_j}H(\mu_i,\nu_j)\right|_{\nu_j=\hat\nu_j}&=0\ \Rightarrow\ \hat\nu_{j}=
\lambda|\vec{x}_j-\vec{R}|.
\end{align}
$\left\langle \hat\mu_{i}\right\rangle$ is the quark kinetic energy, and $\left\langle \hat\nu_{i}\right\rangle$ is the energy of one flux tube, the average being computed with the wave function of the unperturbed spinless
Salpeter Hamiltonian~(\ref{ssh2}). The equivalence relation between Hamiltonians~(\ref{ssh2}) and (\ref{ham3b}) is $H(\hat\mu_i,\hat\nu_j)=H$.

Although the auxiliary fields are operators, the calculations are considerably
simplified if one considers them as variational parameters. They have then to be eliminated
by a minimization of the masses, and their extremal values $\mu_{i,0}$ and
$\nu_{j,0}$ are logically close to
$\left\langle \hat\mu_{i}\right\rangle$ and
$\left\langle \hat\nu_{j}\right\rangle$ respectively \cite{Sem03}. This
technique can give
approximate results very close to the exact ones~\cite{naro08}. If the
auxiliary fields are assumed to be real numbers, the Hamiltonian~(\ref{ham3b})
reduces formally to a nonrelativistic three-body harmonic oscillator, for
which analytical solutions can be found. A first step is to replace the quark
coordinates $\vec x_{i}=\left\{\vec x_{1},\vec x_{2},\vec x_{3}\right\}$ by
the Jacobi coordinates $\vec x^{\, '}_{k}=\{\vec R,\vec \xi,\vec \eta\,\}$ defined as~\cite{coqm}
\begin{equation}\label{cmdef}
\vec R=(\mu_{1}\vec x_{1}+\mu_{2}\vec x_{2}+\mu_{3}\vec x_{3})/\mu_{t},\quad {\rm with}\quad \mu_{t}=\mu_{1}+\mu_{2}+\mu_{3},
\end{equation}
and $	\vec \xi \propto \vec x_1-\vec x_2,\  \vec \eta \propto (\mu_1 \vec x_1+\mu_2 \vec x_2)/(\mu_1+\mu_2)-\vec x_3$.

In the case of two
quarks with mass $m$ and another with mass $m_3$, the mass spectrum of the
Hamiltonian~(\ref{ham3b}) is given by ($\mu_1=\mu_2=\mu$, $\nu_1=\nu_2=\nu$ by symmetry)
\begin{equation}\label{mass1}
M(\mu,\mu_3,\nu,\nu_3)=\omega_\xi(N_\xi+3
/2)+\omega_\eta(N_\eta+3/2)+\mu+\nu+\frac{\mu_3+\nu_3}{2}+\frac{m^2}{\mu}+\frac{m^2_3}{2\mu_3},
\end{equation}
\begin{equation}
{\rm where}\quad \omega_\xi=\frac{\lambda}{\sqrt{\mu\nu}},\quad \omega_\eta=\frac{\lambda}{\sqrt{2\mu+\mu_3}}\sqrt{\frac{\mu_3}{\mu\nu}+\frac{2 \mu}{\mu_3\nu_3}}.
\end{equation}
The integers $N_{\xi/\eta}$ are given by $2n_{\xi/\eta}+\ell_{\xi/\eta}$,
where $n_{\xi/\eta}$ and $\ell_{\xi/\eta}$ are  the radial and
orbital quantum numbers relative to the variable $\vec \xi/\vec \eta$
respectively. Moreover, $\left\langle \vec \xi^{\, 2}\right\rangle$ and $\left\langle \vec \eta^{\, 2}\right\rangle$ are analytically known. This eventually allows to compute $\left\langle (\vec x_1-\vec x_3)^2\right\rangle$ and $	\left\langle (\vec x_2-\vec x_3)^2\right\rangle$,	which are needed to know the one-gluon exchange contribution.

The four auxiliary fields appearing in the mass
formula~(\ref{mass1}) have to be eliminated by solving simultaneously the four
constraints
\begin{alignat}{2}
\label{const}
&\partial_{\mu}M(\mu,\mu_3,\nu,\nu_3)=0, && \quad \partial_{\mu_3}M(\mu,\mu_3,\nu,\nu_3)=0,\nonumber\\
&\partial_{\nu}M(\mu,\mu_3,\nu,\nu_3)=0, && \quad \partial_{\nu_3}M(\mu,\mu_3,\nu,\nu_3)=0.
\end{alignat}
This task cannot be analytically performed in general, but solutions can
fortunately be found in the case of light and heavy baryons.
\subsection{Light baryons}
Since we do not distinguish between the $u$ and $d$ quarks in our quark model and commonly denote them as $n$, there are only four possible configurations: $nnn$, $sss$, $nss$ and $snn$, that can all be described by the mass formula~(\ref{mass1}). Important simplifications occur by setting $m_n=0$, which is a good approximation of the $u$ and $d$ quark bare masses. However, the non vanishing value for $m_s$ causes Eqs.~(\ref{const}) to have no analytical solution unless a power expansion in $m_s$ is performed. This is justified \textit{a priori} since the strange quark is still a light one. After such a power expansion, the final mass formula reads~\cite{us1}
\begin{align}
\label{M_qqq}
M_{qqq}&=M_0 + n_s\, \Delta M_{0s} \quad\quad (n_s=0,1,2,3), \nonumber \\
M_0 &= 6\mu_0-\frac{2 k_0 a \alpha_0}{\sqrt{3}\mu_0}-\frac{3 f a}{2\pi\mu_0}, \quad
\Delta M_{0s}=\frac{m^2_s}{\mu_0}\left[\frac{1}{2}-\frac{k_
0 a \alpha_0}{6\sqrt{3} \mu_0^2}
+\frac{f a}{2\pi}\left(\frac{3}{4\mu^2_0}+
\frac{\beta}{\delta^2}\right) \right] , \nonumber \\\mu_0&=\sqrt{\frac{k_0 a(N+3)}{3}}.
\end{align}
The mass formula $M_{qqq}$ depends only on
$N=N_\xi+N_\eta$. The contribution of terms proportional to
$N_\xi-N_\eta$, vanishing for $n_s=0$ and 3, was found to be
very weak in the other cases by a numerical resolution of Eqs.~(\ref{const}).

An important feature of the above mass formula has to be stressed: It only
depends on $N$ the total number of excitation quanta of the system. But, this
integer is precisely the band number introduced in large $N_c$ QCD to
classify the baryon states in a harmonic oscillator picture. Indeed the
spinless Salpeter Hamiltonian~(\ref{ssh2}) has been transformed into a
harmonic oscillator by the auxiliary field method and it is thus natural
that a such band number appears. The great advantage of the auxiliary field
method is that it allows to obtain analytical mass formulas for a relativistic
Hamiltonian while making explicitly  the band number used in the large
$N_c$ classification scheme to appear. The origin of $N$ is thus explained by
the dynamics of the three-quark system and the comparison with the $1/N_c$
mass formulas is therefore possible.
\subsection{Heavy baryons}

A mass formula for $qqQ$ baryons can also be found from Eq.~(\ref{mass1}).
An expansion in $m_s$ is still needed to get analytical expressions, but an
expansion in $1/m_Q$ can also be done since we deal with one heavy quark.
One obtains~\cite{us3}
\begin{align}
\label{M_qqQ}
M_{qqQ}&=m_Q+M_1 + n_s\, \Delta M_{1s} + \Delta M_{Q}\quad\quad (n_s=0,1,2), \nonumber \\
M_1 &=  4\mu_1 - \frac{2}{3}\left( \alpha_0\sqrt{\frac{k_1 a}{2N_\xi+3}}
+ 2 \alpha_1\sqrt{\frac{2 k_1 a}{N+3}}\right)-\frac{f a}{\pi\mu_1}, \nonumber \\
\Delta M_{1s}&=\frac{m_s^2}{\mu_1}
\left[ \frac{1}{2}
- \frac{1}{12 \mu_1} \left( \alpha_0\sqrt{\frac{k_1 a}{2N_\xi+3}}
+ 2 \alpha_1\sqrt{\frac{2 k_1 a}{N+3}}\right)
+ \frac{f a}{2 \pi}\left( \frac{3}{4 \mu_1^2}+\frac{\beta}{\delta^2} \right) \right], \nonumber \\
\Delta M_{Q}&=\frac{k_1 a}{2m_Q} \left[ \left(1-\frac{f a}{2 \pi \mu_1^2}\right)G(N,N_\eta)
-\frac{\alpha_0}{6} \sqrt{\frac{2N_\eta+3}{2N_\xi+3}}\left(\sqrt{\frac{2(2N_\eta+3)}{N+3}}-1\right)
\right. \nonumber \\
&\phantom{=\frac{k_1 a}{2m_Q} +}\left.+\frac{4 \alpha_1}{3} \frac{2N_\eta+3}{N+3} \right],\nonumber \\
\mu_1&=\sqrt{\frac{k_1 a(N+3)}{2}}, \quad G(N,N_\eta)=\sqrt{2 N_\eta+3}\left( \sqrt{2 (N+3)} - \sqrt{2 N_\eta+3} \right).
\end{align}
At the lowest order in $m_s$ and $1/m_Q$, this mass formula depends only on
$N$. However, when corrections are added, the mass formula is no longer symmetric
in $N_\eta$ and $N_\xi$. Is it still possible to find a single quantum number?
The answer is yes, provided we make the reasonable assumption that an excited
heavy baryon will mainly ``choose" the configuration that minimizes its mass.

The dominant correction of order $1/m_Q$ is the term that depends on the function
$G(N,N_\eta)$. The baryon mass is lowered when $G(N,N_\eta)$ is minimal,
that is to say for $N_\eta=N$. The analysis of the dominant part of the
Coulomb term shows that the baryon mass is also lowered in this case. So it is natural to assume that the favored configuration,
minimizing the baryon energy, is $N_\eta=N$ and $N_\xi=0$. It is also possible to reach the same conclusion by checking that an excitation of type
$N_\eta$ will keep the baryon smaller in average than the corresponding excitation
in $N_\xi$. This is favored because of the particular shape of the potential, having for consequence that the more
the system is small, the more it is light.

As for light baryons, the quark model shows that heavy baryons can be
labeled by a single band number $N$ in a harmonic oscillator picture.
A light diquark-heavy quark structure is then favored since the light quark
pair will tend to remain in its ground state. Note that the diquark picture
combined with a detailed relativistic quark model of heavy baryons leads to
mass spectra in very good agreement with the experimental data~\cite{ebert}.
\subsection{Regge trajectories}

The band number $N$ emerges from the quark model as a good classification
number for baryons. It is now interesting to focus on the behavior of the
baryon masses at large values of $N$, \textit{i.e.} for highly excited states.
In this limit, the formula~(\ref{M_qqq}) gives
\begin{eqnarray}\label{msqr}
M^2_{qqq}&\approx &12\, ak_0(N+3)-\frac{24}{\sqrt 3}ak_0\alpha_0-\frac{16fak_0}{\pi}+6\left[1+
\frac{fak_0\beta}{\pi\delta^2}\right]n_s m_s^2.
\end{eqnarray}
Our quark model thus states that light baryons should follow Regge
trajectories, that is a linear relation $M^2\propto N$, with a common slope, irrespective of the strangeness of the
baryons. The Regge slope of strange and nonstrange baryons is
also predicted to be independent of the strangeness in the $1/N_c$
expansion method~\cite{GM}. Too few experimental data are unfortunately available to check this result. In the heavy baryon sector, the mass formula~(\ref{M_qqQ}) with $N_\xi=0$ and $N_\eta=N$ becomes at the dominant order
\begin{equation}
(M-m_Q)^2=8a\frac{k_1}{k_0}(N+3).
\end{equation}
This model predicts Regge trajectories for heavy baryons, with a slope of $8 a
k_1/k_0 \approx 7.8  a$ instead of $12 a k_0\approx 11.4\, a$ for light baryons.

The Regge slope for light baryons is here given by $12ak_0$. However, from
experiment we know that the Regge slopes for light baryons and light mesons are
approximately equal. For light mesons, the exact value obtained in the
framework of the flux tube model is $2\pi a$, a lower value than the one
obtained from formula~(\ref{msqr}). This is due
to the auxiliary field method that has been shown to overestimate the
masses \cite{hyb1}. What can be it done to
remove this problem is to rescale $a$. Let us define $\sigma$ such that
$12ak_0=2\pi \sigma$; then the formula~(\ref{msqr}) is able to reproduce
the light baryon Regge slope for a physical value $\sigma$ of the flux tube
energy density. The scaling $a=\pi\sigma/(6k_0)$ will consequently be assumed
in the rest of this paper.

\section{Large $N_c$ QCD versus Quark Model results}\label{compar}
\subsection{Light nonstrange baryons}
The coefficients $c_i$ appearing in the $1/N_c$ mass operator can be obtained
from a fit to experimental data. For example, the case $N=0$ is particularly
simple. Equation~(\ref{GS}) can be applied to $N$ and $\Delta$ baryons. Taking
$N_c = 3$ together with $M_N = 940$~MeV for $S=1/2$, and
$M_{\Delta} = 1232$~MeV for $S=3/2$, we get
\begin{equation}\label{C2C4}
c_1^{(N=0)} = 289 ~ \mathrm{MeV},~~~~~   c_4^{(N=0)} = 292 ~ \mathrm{MeV}.
\end{equation}
Since the spin-orbit contribution vanishes for $N=0$, no information can be
obtained for $c_2$. We refer the reader to
Refs.~\cite{SGS,GSS,MS2,Matagne:2004pm} for the determination of $c_i$ at
$N > 0$.
\begin{figure}[ht]
\includegraphics*[width=16cm]{c1ds.eps}
\caption{Plot of $c^2_1$ (left) and $\Delta M_s$ (right) versus the band number $N$. The values computed in the $1/N_c$ expansion (full
circles) from a fit to
experimental data are compared with the quark model results with $\sigma=0.163$~GeV$^2$, $\alpha_0=0.4$, $f=3.6$, and $m_s=0.240$~GeV (empty circles and dotted line to guide the eyes). No data is available
for $N=3$ in large $N_c$ studies. The large $N_c$ data are nearly indistinguishable from the quark model prediction in the left plot.}
\label{Fig1}
\end{figure}

In the $1/N_c$ expansion method, the dominant term $c_1\, N_c$ in the mass
formula~(\ref{massoperator}) contains the
spin-independent contribution to the baryon mass, which in a
quark model language represents the confinement and the
kinetic energy. So, it is natural to identify this term with the
mass given by the formula~(\ref{M_qqq}). Then, for $N_c = 3$ we have
\begin{eqnarray}\label{c1qm}
  c^2_1&=&\frac{M^2_{qqq}}{9}=\frac{2\pi}{9}\sigma(N+3)-\frac{4\pi}{9\sqrt 3}\, \sigma\alpha_0-\frac{f\sigma}{3}.
\end{eqnarray}
Figure~\ref{Fig1} shows a comparison between the values of $c^2_1$
obtained in the $1/N_c$ expansion method and those derived from Eq.~(\ref{c1qm}) for various values of $N$. From this comparison
one can see that the results of large $N_c$ QCD are entirely
compatible with the formula~(\ref{c1qm}) provided  $\sigma=0.163$~GeV$^2$,
a rather low but still acceptable value
according to usual potential models, $\alpha_0=0.4$, and $f=3.6$: These are
very standard values.

\begin{figure}[ht]
\includegraphics*[width=16cm]{c2c4.eps}
\caption{
Values of $c_2$ (left) and $c_4$ (right) versus the band number $N$. The values computed in the $1/N_c$ expansion (full circles) from a
fit to
experimental data are compared with results
from formula~(\ref{c2c4qm})
(empty circles and dotted line to guide the eyes). No data is available
for $N=3$ in large $N_c$ studies.}
\label{Fig2}
\end{figure}
Equation~(\ref{Vsd}) implies that
$c_2$ and $c_4\propto\mu^{-2}_0$. Therefore we expect the dependence of $N$
of these coefficients to be of the form
\begin{equation}\label{c2c4qm}
c_2=\frac{c^0_2}{N+3},\quad c_4=\frac{c^0_4}{N+3}.
\end{equation}
We see that such a behavior is consistent with the large $N_c$ results in
Fig.~\ref{Fig2}. We chose $c^0_2=208\pm60$~MeV so that
the point with $N=1$, for which the uncertainty is minimal, is exactly
reproduced. Let us recall that the spin-orbit term is vanishing for $N=0$,
so no large $N_c$ result is available in this case. To compute the
parameter $c^0_4$ a fit was performed on all the
large $N_c$ results. In this way we have obtained $c^0_4=1062\pm198$~MeV.
Note that $c^0_4\gg c^0_2$. This shows that the spin-spin contribution
is much larger than the spin-orbit contribution, which justifies
the neglect of the spin-orbit one in quark model
studies.

\subsection{Light strange baryons}
We have first to find out the values of $\Delta M_s$ coming from the $1/N_c$
expansion. For $N = 0$, 1, and 3, they can be found in Ref.~\cite{GM}, and the
case $N=4$ is available in Ref.~\cite{Matagne:2004pm}. The situation is
slightly more complicated in the $N=2$ band due to a larger number of
available results. We refer the reader to Ref.~\cite{us2} for a detailed
discussion about the computation of $\Delta M_s$ in this case.

The mass shift due to strange quarks is given in the
quark model formalism by $\Delta M_{0s}$ in Eq.~(\ref{M_qqq}). A comparison of
this term with its large $N_c$ counterpart
is given in Fig.~\ref{Fig1}, where we used the same parameters as for light
nonstrange baryons. The only new parameter is the strange quark mass, that we
set equal to $240$~MeV, a higher mass than the PDG value but rather common in
quark model studies. One can see that
the quark model predictions are always
located within the error bars of the large $N_c$ results.
Except for $N = 3$, whose large $N_c$ value would actually require further
investigations, the central values of $\Delta M_s$ in the large
$N_c$ approach are close to the quark model results and they
decrease slowly and
monotonously with increasing $N$. Thus, in both approaches, one
predicts a
mass correction term due to SU(3)-flavor breaking which decreases with
the excitation energy (or $N$).

\subsection{Heavy baryons}
As mentioned previously, our present study is restricted to ground state heavy
baryons made of one heavy and two light quarks. In the $1/N_c$, $1/m_Q$
expansion the parameters to be fitted are $\Lambda$, $m_Q$ and $\epsilon\Lambda_\chi$.
At the dominant order, the value of $\Lambda$ can be extracted from the mass combinations~\cite{Jenkins:1996de}
\begin{equation}\label{mcomb}
\Lambda_Q= m_Q+ N_c \Lambda,\quad
\frac{1}{3} (\Sigma_Q + 2 \Sigma^{*}_Q) - \Lambda_Q
= 2 \frac{\Lambda}{N_c},\quad
\Sigma^{*}_Q - \Sigma_Q =  \frac{3}{2} \left(\frac{2 \Lambda^2}{N_c m_Q}\right),
\end{equation}
resulting from the mass formula (\ref{mlnc}). Here and below the particle label represents its mass. A slightly more complicated
mass combination, involving light baryons as well as heavy ones, directly
leads to $m_Q$, that is \cite{Jenkins:2007dm}
\begin{equation}\label{E0}
\frac{1}{3}(\Lambda_Q+2\Xi_Q)-\frac{1}{4}\left[\frac{5}{8}(2N+3\Sigma+\Lambda+2\Xi)-\frac{1}{10}(4\Delta+3\Sigma^*+2\Xi^*+\Omega)\right]= m_Q.
\end{equation}
This mass combination gives
\begin{subequations}\label{paramLNC}
\begin{equation}\label{mQdef}
	m_c=1315.1\pm0.2~{\rm MeV},\quad m_b=4641.9\pm2.1~{\rm MeV},
\end{equation}
while the value
\begin{equation}\label{lambdadef}
	\Lambda \approx 324~{\rm MeV}
\end{equation}
\end{subequations}
ensures that the mass combinations~(\ref{mcomb}) are optimally compatible with
the experimental values for $Q = c$ and $b$. A measure of the SU(3)-flavor breaking factor is given by \cite{Jenkins:1996de}
\begin{equation}\label{breakh}
	\Xi_Q-\Lambda_Q=  \frac{\sqrt 3}{2}\, (\epsilon\Lambda_\chi).
\end{equation}
The value $(\epsilon\Lambda_\chi)=206$~MeV leads
to $\Xi_Q-\Lambda_Q=178$~MeV, which is the average value of the
corresponding experimental data.

The new parameters appearing in the quark model are $m_c$, $m_b$, $k_1=0.930$, and $\alpha_1$. For the other parameters we keep the values fitted in the light baryon sector. We take $\alpha_1=0.7\alpha_0$ from the quark model study of
Ref.~\cite{tf_Semay}. The heavy quark masses can be fitted to the
experimental data as follows. The quark model mass formula~(\ref{M_qqQ}) is
spin independent; it should thus be suitable to reproduce the masses of
heavy baryons for which $J^2_{qq}=0$. Namely, one expects that
\begin{align}
	\left.M_{nnc}\right|_{N=0}=\Lambda_c = 2286.46\pm0.14\ {\rm MeV}, \quad
	\left.M_{nnb}\right|_{N=0}=\Lambda_b = 5620.2\pm1.6\ {\rm MeV}.
\end{align}
These values are reproduced by formula~(\ref{M_qqQ}) with $m_c=1.252$~GeV and
$m_b=4.612$~GeV. It is worth mentioning that
we predict $\left.M_{nsc}\right|_{N=0}=2433$~MeV and
$\left.M_{nsb}\right|_{N=0}=5767$~MeV with these parameters.
These values are very close to the experimental $\Xi_c$ and $\Xi_b$ masses respectively.

We can now compare the quark model and the $1/N_c$, $1/m_Q$ mass formulas.
On the one hand the mass combination~(\ref{E0})
leads to $m_c=1315$~MeV and $m_b=4642$~MeV. On the other hand, the quark model
mass formula~(\ref{M_qqQ}) is compatible with the experimental data provided that $m_c=1252$~MeV and $m_b=4612$~MeV. Both approaches lead to quark masses that
differ by less than 5\%. Thus they agree at the
dominant order, where only $m_Q$ is present.

The other parameter involved in the large $N_c$ mass formula is $\Lambda$.
A comparison of the spin independent part of the mass formulas (\ref{mlnc})
and (\ref{M_qqQ}) leads to the following identification for $N_c = 3$
\begin{eqnarray}
\label{rel1}
{c_0}= \frac{1}{3}\left.M_1\right|_{N=0}
=
\frac{4}{3}\mu_1 - \frac{2}{27}\sqrt{\frac{k_1 \pi\sigma}{2k_0}} (\alpha_0
+ 2 \sqrt 2\alpha_1 ) - \frac{f \sigma}{18k_0 \mu_1},\ {\rm with}\ \mu_1=\sqrt{k_1\pi\sigma/4k_0}.
\end{eqnarray}
According to Eqs.~(\ref{largenpar}) and (\ref{lambdadef})
one has $c_0 = \Lambda \simeq 0.324$~GeV.
The quark model gives 0.333~GeV for the
expression after the second equality sign in Eq.~(\ref{rel1}),
which means a very good agreement for the QCD scale $\Lambda$. The terms of order $1/m_Q$ lead to the identity
\begin{eqnarray}
\label{rel2}
c^{'}_0 = 2 m_Q \left.\Delta M_Q\right|_{N=0}
=\frac{k_1 \pi\sigma}{6k_0} \left[3\left(\sqrt{2}-1\right) \left(1-\frac{f \sigma}{12k_0  \mu_1^2}\right)
-\frac{\alpha_0}{6} \left(\sqrt{2}-1\right)
+\frac{4 \alpha_1}{3} \right] .
\end{eqnarray}
Note that to test this
relation the value of $m_Q$ is not needed, like for the identity~(\ref{rel1}).
The large $N_c$ parameter, $\Lambda=0.324$~GeV, gives for the left hand side of
(\ref{rel2}) $c^{'}_0\sim \Lambda^2 = 0.096$~GeV$^2$ and the quark model gives
for the right hand side 0.091 GeV$^2$, which is again a good agreement. Finally, the SU(3)-flavor breaking term is proportional to
$\epsilon\Lambda_\chi \sim m_s - m\sim m_s$ in the mass formula (\ref{breaksim}). Equations~(\ref{breaksim}), (\ref{M_qqQ}), and (\ref{breakh})
 lead to
\begin{eqnarray}
\frac{\sqrt 3}{2}\epsilon\Lambda_\chi=\left.\Delta M_{1s}\right|_{N=0}
=\frac{m_s^2}{\mu_1}
\left[ \frac{1}{2}
- \frac{1}{36 \mu_1}\sqrt{\frac{k_1 \pi\sigma}{2k_0}} \left( \alpha_0
+ 2 \sqrt 2\alpha_1\right)
+ \frac{f \sigma}{12k_0}\left( \frac{3}{4 \mu_1^2}+\frac{\beta}{\delta^2} \right) \right].
\end{eqnarray}
The large $N_c$ value $\epsilon\Lambda_\chi=0.206$~GeV and the quark model estimate
$0.170$~GeV also compare satisfactorily. We point out that, except for $m_c$ and $m_b$, all the model parameters
are determined from theoretical arguments combined with phenomenology, or are
fitted on light baryon masses. The comparison of our results with the
$1/N_c$ expansion coefficients $c_0$, $c^{'}_0$ and $\epsilon\Lambda_\chi$ are
independent of the $m_Q$ values. So we can say that this analysis is
parameter free.

An evaluation of the
coefficients $c_2$, $c_2'$, and $c_2''$ through a computation of the
spin dependent effects is out of the scope of the present approach. But at the dominant order, one expects from Eq.~(\ref{Vsd}) that $c_2\propto\mu^{-2}_1$ and
$c_2''\propto\mu^{-1}_1$. The ratio $c_2''/c_2$ should thus be of order
$\mu_1=356$~MeV, which is roughly in agreement with
Eq.~(\ref{largenpar}) stating that $c_2''/c_2 \sim \Lambda$. This gives an
indication that the quark model and the $1/N_c$ expansion method would
remain compatible if the spin-dependent effects were included.

\section{Conclusions}\label{conclu}

We have established a connection between the quark model and
the $1/N_c$ expansion both for light baryons and for heavy baryons containing
a heavy quark. In the latter case the $1/N_c$ expansion is
supplemented by an $1/m_Q$ expansion due to the heavy quark. A clear correspondence between the various terms appearing
in the $1/N_c$ and quark model mass formulas is observed, and the fitted coefficients of the $1/N_c$ mass formulas can be quantitatively reproduced by the quark model.

These results bring reliable
QCD-based support in favor of the constituent quark model assumptions and lead
to a better insight into the coefficients $c_i$ encoding the QCD dynamics
in the $1/N_c$ mass operator. In particular, the dynamical origin of the band
number labeling the baryons in large $N_c$ QCD is explained by the quark model.

As an outlook, we mention two important studies that we hope to make in the
future. First, the $N=1$ baryons of $qqQ$ type are poorly known in the
$1/N_c$, $1/m_Q$ expansion. They should be reconsidered and compared to the
quark model. Second, the ground state baryons made of two heavy quarks and a
light quark could be studied in a combined $1/N_c$, $1/m_Q$ expansion-quark
model approach, leading to predictions for the mass spectrum of these baryons.

\section*{Acknowledgement}
F.B. and C.S. thank the F.R.S.-FNRS (Belgium) for financial support.

redpajama_set_name: RedPajamaArXiv


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Sunset Sails Tours Morning or Afternoon Tour
Cruise along one of Costa Rica's most scenic coastlines on a sailing and snorkeling tour of Manuel Antonio. Relax on deck and sip unlimited drinks from an open bar as you get a new perspective on the unspoiled nature preserve and try to spot dolphins, turtles, and migrating whales. Stop to swim and snorkel among tropical fish in the clear waters off Biesanz Beach, and then reward your efforts with a gourmet lunch prepared right on board.
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Set off on horseback through the mountains and trails around beautiful Manuel Antonio on this full-day, guided tour with lunch included. After a safety briefing and riding instructions, hop on your horse and follow your guide into the mountains to an altitude of 1,900-feet (600-meters) taking in amazing views, wildlife, and vegetation along the way. Enjoy a swimming break on the way down and a local lunch at the ranch.
Manuel Antonio National Park Adventure
A guided tour enriches your experience in Manuel Antonio National Park by providing information about the park's plant and animal life and expert navigation between the park and your regional hotel. Plus, this tour offers a stress-free way to visit one of Costa Rica's must-see destinations in just one day.
Catamaran Cruise from Manuel Antonio with Snorkeling
Ride along the forested coast of Manual Antonio National Park on this 4-hour catamaran tour. Morning tours feature a snorkeling adventure in the secluded bay of Playa Biezans, while evening tours allow you to take in views of the sunset over the Pacific Ocean. This tour includes round-trip transportation from your lodging in the Manuel Antonio area as well as snorkel equipment (morning tour), a guide, and lunch or dinner.
Damas Island Mangrove Kayaking Tour from Manuel Antonio
Paddle past the giant twisted root systems that characterize mangrove forests on this kayak tour of the largest mangrove ecosystem in Central America at Damas Island. This biodiversity hotspot is home to tons of birds, reptiles, and aquatic animals that you can spot easily with the help of your guide. This tour includes round-trip transportation from your Manuel Antonio or Quepos lodging as well as lunch or dinner.
Catamaran Ocean King Manuel Antonio
Get a new perspective on the Costa Rican coastline from the back of an all-inclusive catamaran, visit islands you might otherwise have overlooked, and enjoy time to snorkel during this half-day excursion. Soak up the sights as you make the most of free alcoholic beverages, snacks, and fresh fruit, relax on the tanning meshes, or take a dip in the Jacuzzi.
Zip lining, rappel and a Tarzan Swing
Get your adrenaline pumping during this adventure tour in the Naranjo Biological Corridor of Costa Rica. Soar through the treetops on a zip line, come face to face with local wildlife like white-faced monkeys and tropical birds, and traverse an obstacle course with a series of platforms, suspension bridges, a Tarzan swing, and a rappel. End the tour with a delicious Costa Rican meal and traditional snacks.
Chocolate Tour Manuel Antonio
Costa Rica's lush jungles have long been a notable area to grow cash crops such as coffee, chocolate, and sugar cane. On this private experience, visit a plantation in Manuel Antonio and learn how these three crops are produced. Take a guided tour of a plantation and traditional sugar cane mill, and see how some of your favorite treats are made.
Manuel Antonio National Park Tour
Experience Costa Rica's tropical rainforests on this half-day, guided, nature excursion through Manuel Antonio National Park. Learn about this complex ecosystem while hiking (or strolling) and listen as a naturalist guide points out animal and plant species and explains the biodiversity of this nature sanctuary.
Manuel Antonio National Park Hiking Tour
Turn an ordinary walk into an educational adventure with a guided nature walk in Manuel Antonio National Park, widely considered one of the most beautiful parks in Costa Rica. Go with a guide who can help you spot sloths, monkeys, iguanas, and more while providing commentary about their lives and behaviors in the rain forest.
Mangrove Boat Tour Damas Island
Pickup time for this tour depends to the high tide. We'll give you the pickup time right after receiving your booking. The mangrove forest is one of the most vital and astounding ecosystems in the world. Damas Island, located just 10 minutes from Manuel Antonio is currently one of the most important remaining mangroves in Costa Rica. Covering thousands of acres of protected forest, this amazing biodiversity is home to a large number of birds, reptiles, mammals and insects. Our experienced guides will take you on an unforgettable boat tour through the channels of the mangrove forest, far away from civilization. You can discover an abundance of species native to the area such as white-faced monkeys, anteaters, boas, iguanas, birds and thousands of colorful crabs.
Manuel Antonio National Park Wildlife Tour
Our job is the best in the World! We show people not only some of the most amazing landscapes in Costa Rica, but we get to witness the awe in people's eyes when we show our country and our region. We believe that tropical nature has many more secrets than the ones you can perceive with your senses, the relations, and all the life systems that depend on these connections. And it is a privilege to discover them for all people's eyes and minds. Our guides are all professionals, certified and passionate about nature. They all have a true appetite for knowledge and they will provide you with a true Costa Rican rainforest set of experiences.
Mulguri Waterfalls & Eco Adventure Manuel Antonio
When it comes to your perfect Costa Rican adventure, this tour from Manuel Antonio to Quebrada de Arroyo, has it all. Ride a 4x4 into the Costa Rican rain forest,visit a waterfall, walk across a swinging bridge, and swim in natural pools, all on a hassle-free guided excursion. Complete the tour with a fresh lunch at a farm in the countryside before returning to your hotel.
Manuel Antonio National Park Group Guided Tour
If you're looking for wildlife in Costa Rica, one of the best places to see it is the pristine coastal forests of Manuel Antonio National Park. Get more out of a visit to the famous park on a tour with a certified naturalist guide who knows all the best places to find sloths, monkeys, iguanas, toucans, and many other animals. Learn about the park's amazing ecosystems along the way, and get a closer look using a provided Swarovski spotting scope.
Horseback Riding Tour from Manuel Antonio
See what life is like outside of the city on this horseback riding tour through the countryside. Alongside a guide, ride a well-trained horse through small towns and forested land en route to a tucked-away waterfall, followed by a typical Costa Rican lunch.
Damas Island Mangrove Boat Tour from Manuel Antonio
Weave your way past the giant twisted root systems that characterize mangrove forests on this boat tour of the largest mangrove ecosystem in Central America at Damas Island. This biodiversity hotspot is home to tons of birds, reptiles, and aquatic animals that you can spot easily with the help of your guide. This tour includes round-trip transportation from your Manuel Antonio or Quepos lodging as well as lunch or dinner.
Day Trip to Caño Negro Including Río Frio Boat Experience from La Fortuna
This well-rounded tour is the perfect way for nature lovers to experience the best of Costa Rica's outdoor beauty. Enjoy a scenic boated on the Rio Frio with departure near the border of Nicaragua. Cruise through the Cano Negro Wildlife Refuge and see the incredible biodiversity that makes this nation to unique. You'll have up close encounters with birds, snakes, herons and other animals, as well as various species of monkeys and sloths.
Our environmental interpretation tour. While touring the main trails, you will be able to observe numerous species of flora and fauna. Our specialized bilingual tour guide will be willing to share his knowledge with you about the ecosystem for you to learn and enjoy the natural, historical and cultural environment of this astonishing protected area.
Manuel Antonio National Park Tour from Uvita
Explore Manuel Antonio National Park on a half-day guided tour from Quepos. Your guide leads a leisurely 2-mile hike to a gorgeous beach next to lush rain forest. Have about 20 minutes to enjoy the sand and sea, then continue to walk with frequent stops to look at plants and animal life. High-quality telescopes are provided for prime viewing of sloths, monkeys, colorful birds, and more.
Private Bird Watching Esquipulas Manuel Antonio
The tour is completely PRIVATE. Esquipulas is a small countryside town located at the foothills of San Marcos de Tarrazú (one of the highest mountains in Costa Rica). Esquipulas is considered to be the best spot for birding at the area of Manuel Antonio and Quepos. Just about 20 minutes drive approximately from most of the hotels in Manuel Antonio. You'll be 400 mts above the sea level (great altitude for a bird watching morning). Esquipulas features a mixture of primary and secondary forest, house gardens and cattle pastures, making it home to a wide variety of birds including Tanagers, Trogons, Hummingbirds, Flycatchers, Manakins, and Toucans among many others. Approximately 304 bird species have been reported in Esquipulas.
What are the best Eco Tours in Quepos?
The best Eco Tours in Quepos according to Viator travelers are:
What Eco Tours in Quepos are taking additional safety precautions?
These Quepos experiences are providing additional COVID-19 safety measures:
What Eco Tours in Quepos are good for avoiding crowds?
These hidden gems in Quepos may have limited interaction with crowds:
More Tours in Quepos
Things to do near Quepos
Things to do in Limon
Day Trips from Quepos
Quepos to San Jose
Quepos to Jaco

redpajama_set_name: RedPajamaCommonCrawl


Whatever you're planning, we have applause worthy resources and teams of professionals. With our special location in the heart of Down Town Vancouver and Burnaby, there's nothing we haven't seen, from Weddings to Meeting Rooms and much more. Our smartly designed, full-service facilities are ideal for everything. Put the Executive Hotel Burnaby in your corner and the stage is set for success.
The range and scale of our event venues is impressive, yet inviting; the service is to drawer with focus on skill and understanding our clients and the accommodations are graced both by elegance and comfort. All of our special event rooms have generous pre-wedding space to accommodate your wedding cocktail reception prior to dinner.
You deserve to remember the most important day of your life in perfect clarity.Let Executive Suites Hotel Burnaby give you the memories you deserve.Reserve Now and Get your discounted rate and Wedding Honeymoon Suite Upgrade, and for your special discount, contact our Reservation Team for more details.


Barry's Tea made an appearance in the recent season ending episode on Saturday Night Live with Justin Timberlake and Lady Gaga.
Just click on this link to see a copy of a photo. You can see Barry's in the background behind Justin Timberlake.
Thanks to David Ding for the photo.


Saint Paul's is an inclusive church and all are very welcome to worship with us. We gladly recognise that everyone, irrespective of age, colour of skin, gender, marital status, sexuality, nationality, disability or background, is a Child of God, valued and loved.
This beautiful church was built over 150 years ago as a mission church for Brighton's fishermen, or more likely for their wives.
Set in busy West Street, close to the commercial centre of this thriving new city, Saint Paul's is a haven of calm, beauty and devotion, offering a warm welcome to any who want to rest, to admire or to pray.
Saint Paul's is a jewel of the Anglo Catholic movement now hidden behind the Brighton Centre, the Kings West Cinema complex and Churchill Square.
However, the unique and most distinctive lantern tower can still be seen from a great distance, a beacon to guide your steps to our gates.
Indeed, the tower was used as a navigation point by the fishermen when the Brighton skyline was lower.


text:
Research has shown that consumer behaviour is difficult to predict,why?
Consumer behaviouris the study of individuals, groups, or organizations and all the activities associated with thebuy disposal ofmaterial and work and how the comuster's emotions, attitudes andaffect buying behaviour. Consumer behaviour emerged in the 1940s and 50s as a distinct sub-discipline ofprocess of market but has become an inter-disciplinary social science that blends elements frompersonal(by age,gender,culture etc.),psychology,social marketing.
The study of consumer behaviour formally investigates individual qualities such as life-history lifestyles, nature and behavioural variables (such as usage rates, usage occasion,honesty,brand avocate, and willingness to providetransfer), in an attempt to understand people'sneedanddemand.
Research has shown that consumer behaviour is difficult to predict, even for experts in the field; however, new research methods, such as cultural anthropology,consumer neuroscience, andmachine understanding are shedding new light on how consumers make decisions. Theample produced by these databases enables detailed examination of behavioural factors that contribute to customer re-purchase intentions,costumer relation, loyalty and other behavioural intentions such as the willingness to provide positive referrals, become brand advocates or engage in customer citizenship activities. Databases also assist in marketing especially behavioural segmentation such as developing loyalty segments, which can be used to develop tightly targeted, customized marketing strategies on a one-to-one basis.
How far should courts go in protecting employees from wrongful termination?
The issue in the present cause is whether termination of an at-will employee for his refusal to dismiss his pending claims against a third party…constitutes a violation of Oklahoma's public….
What is the difference between justification and sanctification in Romans?
Introduction to the New Testament Assessment 2 – Major Essay Weighting :35% Word Count :1500 words Task : Select one of the following questions to research. Your answers should include….
write a 2000-word business report in which you apply learnings from the capstone topics and apply them to the organisation by undertaking additional research.
Your task Using the same organisation chosen for Assessment 1, you are required to write a 2000-word business report in which you apply learnings from the capstone topics and apply….


text:
Q: PSTricks standalone drawing cropped wrongly I'm trying to create a standalone drawing with pstricks compiled using latex>dvips>ps2pdf. I don't have any compiling errors, but the image is not cropped properly in the vertical direction. The following code gives me the image below it.
\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pstricks}
\begin{document}
\begin{pspicture}[showgrid](-10,-10)(10,10)
\end{pspicture}
\end{document}

If the size of the picture is smaller than 13 in height the grid is no longer visible. It seems that the original page is always cropped in the center although the pspicture is aligned at the top.
It used to work properly but stopped working suddenly, so I suspect some update might be the culprit. I reinstalled everything I could think off and the problem is still there. I am using MiKTeX 2.9.6
Running xelatex results in correct cropping, however I want to use pst-optexp and xelatex fails when drawing beams so that is not an option.

redpajama_set_name: RedPajamaStackExchange


What is your memory like?
Do you have total recall?
Or are you more like Dory from Finding Nemo?
Like most people you're going to be somewhere in the middle.
You remember a lot, but some things slip.
You probably write lists of things to get done, you'll have a few goals or dreams noted down and some larger personal projects planned out, however roughly.
But on the day-to-day do you sometimes struggle to remember those things you've learned recently?
Particularly if you're on a personal development programme. Do you struggle to remember and keep a track of all the things you have decided that you'd like to change about yourself, possibly based on something you read or heard?
Or you have new regimes, particular changes to your workflows or new habits that you know you want to form, but you find it can be difficult to keep track of the next steps?
Even if you use a trusted digital system like OneNote or a physical notebook, to store this information, it then becomes a problem of indexing & retrieval. You'll have sections containing different pages with different types of information in, but then you need to be remembering where each different thing is. How do you get that holistic summary, the 1000 mile high view?
This is particularly a problem if you have ADD tendencies. Keep track of one or two new things to accomplish and you're fine as long as they are not boring – you'll then do anything to avoid doing them – but try to keep track of a bunch of new things, stuff not ingrained habitually and it can be like wading through a fog of information. Stuff floats in and out of focus, there's this sense of disorganisation, that there's a bunch of things you know you want to be doing, it's all written down, there's sort of a plan, but it's hard to fit it all in your head at the same time.
If so you might want to try this really simple approach that will remove the hard work of trying to remember it all.
Let's assume that you do use a trusted system to store lists of things. Details of projects, random inspirational quotes, which books to read next and so on.
Go through this system and pick out all the things that you want to apply to your life for the – say – next 6 months: aspirations, a few goals, a change in mindset, some habits, reminders about tone of voice in your writing.
Copy them and summarise into a personal statement; your own personal manifesto.
It should be short so it would fit onto a single sheet of A4 if printed and you should store it somewhere where you will look at it very regularly.
Let's give a hypothetical example.
Jane is freelance front-end web developer who is 35 years old, married with 2 kids who are a few years off secondary school age. She has aspirations to launch an online service putting local crafts people in touch with people who need bespoke pieces made to specification, she used to be a keen spoon carver until life got in the way.
Her and her partner are hoping to move to Spain one day, so she would really like to learn Spanish. She's mad on horses, but doesn't have the space or income to keep one. She has a blog that she'd like to publish more on but she has confidence issues: knowing what to write about and a bit of imposter syndrome.
It is hard for Jane to be motivated to exercise,but she really likes cake and is keen to keep in shape.
She is also rather time poor. On top of her business she has a family and a house to help run.
I, Jane Doe, am constantly improving. I am positive and I am enjoying every day as it comes.
I am kind to myself, I know that I am doing the best that I can.
I don't allow screens in my bedroom, except my Kindle.
going to bed by 9:30pm.
I use my commute to learn Spanish, using an app on my phone.
Tuesday and Thursday evenings are my time to work on my side project. I try not to get frustrated that I can't spend more time on it. I remind myself that it's better to spend a few hours per week on it than none at all.
Saturday mornings are for chores and kids' clubs.
Every other Saturday afternoon I go horse riding at the local riding school with my daughter.
Sundays are left free, but I always find an hour to plan out my week.
My family are the most important thing to me, I am here for them but also making sure that I take care of myself.
Note the underlining. Jane uses OneNote, so these are links to OneNote pages containing more information on these things.
Of course your statement will be different because your situation is different as are your aspirations.
But, even if you find it easy to retain and recall knowledge and feel that a statement like this is a waste of time, consider that writing it down will free your mind up to store even more important things.
If you do decide to make your own personal statement then make sure you read it at least once a week.
Keep tweaking it. New things will come in, new things will drop off to allow you to make everything fit.
A summary like this keeps a lot of stuff from floating around in your head, it also keeps it right up front. You'll be more motivated to keep on track as there's no longer an excuse to forget.
Good luck trying it out, let me know how you get on.
Time: 2 hours. I'll probably re-work this, with a better example over the coming weeks. I follow this practice myself, not sure if it's a thing, or just something I made up. It definitely helps to maintain perspective.


text:
United Nations wants to scrub Black Pete's face
The Daily Herald
AMSTERDAM--The United Nations Committee on the Elimination of Racial Discrimination has released its report on discrimination in the Netherlands following a meeting with the Dutch delegation in Venice, Italy, last week. The committee highlighted a number of concerns and made recommendations regarding, among other things, Black Pete, ethnic profiling by the police, racist statements made by politicians, anti-Semitic chants during soccer games, the asylum policy and ethnic-bullying in schools.
"Considering that even a deeply rooted cultural tradition does not justify discriminatory practices and stereotypes, the Committee recommends that [the Netherlands – Ed.] actively promotes the elimination of those features of the character of Black Pete which reflect negative stereotypes and are experienced by many people of African descent as a vestige of slavery. The Committee recommends that the State find a reasonable balance, such as a different portrayal of Black Pete and ensure respect of human dignity and human rights of all inhabitants of the State," the Committee writes.
Black Pete, or "Zwarte Piet" in Dutch, helps the Dutch version of Santa Claus distribute presents every year in early December and is displayed as a silly, mischievous and indolent character, usually animated by an actor in blackface. In recent years, he has become a lightning rod for a cultural debate, and has even sparked violence.
During his weekly press conference on Friday, Prime Minister Mark Rutte said Black Pete was not a matter of state. "Beware of a country where the State decides what folk tradition should look like. I really think that is something for the people to decide and not a matter of politics," said Rutte.
The Black Pete issue was a small element of the report on the Netherlands which is produced every five years and looks at racism and discrimination in general.
The committee noted that not all Dutch municipalities have an anti-discrimination policy that is in line with the State's policy on anti-discrimination and added that it is the national government's responsibility to ensure that all cities comply.
They also expressed concerns about "incidents of racist and xenophobic hate speech emanating from a number of extremist political parties and politicians," the prevalence of "racist discourse in the media" and the increase of racist statements and threats on the Internet.
In this regard, the Committee is particularly concerned about the sharp increase in discrimination against members of Jewish and Muslim communities, including the reported increase in verbal abuse, harassment, and physical violence against Jewish and Muslim persons.
The fact that anti-Semitic chants are "commonplace at football stadiums" is also a big problem, the Committee stated.
The UN Committee recommends that the Netherlands "adopt a firm stand against the use of hate speech for political purposes, increase efforts to combat racially motivated hate speech and ensure that criminal acts perpetrated on grounds of 'intersectionality' between ethnic origin and religion are duly investigated and prosecuted."
The Committee also recommends that a national plan of action against racial discrimination be developed and adopted, especially given the fact of continuing racial profiling by the police which has "produced feelings of mistrust among minority groups and discourages them from accessing help when they are victims of crime or rights abuses."
According to the Committee, the current policy on migrant integration has shifted from the State to migrant communities. "This approach puts migrants in particularly vulnerable situations at risk of receiving insufficient attention and support, leaves them vulnerable to social exclusion and hampers their integration."
They are also concerned about the asylum policy stating that undocumented migrants only receive assistance if they comply with their own expulsion.
"The Committee reiterates its previous recommendations, and urges the State to ensure that its integration policies reflect the responsibilities of the State," the Committee said in its report.
The government should also ensure that undocumented migrants are provided with food and shelter in all circumstances prior to deportation and that they have access to healthcare in all parts of the Dutch Kingdom, which is currently not the case in Curaçao and Aruba.
The Netherlands has to report back to the Committee in 2019 on changes and improvements made.
The Committee on the Elimination of Racial Discrimination (CERD) is the body of independent experts that monitors implementation of the Convention on the Elimination of All Forms of Racial Discrimination by its State parties.
All States parties are obliged to submit regular reports to the Committee on how the rights are being implemented. States must report initially one year after acceding to the Convention and then every two years. The Committee examines each report and addresses its concerns and recommendations to the State party in the form of "concluding observations".
In addition to the reporting procedure, the Convention establishes three other mechanisms through which the Committee performs its monitoring functions: the early-warning procedure, the examination of inter-state complaintsand the examination of individual complaints.
The Committee meets in Geneva and normally holds two sessions per year consisting of three weeks each.
The Committee also publishes its interpretation of the content of human rights provisions, known as general recommendations (or general comments), on thematic issues and organizes thematic discussions.
For more information about the work of the Committee on the Elimination of Racial Discrimination, click here.
Labels: Caribbean, Netherlands, racism


text:
El Barranc de Pinós, que en el tram inicial del seu curs és anomenat Rasa de Pinós, és un torrent afluent per l'esquerra de la Riera de Madrona que neix al vessant nord de Santes Creus de Bordell. De direcció global cap al nord, després de deixar a llevant la masia de Pinós, desguassa al seu col·lector a poc més de 500 m. al nord de Cal Llobet. Fa tot el seu curs pel terme municipal de Pinell de Solsonès

Xarxa hidrogràfica

La seva xarxa hidrogràfica, que també transcorre íntegrament pel terme municipal de Pinell de Solsonès, està constituïda per quatre cursos fluvials la longitud total dels quals suma 3.561 m.

Enllaços externs
 Taula amb les dades detallades de la xarxa hidrogràfica de la Riera de Madrona

Referències

Rius de la conca de la Riera de Madrona
Rius de Pinell de Solsonès

redpajama_set_name: RedPajamaWikipedia


text:
"The Most Toys" is the 22nd episode of the third season of the American science fiction television series Star Trek: The Next Generation, and the 70th episode of the series overall.

Set in the 24th century, the series follows the adventures of the Starfleet crew of the Federation starship Enterprise-D.  In this episode, Lieutenant Commander Data (Brent Spiner) is kidnapped by an obsessive collector, who leads the Enterprise crew to believe that Data was destroyed in a shuttlecraft accident. The episode's title references a quote popular in the 1980s, "Whoever dies with the most toys wins".

Plot

The Enterprise-D is called to assist the colony on planet Beta Agni II, which has suffered contamination to its water supply. They meet with the Jovis, a ship owned by the Zibalian trader Kivas Fajo (Saul Rubinek), a trader who happens to have hytritium, the extremely rare compound needed to neutralize the contamination. The volatile substance cannot be beamed aboard, so Lieutenant Commander Data (Brent Spiner) is assigned to make several shuttle trips to collect the cargo. Just before the final trip, Data is kidnapped, and his shuttle is rigged to explode. The Enterprise crew scan the debris and finding trace elements matching Data, they believe he is dead, and are forced to leave to continue their mission.

Data is reactivated in a secured room and is met by Fajo, who explains he collects rare and valuable objects and has kidnapped Data due to his uniqueness. Fajo's assistant Varria tells Data to change out of his Enterprise uniform and to sit in his chair. Data refuses to follow orders and remarks that they are both Fajo's prisoners.

Mourning the loss of their friend, Geordi is certain that he is missing something about Data's destruction. Geordi takes his hypothesis to Picard and Riker, stating that the reason he can't find anything is there's nothing to indicate a malfunction. He explains that the only option is pilot error, but doesn't believe it as the odds are too vast to calculate. Picard gives him some words of solace and dismisses him. Picard and Riker select Worf as Data's replacement.

In an effort to make Data comply with his wishes, Fajo says that he isn't at war with anyone and is in fact Data's liberator. He prods Data about whether or not he is capable of killing anyone, and Data states that he is programmed to never kill except in defense, and thus would be incapable of murder. When Data still refuses to submit, Fajo splashes a solvent on Data's uniform that dissolves it so he will be compelled to change his clothes.

Geordi and Wesley run through Data's communications during the shuttle trips, with Geordi noting that Data follows protocol to the letter. They observe that Data didn't report the shuttle clearing the cargo bay of the Jovis on the final transmission, per protocol. Geordi and Wesley conclude that for Data to not follow standard procedures there would have to be something wrong with Data himself.

Data remains defiant against Fajo's attempts to make him an object of display, purposely remaining silent and immobile when Fajo shows off his collection to a rival trader (Nehemiah Persoff). Only when Fajo threatens to kill Varria with a very rare and illegal Varon-T disruptor does Data agree to follow Fajo's orders, and sits in the chair.

The Enterprise crew arrives at the colony and uses the hytritium to neutralize the contamination, but finds it works far more quickly than it should, and deduce that the contamination had been caused deliberately, leading them back to Fajo. They return to the last-known location of the Jovis to track Fajo down.

Varria decides to help Data escape. During the attempt they set off alarms that alert Fajo, and when he gets there, he uses the Varon-T disruptor on Varria, killing her without remorse. Data picks up the spare Varon-T that Varria had possessed and threatens to use it on Fajo. Fajo in turn threatens to murder more of his assistants if Data doesn't comply with his demands, believing that Data's programming will prevent him from shooting Fajo and to preserve the assistants' lives by submitting. Fajo further taunts Data to shoot him, mocking him as "just an android" incapable of feeling rage at Varria's death. Data states that he cannot allow this to continue and gets ready to shoot Fajo, much to the latter's shock. The Enterprise arrives and suddenly beams Data back aboard, discovering that the disruptor was in the process of discharging. Data is met in the transporter room by Commander Riker, and requests that Fajo be taken into custody, with Riker responding that arrangements have already been made. When Riker asks why the disruptor was energized, Data only offers that something may have happened during transport.

Data visits Fajo in the brig, where Fajo laments the reversal of their situation, but says defiantly that he will again add Data to his collection one day. Data informs Fajo that his stolen collection has been confiscated, and all his possessions returned to their rightful owners. Fajo remarks, "It must give you great pleasure." Data replies, "No, sir, it does not. I do not feel pleasure. I am only an android." He then leaves a stunned Fajo alone in the brig.

Production

The episode's title comes from a popular saying found on bumper stickers and T-shirts in the 1980s which read, "He who dies with the most toys wins." The quote was originally attributed to flamboyant millionaire Malcolm Forbes. The characters name Kivas Fajo comes from script coordinator Lolita Fatjo, and a mineral mentioned as an item Spock deals in for the episode Errand of Mercy.
Writer  Shari Goodhartz was dissatisfied with the ending and wished she had been able to come up with something more clever, finding it a little too convenient. Spiner agreed with Goodhartz that Data purposefully shot Fajo, but the producers wanted it to be kept ambiguous. Goodhartz said "If I had a chance to do it over, with all the experience I have behind me now, I would argue passionately for Data's actions and their consequences to have been clearer, and hopefully more provocative."

David Rappaport, a well-known British dwarf actor, had originally been cast for the part of Kivas Fajo. Rappaport struggled with depression during his life, and attempted suicide shortly after filming some scenes as Fajo. (Rappaport later died by suicide on 2 May 1990, three days before the airing of this episode). Saul Rubinek was brought in to take over the role and complete the episode. Select scenes with Rappaport were included in a special In Memoriam reel on disc five of the third-season TNG Blu-ray set.

Makeup supervisor Michael Westmore had designed an alien look for Rappaport but when the role was recast there was not enough time to recreate the alien prosthetics for another actor and had to settle for a small face tattoo. Furthermore, Fajo's assistant Varria had a flatted face and antennae that came out of her forehead, that wove into an alien hairdo. Actress Jane Daly did not like wearing the makeup or the elaborate hairdo and when the costume went for approval she convinced Gene Roddenberry to remove the antennae and change the hair style. Westmore said that instead of looking alien they were left with "a woman with a flat face and an Annette Funicello hairdo" and compared the look to a car crash victim, and noted that they inserted a line into the script to cover how terrible she looked. Westmore said it was his least favorite episode of all his work on Star Trek.

Famous artwork is heavily featured in this episode, to demonstrate Fajo's taste in what he considers unique and valuable.
 Among the artifacts that Fajo has collected, there is a copy of Salvador Dalí's The Persistence of Memory. The copy was created by artist Elaine Sokoloff.
 Although it is never seen, Vincent van Gogh's The Starry Night is mentioned by the Enterprise computer as one of the artifacts collected by Fajo.
 In a small scene before the one where Fajo threatens to kill Varria with a disruptor in order to get Data to obey him, Data is looking at Leonardo da Vinci's famous Mona Lisa, trying to imitate her famously enigmatic smile.

Reception
Zack Handlen of The A.V. Club gave the episode a grade A−. Handlen wrote that in one way the episode could be considered a variation on the episode The Measure of a Man, but that it stands quite well on its own and that "subtle character exploration" of Data gives it its edge. Keith R.A. DeCandido reviewed the episode and gave it 8 out of 10, praising the ambiguous ending, and the performances of Spiner and Rubinek.

In 2014, io9 ranked "The Most Toys" as the 95th best episode of Star Trek in their list of the top 100 Star Trek episodes.

In 2021, Robert Vaux writing for Comic Book Resources, said this was a "strong episode" in season 3, and that it tested the morality of the crew.

Home video
The episode was released with Star Trek: The Next Generation season three DVD box set, released in the United States on July 2, 2002. This had 26 episodes of Season 3 on seven discs, with a Dolby Digital 5.1 audio track. It was released in high-definition Blu-ray in the United States on April 30, 2013.

References

Resources
 Star Trek The Next Generation DVD set, volume 3, disc 6, episode 2

External links

Star Trek: The Next Generation (season 3) episodes
1990 American television episodes
Television episodes about abduction


Falaj Daris Hotel is ideally located just about 4Kms away from Nizwa town. Perfect base to explore the interior and after a tiring day to relax! The hotel is situated 150Kms from Seeb International airport. The hotel has recently undergone a complete renovationand refurbishment. The hotel now has 55 beautifully appointed international standard rooms including 2 suites.


It's been a long time since there's been new material on the blog. I've been traveling a lot - Italy, USA, training, and planning for Taira sensei to come to New Zealand in October.
Amongst all of that, many of you know we have been talking about migrating the Gojuryu Kenkyukai web site somewhere else. The site is old fashioned, we didn't have good integration with PayPal or other things, and many people were members without paying, because we'd messed up that PayPal and a few other things. On top of that, the server just died and it look unrecoverable. We can restore the old functionality from backups, but that is a lot of work for nothing.
We are going to migrate all the old video, probably to Vimeo, and properly manage it using commercial software. We will put up the accounts we have on record, and we'll progress with the grand re-organisation we've been planning. We'll even put up new video for subscribers.
So bear with us, we're doing things. And there will be video from the NZ seminars, accessible through the 'new' site.


Click the button below to add the 500K Linear Guitar Pot w/ Push-Push Switch-Long Shaft to your wish list.
500K linear taper control pot with double pole/double throw (DPDT) push push switch with long shaft. Use for coil splitting, reverse phase switching and other functions in Les Pauls and other thick top guitars.


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Lucasfilm Developing Kylo Ren Prequel With Adam Driver
By Matt Joseph @wgtc_site 3 months ago
If you couldn't already tell, 2019 has all the makings of a massive year for Disney and Lucasfilm's Star Wars franchise.
From Galaxy's Edge to The Mandalorian to the hugely anticipated Rise of Skywalker, it truly feels as if this will go down as a historic year in Star Wars history. Already we had the launch of the Galaxy's Edge theme park back in May and The Mandalorian is getting ready to makes its big premiere on Disney Plus next month.
But closer to Christmas we'll finally get to lay eyes on Episode IX and it seems Disney is working on several tie-in comics to help heighten the anticipation ahead of December 20th. One of them's The Rise of Kylo Ren, which will dive into the hazy origins of Adam Driver's dark prince. But for fans of the character, the good news doesn't end there, as Lucasfilm still has big plans for him moving forward.
According to sources close to WGTC – the same ones who told us about Ewan McGregor's Obi-Wan return back in May, along with the "special connection" Palpatine and Rey share in Rise, which has since been confirmed – Lucasfilm is planning some sort of Kylo Ren prequel and Driver is reportedly involved. It's unclear if it'd be a movie or a Disney Plus show and is only in the early stages of development right now, but they apparently hope to explore Ben Solo's younger days and look at what made him into the villain we saw in the Sequel Trilogy.
Relive The Final Star Wars: The Rise Of Skywalker Trailer With These Glorious Screenshots
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Details beyond that remain unclear and with everything else they've got on their plate right now, we imagine it'll be a while before this project gets off the ground. There's also a chance that it could go in a different direction or morph into something else entirely. After all, look at how the Obi-Wan movie ended up as a TV show while the Boba Fett film was outright cancelled.
For now, though, the plan appears to be to do some sort of Kylo Ren prequel. And given that this intel comes to us from the same sources who also told us all those other Rise of Skywalker spoilers which will be proven right very, very soon, we have no reason to doubt it.
Tags: Kylo Ren, Star Wars


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Happy 126th Birthday Blanche Sweet
Today is the 126th birthday of the silent movie actress Blanche Sweet. She made over 160 movies, nearly all of them silent and was one of the many actors that did not make the transition to 'talkies'. The world is a better place because she was in it and still feels the loss that she has left.
NAME: Blanche Sweet
PLACE OF BIRTH: Chicago, Illinois, U.S.
DATE OF DEATH: September 6, 1986
PLACE OF DEATH: New York City, U.S.
REMAINS: Ashes spread at Brooklyn Botanical Gardens
HUSBAND: Marshall Neilan (m. 1922; div. 1929)
HUSBAND: Raymond Hackett (m. 1935; died 1958)
BEST KNOWN FOR: Sarah Blanche Sweet was an American silent film actress who began her career in the earliest days of the Hollywood motion picture film industry.
Born Sarah Blanche Sweet in Chicago, Illinois, in 1896, she was the daughter of Pearl, a dancer, and Gilbert Sweet, a wine merchant. Her mother died when Blanche was an infant, and she was raised by her maternal grandmother Cora Alexander – and known as Blanche Alexander.
Cora Alexander found her many parts as a young child. At the age of four she toured in a play called The Battle of the Strong with Marie Burroughs and Maurice Barrymore.
A decade later, Sweet acted with Barrymore's son Lionel in a D. W. Griffith-directed film. In 1909, she started work at Biograph Studios under contract to director D. W. Griffith. By 1910, she had become a rival to Mary Pickford, who had also started for Griffith the year before.
Sweet was known for her energetic, independent roles, at variance with the 'ideal' Griffith type of vulnerable, often fragile, femininity. After many starring roles, her first real landmark film was the 1911 Griffith thriller The Lonedale Operator. In 1913, she starred in Griffith's first feature-length film Judith of Bethulia. In 1914, Sweet was initially cast by Griffith in the part of Elsie Stoneman in his epic The Birth of a Nation but the role was eventually given to rival actress Lillian Gish, who was Sweet's senior by three years. That same year Sweet parted ways with Griffith and joined Paramount (then Famous Players-Lasky) for the much higher pay that studio was able to afford.
Because the Biograph company refused to reveal the names of its actors, the British distributor M. P. Sales billed Sweet as Daphne Wayne.
Throughout the 1910s, Sweet continued her career appearing in a number of highly prominent roles in films and remained a publicly popular leading lady. She often starred in vehicles by Cecil B. DeMille and Marshall Neilan, and she was recognised by leading film critics of the time to be one of the foremost actresses of the entire silent era. It was during her time working with Neilan that the two began a publicized affair, which brought on his divorce from former actress Gertrude Bambrick. Sweet and Neilan married in 1922. The union ended in 1929 with Sweet charging that Neilan was a persistent adulterer.
During the early 1920s Sweet's career continued to prosper, and she starred in the first film version of Anna Christie in 1923. The film is also notable as being the first Eugene O'Neill play to be made into a motion picture. In successive years, she starred in Tess of the d'Urbervilles and The Sporting Venus, both directed by Neilan. Sweet soon began a new career phase as one of the newly formed MGM studio's biggest stars.
Sweet's career faltered with the advent of talkies. Sweet made just three talking pictures, including her critically lauded performance in 1930's Show Girl in Hollywood, before retiring from the screen that same year and marrying stage actor Raymond Hackett in 1935. The marriage lasted until Hackett's death in 1958.
Sweet spent the remainder of her performing career in radio and in secondary Broadway stage roles. Eventually, her career in both of these fields petered out, and she began working in a Los Angeles department store. In the late 1960s, her acting legacy was resurrected when film scholars invited her to Europe to receive recognition for her work.
In 1975, she was honored with the George Eastman Award for distinguished contribution to the art of film.
In 1980, Sweet was one of the many featured surviving silent film stars interviewed at length in Kevin Brownlow's documentary about the silent film era Hollywood.
Sweet is the subject of a 1982 documentary by Anthony Slide, titled "Portrait of Blanche Sweet," in which she talks of her life and her career. On September 24, 1984, a tribute to Sweet was held at the Museum of Modern Art in New York City. Sweet introduced her 1925 film The Sporting Venus.
Sweet died of a stroke in New York City on September 6, 1986. Her ashes were later scattered within the Brooklyn Botanical Gardens.
blanche sweet
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Community Sector Welcome Legislative Ban on Gag Clauses
The community services sector has welcomed the Commonwealth Government's announcement this morning of its intention to introduce a legislative ban on 'gag clauses' which attempt to undermine the independence and legitimacy of civil society advocacy, says the WA Council of Social Service.
"The independence and sovereignty of community service organisations is vital to the health of our democracy and civil society," says the Council CEO, Irina Cattalini.
"Legislative protection of the right to advocate freely is welcome; however, the importance of this right also needs to be embedded as part of our culture and understanding across all levels of the community and Government."
The Council notes that this issue has been raised by the community sector throughout the consultation on the new Australian Charities and Not-for-Profits Commission (ACNC), and was recommended by the Western Australian Greens Senator Rachel Siewert in her minority report on the ACNC Bills.
The proposed legislation will prohibit the use of gag clauses in Commonwealth funding contracts with the not-for-profit sector.
To ensure service providers are free to advocate for the best interests of the disadvantaged and vulnerable, the Council is also calling for the Government to prevent other burdensome processes that act in similar ways to 'gag clauses' such as requirements for organisations to seek pre-approval before releasing statements or reports.
The Commonwealth proposal follows in stark contrast to what has been reportedly appearing in Queensland funding contracts, as a direct challenge to the vital role that independent civil society organisations play in a healthy democracy:
"Where the organisation receives 50% or more of its total funding from … Queensland Government agencies, the Organisation must not advocate for State or Federal legislative change. The Organisation must also not include links on their website to other organisations' websites that advocate for State or Federal legislative change."
"It is concerning that the Queensland clause fundamentally misunderstands the value of civil society organisations – which is far greater than their monetary value," says Ms Cattalini.
"The value of community service organisations comes from their mission, from their voluntary commitment to the cause of contributing to the social wellbeing of their communities, to connecting people and enhancing social capital. Governments can never buy or own that value, regardless of how much funding they contribute to the good work of civil society," concludes Ms Cattalini.
Irina Cattalini, CEO 042 422 438 or (08) 9420 7222


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Research Warns Of Early False Negative In COVID Tests
by Paromita Datta published on - July 13, 2020
Early testing for COVID-19 may not show accurate results. Research by John Hopkins School of Medicine, published in the Annals of Internal Medicine found that early testing for the presence of SARS-CoV-2 is likely to give us a false negative even when the patient may be infected. SARS-COV-2 is the virus that causes COVID-19. [1]
COVID testing must be rigorous and multi-faceted for high-risk individuals. Photo Credit: Shutterstock
The researchers focused on the reverse transcriptase polymerase chain reaction (RT-PCR), the test most commonly used for high-risk people. Previous use of this test has shown that can produce false negative in early stages, particularly when the tested sample does not contain sufficient presence of the virus. The researchers analyzed 7 previously published studies on RT-PCR performance.
In all, the studies covered 1,330 respiratory swab samples from outpatients and inpatients with SARS-CoV-2 infection. They found that during the first four days of the infection, before the onset of the symptoms, the probability of a false-negative result decreases from 100 percent (day 1) to 67 percent (day 4). The probability further keeps dropping as the infection progresses till day 9 when it again starts climbing.
The results indicate that false negative for the SARS-COV-2 virus is high during the first four days of the infection. This means that we must re-evaluate early test result interpretations and monitoring among high-risk individuals. RT-PCR cannot be the sole testing mechanism where clinical suspicion is high, concluded the researchers.
For the latest updates on COVID-19, please visit the CDC or the NIH. [2] [3]
Last updated - July 13, 2020.
Paromita Datta covers the latest health and wellness trends for Organic Facts. An ex-journalist who specialized in health and entertainment news, Paromita was responsible for managing a health supplement for The New Indian Express, a leading national daily in India. She has completed her post-graduation in Business Administration from the University of Rajasthan and her diploma in journalism from YMCA, Delhi. She has completed an e-course, Introduction to Food and Health, from Stanford University, US.