text:
\section{Introduction}
\setcounter{equation}{0}

One of the most puzzling aspects of the Standard Model (SM) is the absence of CP violation in strong interactions, as measured by the topological angle
\begin{equation}
\bar\theta=\theta_{\rm QCD}-\theta_{\rm F} \, ,
\end{equation}
where $\theta_{\rm QCD}$ denotes the coefficient of $\alpha_s^2/ 8 \pi \, G\tilde G$ and $\theta_{\rm F} = \arg \det M_u M_d$.  From the contribution to the neutron electric dipole moment one finds
$\overline{\theta} <10^{-10}$ from the 95\% CL bound $|d_n| \le 3.6 \times 10^{-26} e \, {\rm cm}$~\cite{nEDM}, although generically one would expect $\overline{\theta}$ to be of the order of the observed CP violating phase in weak interactions, i.e. $\overline{\theta} \sim {\cal O}(1)$. Indeed it is the presence of the large CKM phase that prevents to forbid $\overline{\theta}$ by imposing CP as a fundamental symmetry.

The most popular explanation for this puzzle is the Peccei-Quinn mechanism~\cite{Peccei:1977ur,Peccei:1977hh}, which has the axion as a low-energy remnant~\cite{WW1, WW2}. This prediction makes axion models testable in upcoming experiments, which search for the axion with haloscopes like ADMX~\cite{ADMXfuture}, helioscopes like IAXO~\cite{IAXO1,IAXO2} or even precision flavor experiments like NA62~\cite{NA621,NA622, Japs, Axiflavon, Astrophobic}.

An alternative explanation for the smallness of $\overline{\theta}$ is provided by the Nelson-Barr mechanism \cite{Nelson1,Barr1,Nelson2,Barr2}, where CP is broken spontaneously at high scales. The original Lagrangian is CP invariant and hence $\theta_{\rm QCD}$ is zero. CP is broken spontaneously by large vacuum expectation values (VEVs), and CP violation is mediated to the low-energy Lagrangian only via mixing with heavy vectorlike quarks. If the Lagrangians respects two simple conditions (the so-called Barr-criteria), the resulting SM quark mass matrices are complex but have a real determinant, thus providing the CKM phase but rendering $\theta_F =0$ at tree-level. Finite and calculable contributions to $\theta_F$ arise at loop-level, but are generically suppressed by small Yukawa couplings and/or small mass ratios~\cite{Nelson1, Nelson2, Barr2, Vecchi}. The general Nelson-Barr framework has been realized in a minimal setup in Refs.~\cite{Branco1, Branco2}, and recently been combined with the idea of cosmological relaxation~\cite{Relaxion} in Ref.~\cite{Diego}.

In contrast to axion models, in Nelson-Barr scenarios the effective theory below the scale $V_{\rm CP}$ of spontaneous CP breaking is just the SM. This scale is in general required to be very large  in order to  suppress loop corrections to $\overline{\theta}$ that are proportional to $v^2/V_{\rm CP}^2$~\cite{Branco1, Branco2}. Since $V_{\rm CP}$ sets the scale of the heavy vectorlike fermions, they are too heavy to be observed in the near future. Therefore the main drawback of Nelson-Barr models is the {\it lack of predictivity}, in addition to theoretical shortcomings discussed in e.g. Ref.~\cite{Dine}.

In this paper, we address the issue of predictivity by embedding the Nelson-Barr mechanism into an E$_6$ Grand-Unified framework. This allows to connect the phases in the neutrino sector to the CKM phase, and  in particular to predict the Dirac CP phase that will be measured in the near future. Indeed the heavy vectorlike quarks needed in the Nelson-Barr setup naturally find their theoretical motivation in Grand-Unified theories (GUTs), as proposed already in Ref.~\cite{Barr2}. Among the possible simple GUT groups, $E_6$ \cite{Gursey:1975ki,Shafi:1978gg,Stech:1980fn,Barbieri1980369,  Borut3}  is ideally suited for the implementation of the Nelson-Barr mechanism, because the fundamental representation of $E_6$ contains in addition to chiral SM fermions a vectorlike pair of right-handed (RH) down quarks, besides a vectorlike pair of left-handed (LH) leptons and two RH neutrinos. Spontaneous CP breaking will induce a mixing between these vectorlike fields with the chiral fermions, and complex phases will enter low-energy quark, charged lepton and neutrino masses in a correlated manner. Definite predictions in the neutrino sector are then possible because of the very restricted form of the fundamental Yukawa sector, imposed by the E$_6$ GUT structure together with spontaneous CP violation. While in usual GUT scenarios the unification of Yukawa couplings is often problematic for light fermion generations, it turns out that the mixing with the heavy vector-like fields allows to cure these problems and to obtain a perfect fit to the full SM fermion sector.

Therefore in our model the Nelson-Barr mechanism becomes predictive in the neutrino sector because of the E$_6$ GUT structure, which in turn is  phenomenologically viable because of the mixing with the heavy fermions needed to generate the CKM phase.

The rest of this paper is organized as follows: in Section 2 we present the general setup of the model and derive analytical expressions for the low-energy quark, charged lepton and neutrino masses. In Section 3 we perform a numerical fit to fermion masses and mixings and demonstrate that a perfect fit can be obtained for all observables with definite predictions for the neutrino sector. In Section 4 we discuss loop corrections to $\overline{\theta}$, which will constrain the overall scale of spontaneous CP breaking that is left undetermined by the fit. We finally summarize and conclude in Section 5.

\section{An $E_6$ Nelson-Barr Model}

We embed the SM fermions in three E$_6$ fundamentals ${\bf 27}_i$ that decompose under SU(5) as
\begin{align}
{\bf 27} = ({\bf 10} + {\bf \overline{5}} + {\bf 1})_{\bf 16} + ({\bf 5} + {\bf \overline{5} })_{\bf 10} + {\bf 1}_{\bf 1} \, ,
\label{eq:27}
\end{align}
where the subscripts denote the SO(10) decomposition. Thus for each generation of chiral SM fermions residing in the ${\bf 10_{16}}$ and ${\bf \overline{5}_{16}}$, there is a vectorlike pair of RH down-quarks and LH lepton doublets contained in  $({\bf 5 + \overline{5})_{10}}$ and two SM singlets ${\bf 1_{16}}$ and ${\bf 1_1}$.

The vectorlike $({\bf 5 + \overline{5})_{10}}$  pair will get a large mass  at an intermediate scale $M \sim 10^9 {\, \rm GeV}$, and a mass term of similar order that mixes the heavy fermions in the ${\bf \overline{5}_{10}}$ with the chiral RH down quark and LH charged leptons in the ${\bf \overline{5}_{16}}$. According to the Nelson-Barr mechanism, this mixing is the only way how a complex phase enters  the low-energy effective (down) Yukawa couplings, which are of the form $y_d \sim y \cdot a$, where $y$ is a real and $a$ a hermitian $3 \times 3$ matrix. Indeed this matrix has a physical phase while the determinant stays real.

The SM singlet ${\bf 1_1}$ will acquire a mass at the GUT scale $M_{\rm GUT} \sim  10^{16} {\, \rm GeV}$ from $E_6$ breaking, while the other singlet ${\bf 1_{16}}$ gets a mass at an intermediate scale $M_\nu \sim  10^{11} {\, \rm GeV}$ and induces neutrino masses via the Type-I seesaw mechanism.

All fermion mass terms and the breaking of $E_6$ to the SM gauge group arise from adding scalars in ${\bf 27}_H$, ${\bf 351^\prime}_H$ and ${\bf 78}_H$ that develop large VEVs. The latter field is only responsible for breaking SO(10) at $M_{\rm GUT}$, while the other two fields couple to fermions according to the $E_6$-invariant Yukawa Lagrangian
\begin{align}
{\cal L}_{\rm yuk} & = {\bf 27}_ i {\bf 27}_j \left( Y_{27, ij} {\bf 27}_H + Y_{351^\prime,  ij} {\bf 351^\prime}_H \right) +{\rm h.c.}
\label{L1}
\end{align}
We impose CP as a symmetry of the Lagrangian, so that the couplings $Y_{27}$ and $Y_{351^\prime}$ can be taken as real and symmetric $3 \times 3$ matrices. Without loss of generality we can choose the flavor basis such that $Y_{351^\prime}$ is diagonal. The E$_6$ structure therefore drastically reduces the number of flavor sector parameters, so that there are just 3+6 real parameters responsible for generating masses and mixings for quarks, charged leptons and neutrinos. While in usual GUT models such a unified structure often prevents to correctly account for all mass hierarchies, it turns out that in our setup the additional mixing in the RH down and LH charged lepton sector allows for an excellent fit to the full set of SM masses and mixings, as we are going to see in the next section.

We do not spell out the scalar potential, which is simply assumed to generate the appropriate VEVs  and make all physical scalars except the SM Higgs ultra-heavy, around the scale $M_\nu$ or $M_{\rm GUT}$. Because of this largely model-dependent scalar sector we will not study gauge coupling unification in detail, but simply assume that there are suitable threshold correction at $M$ and $M_\nu$ that lead to unification around $M_{\rm GUT}$ (it might be necessary to embed our framework into a supersymmetric setup for this purpose). This approach is justified mainly by phenomenology, since our model makes definite predictions for the neutrino sector that can be tested in the near future.

According to this bottom-up spirit, we first allow only SM singlets $s$ and doublets $h,h^c$ in the ${\bf 27}_H$, ${\bf 351^\prime}_H$ and ${\bf 78}_H$ to take VEVs, where the singlet VEVs are large, i.e ${\cal O} (M_{\rm GUT})$, ${\cal O} (M_\nu)$ or ${\cal O} (M)$, and the SU(2)$_L$ breaking VEVs are at most of the order of the electroweak scale. The complete list of fields with the SM quantum numbers of $s,h,h^c$ contained in the ${\bf 27}_H$, the ${\bf 78}_H$ and ${\bf 351^\prime}_H$ can be found in the Appendix. A second requirement on the scalar VEVs comes from imposing the so-called Barr criteria, which ensure that the low-energy quark mass matrices have real determinants at tree-level. With the shorthand notation for the fermions in Eq.~\eqref{eq:27}, $t = {\bf 10}_{\bf 16}, \overline{f} = {\bf \overline{5}}_{\bf 16}, \overline{F} ={\bf \overline{5}}_{\bf 10}, F = {\bf 5}_{\bf 10}$, the Barr criteria require that
\begin{itemize}
\item $i$) No SU(2) breaking mass terms for $t - \overline{F}$ are present
\item  $ii$) Only mass terms for  $\overline{f} - F$ are  complex
\end{itemize}
If these criteria are fulfilled, one can easily check that the resulting down-quark mass matrix has a real determinant
, but has entries  that are in general complex
 and thus can provide the CKM phase. Decomposing the Lagrangian in Eq.~\eqref{L1} under SU(5), one can see from criterion $i$) that the VEVs of the fields $h^c_{\bf 27,16 , \overline{5}}, h^c_{\bf 351, 144, \overline{45}},  h^c_{\bf 351, 144, \overline{5}}$ have to vanish (the subscripts denote the quantum numbers under E$_6$, SO(10) and SU(5), see Appendix for details). Criterion $ii$) implies that only the singlet VEVs $s_{\bf 27, 16, 1} , s_{\bf 351, 144, 24}, $ are complex.

 Apart from imposing these conditions on the VEVs, which have to be fulfilled to high degree in order to solve the strong CP problem,  we set some electroweak VEVs to zero that merely lead to sub-leading corrections or can be absorbed into other VEVs. Moreover, for simplicity we also assume that the singlet VEVs giving rise only to neutrino masses are real, although they are not directly constrained by the Barr criteria. As we will discuss below, a complex phase in those VEVs would only affect the Majorana phases, not the Dirac CP phase. We therefore assume the following VEVs in the scalar sector:
\begin{align}
\langle h_{\bf 27,10, 5} \rangle & = v_{u1} \, , & \langle h_{\bf 351, 10,5}  \rangle & = v_{u2} \, , & \langle h^c_{\bf 27, 10, \overline{5}} \rangle & = v_{d1} \, , & \langle h^c_{ \bf 351, 10, \overline{5}} \rangle & = v_{d2} \, ,  \nonumber \\
\langle s_{\bf 27, 16, 1} \rangle & \equiv V^c_{10} \, , &  \langle s_{\bf 351, 144, 24} \rangle & \equiv V^c_{5} \, , &
\langle s_{\bf 27, 1, 1} \rangle & \equiv V_{6}   \, , & \langle s_{\bf 351, 54, 24} \rangle & \equiv V_{5}   \, , \nonumber \\
\langle s_{\bf 351, \overline{126}, 1} \rangle & \equiv V_{10}/2  \, , & \langle s_{\bf 351, 1,1} \rangle & \equiv \tilde{V}_{6}/2 \, , & \langle s_{\bf 351, \overline{16}, 1}  \rangle & \equiv V_{10}^\prime \, , & \langle s_{\bf 78, 45, 24}  \rangle & \equiv \tilde{V}_{5} \, ,
\label{vevdef}
\end{align}
where all VEVs are real and positive except $V_{10}^c, V_5^c$, of which at least one is complex. Here the subscripts $6,5,10$ denotes the breaking of E$_6$, SU(5) and SO(10), respectively. Apart from the electroweak VEVs, which are all of the order of the weak scale $v = 174 {\, \rm GeV}$, there are three heavy scales $M$, $M_\nu$ and $M_{\rm GUT}$, which set the order of magnitude of the singlet VEVs as
\begin{gather}
 V_6 \sim V_5  \sim  |V_5^c| \sim  |V_{10}^c| \equiv M \sim  10^{9} {\, \rm GeV} \, ,  \nonumber \\
V_{10}^\prime \sim V_{10}  \equiv M_\nu \sim 10^{11} {\, \rm GeV} \, , \nonumber \\
\tilde{V}_{6} \sim \tilde{V}_5 \equiv M_{\rm GUT} \sim  10^{16} {\, \rm GeV} \, .
\label{singletscales}
\end{gather}
The VEVs determine the breaking pattern of E$_6$ to the SM and set the scale of heavy gauge boson and fermion masses. At $M_{\rm GUT}$ the VEVs  $\tilde{V}_{6}$ and  $\tilde{V}_5$ break $E_6$ to $G_{\rm SM} \times $U(1)$_5$, while the residual U(1)$_5$ factor is broken at $M_\nu$ by $V_{10}$ and $V_{10}^\prime$.  Via the Yukawa couplings in Eq.~\eqref{L1} the VEVs  in Eq.~\eqref{vevdef} generate all fermion masses, which we parametrize as
\begin{align}
\left( m_{10} \right)_{ij}  & =  Y_{27, ij} v_{u1} + Y_{351^\prime, ij}   v_{u2}  \, , & \left( m_5 \right)_{ij}  & =  Y_{27, ij} v_{d1} + Y_{351^\prime, ij}  v_{d2}    \, ,  \nonumber \\
\left( M_{fF} \right)_{ij} & =Y_{27, ij} V_{10}^c + Y_{351^\prime, ij}  V_{5}^c  \, , &
  \left( M_{FF} \right)_{ij}  & =Y_{27, ij} V_6 + Y_{351^\prime, ij}  V_5    \, , \end{align}
  and
  \begin{align}
  \left( M_{NN } \right)_{ij}  & =  Y_{351^\prime, ij}  V_{10}    \, ,  &     \left( M_{N^\prime N^\prime} \right)_{ij}  & = Y_{351^\prime, ij} \tilde{V}_6 & \left( M_{NN^\prime} \right)_{ij}  & =  Y_{351^\prime, ij}  V_{10}^\prime   \, .
 \label{massdef}
\end{align}
Note that all mass matrices are real and symmetric except $M_{fF}$. Neglecting Clebsch-Gordon coefficients, the fermion masses can be written in SU(5) notation as
\begin{align} \label{eq:fermionmasses}
{\cal L}_{\rm mass} & = t_i t_j (m_{10})_{ij}  + t_i \overline{f}_{j}  (m_5)_{ij} \nonumber\\
&  + \overline{f}_{i} N_{j} (m_{10})_{ij}    + \overline{F}_{i} N^{\prime}_{j} (m_{10})_{ij} + F_{i} N^{ \prime}_{j} (m_5)_{ij}  \nonumber\\
& + \overline{f}_{i} F_{j} (M_{fF})_{ij}  + \overline{F}_{i} F_{j} (M_{FF})_{ij}  \nonumber\\
&  + \frac{1}{2} N^{ }_{i} N^{ }_{j} (M_{N N})_{ij}  +  \frac{1}{2} N^{ \prime}_{i} N^{ \prime}_{j} (M_{N^\prime N^\prime})_{ij} +  \frac{1}{2} N_{i} N^{ \prime}_{j} (M_{NN^\prime})_{ij}   +{\rm h.c.},
\end{align}
where we have introduced the shorthand $N = {\bf 1_{16}}, N^\prime = {\bf 1_{1}}$.
The first and third line generate masses for quarks and charged leptons, while the second and fourth line are responsible for neutrino masses. The first two lines comprise weak scale SU(2) breaking masses, while the last two lines are heavy mass terms for vector-like fields from the singlet VEVs in Eq.~\eqref{singletscales}. In particular the heavy RH down quarks and LH lepton doublets get a mass at $M$, while the heavy RH neutrinos $N^\prime$ and $N$ get a mass at $M_{\rm GUT}$ and $M_\nu$, respectively. Together with the scalars at $M_\nu$, we have thus fixed the mass scales of all heavy fields (apart from the  additional hierarchies for heavy fermions from hierarchical Yukawa couplings), which we summarize in Fig.~\ref{scales}.
\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.3]{./scales.pdf}
\caption{\label{scales} Sketch of heavy particle scales, see text for details.}
\end{center}
\end{figure}

We will now first neglect the weak scale VEVs and diagonalize the heavy sector given by the last two lines above. In this way we can identify the linear combination of $\overline{f}$ and $\overline{F}$ that remains light and determine the SM quark and charged lepton masses. Similarly we can integrate out the heavy neutrino mass eigenstates to  obtain light neutrino masses.
\subsection{Quark and Charged Lepton Sector}
We first derive the light mass matrices in SU(5) language and include Clebsch-Gordon coefficients later on. We begin by rewriting $\overline{f}_i,\overline{F}_i$ in terms of light fields $\overline{f}_{Li}$ and heavy fields $\overline{F}_{Hi}$ (that get a mass with $F_i$) with the ansatz
\begin{align}
\overline{f} & = a_{f} \cdot \overline{f}_L + A_{f} \cdot \overline{F}_H \, , & \overline{F} & = a_{F} \cdot \overline{f}_L + A_{F} \cdot \overline{F}_H \, ,
\end{align}
with some $3 \times 3$ matrices $a_{f}, A_{f}, a_{F}, A_{F}$. Requiring canonically normalized kinetic terms  gives three conditions
\begin{align}
a_{f}^\dagger a_{f} + a^\dagger_{F} a_{F} & = 1_3 \, , & A_{f}^\dagger A_{f} + A^{\dagger }_{F} A_{F}  & = 1_3 \, , & a_{f}^\dagger A_{f} + a_{F}^\dagger A_{F} & = 0 \, ,
\end{align}
and imposing that the light field $ \overline{f}_{L}$ has no mass term with $F$ yields a fourth condition
\begin{align}
a_{f}^T M_{fF} + a_{F}^T M_{FF} = 0 \, .
\end{align}
One can now solve these four equations, but since we are only interested in light fields we need only $a_f$ and $a_F$, which are given by:
\begin{align}
a_f & = \left[ 1_3 + Z^\dagger Z \right]^{-1/2} \, , & a_F & = - Z \cdot a_f \, , & Z & = \left[ M_{fF} (M_{FF})^{-1} \right]^T  \, .
\end{align}
The quark Lagrangian in terms of light fields $ \overline{f}_L$ is
\begin{align}
{\cal L} & = t_{i} t_{j} (m_{10})_{ij} + t_{i} \overline{f}_{Lj}  (m_5^{\rm eff})_{ij}  + \cdots \end{align}
with
\begin{align}
m_5^{\rm eff}  & = m_5 \cdot a_f \,  .
\end{align}
Note that while $m_{10}$ and $m_5$ are real symmetric matrices, $a_f$ is hermitian and therefore carries a complex phase into the light Yukawa matrix $m_5^{\rm eff}$ whose determinant is nevertheless real.

Upon including Clebsch-Gordon coefficients, quark and charged lepton masses $M_i$ are finally given by
\begin{align}  \label{eq:quarkandleptonmasses}
M_u & = m_u \,, & M_d & = m_d \cdot a_d \,, & M_e & = a_e^T \cdot m_e \,,
\end{align}
with the real symmetric matrices $m_i$
\begin{align}
m_u & = H r_{\beta 1} + F r_{\beta 2} \, , \\
m_d & = H + F \, ,
\\
m_e & = H - 3  F \, ,
\end{align}
and the hermitian matrices $a_i$
\begin{align}
a_d & = \left[ 1 + Z_d^\dagger Z_d \right]^{-1/2} \, , & Z_d & = r_{10,6} \left( H + F r_{5,6} \right)^{-1} \left( H + F  c_{5,10} \right) \,  ,\\
a_e & = \left[ 1 + Z_e^\dagger Z_e \right]^{-1/2} \, , & Z_e & = r_{10,6} \left( H - \frac{3}{2} F r_{5,6} \right)^{-1} \left( H -   \frac{3 }{2 } F c_{5,10} \right) \, .
\end{align}
The masses depend on the two real symmetric matrices $H$ and $F$ (where we have chosen $F$ to be diagonal)
\begin{align}
H & \equiv Y_{27} v_{d1} \, , \\
F & \equiv Y_{351^\prime}  v_{d2}   \, ,
\end{align}
and five VEV ratios $r_{\beta 1}, r_{\beta 2}, r_{10,6}, r_{5,6}, c_{5,10}$
\begin{gather}
r_{\beta 1}  \equiv \frac{v_{u1}}{v_{d1}} \, ,  \qquad \qquad \qquad r_{\beta 2}  \equiv \frac{v_{u2} }{v_{d2}} \, , \nonumber \\
r_{10,6}  \equiv \frac{|V_{10}^c|}{V_{6}}  \, ,   \qquad \qquad  r_{5,6}  \equiv \frac{V_{5}}{V_{6}} \frac{v_{d1} }{v_{d2} }     \, ,   \qquad \qquad c_{5,10}  \equiv \frac{V_{5}^c}{V_{10}^c}   \frac{v_{d1} }{v_{d2}} \, .
\label{defratios}
\end{gather}
Since only the ratio $c_{5,10}$ is complex, the quark and charged lepton sectors depend in total on 6+3+5 = 14 real parameters and 1 complex phase. As we will see later, SM fermion masses and mixings can be reproduced if all ratios are ${\cal O}(1)$. \subsection{Neutrino Sector}
The heavy singlet mass terms are given by
\begin{align}
{\cal L}_{N,N^\prime} & =  \frac{1}{2} \left( N_i , N^{ \prime}_i \right) {\cal M}_{N,ij} \begin{pmatrix} N_j \\ N^{ \prime}_j
\end{pmatrix}  \, ,
\end{align}
with the heavy $6 \times 6$ neutrino mass matrix
\begin{align}
{\cal M}_{N,ij} = \begin{pmatrix} M_{N N, ij}  & M_{N N^\prime, ij} \\ M_{N N^\prime, ij} & M_{ N^\prime N^\prime, ij} \end{pmatrix} \, .
\end{align}
Note that the $3 \times 3$ sub-matrices defined in Eq.~(\ref{massdef}) are all real and proportional to $Y_{351^\prime}$ that we have chosen to be diagonal. Therefore ${\cal M}_{N,ij}$ is a $2 \times 2$ block matrix of diagonal (and real) $3 \times 3 $ matrices. In order to diagonalize it, we therefore need only to diagonalize the real symmetric $2 \times 2$ matrix ${\cal M}$ defined by
\begin{align}
{\cal M} = \begin{pmatrix}  V_{10} & V_{10}^\prime \\ V_{10}^\prime &  \tilde{V}_{6} \end{pmatrix} \, .
\end{align}
The eigenvalues of this matrix set the scale of light neutrino masses via the Type-I seesaw mechanism. Since we are taking strongly hierarchical VEVs $V_{10} \sim V_{10}^\prime \ll \tilde{V}_6$, we can neglect the off-diagonal entries and the seesaw contribution of $N^{ \prime}$, and integrate out $N$ using the couplings of the light neutrinos $\nu_L$ contained in $\overline{f}_L$
 \begin{align}
{\cal L} & =  \nu_L^T  a_e^T  \left( H r_{\beta1} - 3 F r_{\beta2} \right)  N    +{\rm h.c.}
\end{align}
Light Majorana neutrino masses $m_\nu$ defined as
$
{\cal L}_{\nu}  = - 1/2  \, m_{\nu, ij} \nu_{L,i} \nu_{L,j}  + {\rm h.c.} \, ,
$
are given by \begin{align} \label{eq:neutrinomassses}
m_\nu & \approx   r_{\epsilon}  \left[  a_e^T \cdot \left( H r_{\beta1} - 3 F r_{\beta2} \right)  \cdot F^{-1} \cdot \left( H r_{\beta1} - 3 F r_{\beta2} \right) \cdot  a_e \right] \, ,
\end{align}
where have introduced the VEV ratio
\begin{align}
r_{\epsilon} & \equiv \frac{v_{d2}  }{V_{10}} \lll 1 \, .
\end{align}
Here we are neglecting contributions from the other heavy neutrinos at $M_{\rm GUT}$ and the heavy mixing due to the presence of $V_{10}^\prime$, but we have checked that including these correction only amounts to tiny corrections to Eq.~\eqref{eq:neutrinomassses}, of the order of the naive scale suppression factor  $M_\nu/M_{\rm GUT} \sim 10^{-5}$. Therefore possible phases in $V_{10}^\prime$ and $\tilde{V}_6$ would not affect the light neutrino sector, while a possible phase in $V_{10}$ would only lead to an overall phase of the light neutrino mass matrix, and thus only affects Majorana phases, not the Dirac CP phase.

Counting parameters, we see that the neutrino sector depends on a single additional real VEV ratio  $r_{\epsilon}$ compared to the quark and charged lepton sector. Therefore we have in total 15 relevant real parameters + 1 phase to describe the measured 17 + 1 SM parameters: 9 quark and charged lepton masses, 2 neutrino mass differences, 6 mixing angles and 1 CKM phase.  This means that there are two predictions that make the fit of the parameters to experimental data non-trivial. Moreover the model makes definite predictions for yet unmeasured observables in the neutrino sector (Dirac phase, two Majorana phases, overall neutrino mass scale, effective scale for neutrinoless double beta decay) and is therefore testable. We discuss the fit and these predictions in the next section.

\section{Fit to Fermion Masses and Mixings}

\begin{small}
\begin{table} [t]
\centering
\begin{math}
\begin{array}{|c|c||c|c|}
\hline
 \multicolumn{4}{|c|}{\text{Fermion observables at the electroweak scale $\mu=M_Z$} }\\
\hline
 m_d(\text{MeV}) &2.75 \pm 0.29 	&\Delta_{12}(\text{eV$^2$})&(7.50 \pm 0.18)\times10^{-5} \\
 m_s(\text{MeV}) &54.3 \pm 2.9		&\Delta_{31}(\text{eV$^2$})&(2.52 \pm 0.04)\times
10^{-3}\\
 m_b(\text{GeV}) & 2.85 \pm 0.03				& \sin  \theta _{12}^q & 0.2254 \pm 0.0007 \\
 m_u(\text{MeV}) & 1.3 \pm 0.4				& \sin  \theta _{23}^q & 0.0421 \pm 0.0006 \\
 m_c(\text{GeV}) & 0.627 \pm 0.019 		& \sin  \theta _{13}^q & 0.0036 \pm 0.0001 \\
 m_t(\text{GeV}) &171.7\pm 1.5				& \sin ^2 \theta _{12}^l & 0.306\pm 0.012 \\
 m_e(\text{MeV}) &0.4866\pm 0.0005 		&\sin ^2 \theta _{23}^l&0.441 \pm 0.024  \\
 m_{\mu }(\text{MeV})&102.7\pm 0.1 		& \sin ^2\theta _{13}^l & 0.0217 \pm 0.0008 \\
 m_{\tau }(\text{GeV})&1.746\pm 0.002	&\delta_{\rm CKM}&1.21 \pm 0.05\\
\hline
\end{array}
\end{math}
\vspace{0.5cm}
\caption{SM input parameters at the electroweak scale, where quark and lepton masses and the quark mixing parameters are taken from Ref.~\cite{Antusch:2013jca}, and neutrino mixing parameters  from Ref.~\cite{Esteban:2016qun} for Normal Ordering (NO). As explained in the text, we use a $0.1 \%$ uncertainty for the charged lepton masses in the fitting procedure. To simplify the fitting procedure, we used for all observables the arithmetic average of the errors when not symmetric.
}
\label{tab:smmasses}
\end{table}
\end{small}

In order to verify whether the 17+1 fermion observables of the Standard Model (see Table~\ref{tab:smmasses} for our input) can be successfully reproduced in our model, we have performed a fit of the matrices $H, F$ and the six VEV ratios $r_{\beta 1} ,  r_{\beta 2},r_{10,6} , r_{5,6}, c_{5,10} , r_{\epsilon} $ using Eq.~(\ref{eq:quarkandleptonmasses}) and Eq.~(\ref{eq:neutrinomassses}), corresponding to 15 real parameters + 1 complex phase. The fit was done using the Metropolis-Hastings algorithm \cite{Metropolis53,Hastings70} following a top-down approach. The parameters were chosen randomly at $Q = 10^{16} {\, \rm GeV}$ and used as boundary conditions for the Yukawa RGEs, which were then solved numerically using REAP \cite{Antusch:2005gp}. Afterwards, the computed values of the observables at the electroweak scale $M_Z$ were compared with the experimental values (following earlier studies, we assume a $0.1 \%$ uncertainty for the charged lepton masses \cite{Dueck:2013gca,Meloni:2014rga}, because otherwise a numerical fit would be very challenging). The quality of a fit point is determined by
\begin{equation} \label{eq:chisquare}
    \chi^2 \equiv \sum_{i=1}^n \left(\frac{{\cal O}^{\rm exp}_i-{\cal O}^{\rm fit}_i}{\sigma^{\rm exp}_i}\right)^2 \, ,
\end{equation}
where ${\cal O}^{\rm exp}_i$ denotes the experimental value of the observable ${\cal O}_i$, $\sigma^{\rm exp}_i$ its experimental error and ${\cal O}^{\rm fit}_i$ the corresponding fit value.

\vspace{0.3cm}

\noindent Despite the overdetermination\footnote{There must be two relations involving just SM observables, however due to the highly non-trivial dependence on the fundamental parameters we were not able to find analytical expressions for these relations.} we find a perfect fit with $\chi^2/{\rm dof} \approx 0.9$ for NO in the neutrino sector, with corresponding model parameters at the GUT scale given by
\begin{gather}
    H=\left(
\begin{array}{ccc}
 -0.00814 & 0.0292  & -0.0894  \\
0.0292 & -0.217 & 2.49 \\
 -0.0894  & 2.49 &  -12.8 \\
\end{array}
\right) \, , \qquad
F=\left(
\begin{array}{ccc}
 -0.00248  & 0. & 0. \\
 0. & 0.0489  & 0. \\
 0. & 0. & 30.7 \\
\end{array}
\right) \notag \\ \nonumber \\
r_{\beta 1} = -1.28 \, ,  \quad r_{\beta 2}  = 2.26 \, , \quad  r_{10,6}  = 2.21 \, , \quad  r_{5,6}  = -0.433     \, ,  \nonumber \\
 c_{5,10}  = 2.20 \cdot e^{1.60 \, i } \, , \quad     r_{\epsilon}=  1.73  \cdot 10^{-10} \, ,
\end{gather}
and the fitted standard model fermion observables are summarized in Table~\ref{tab:fitresults}.
\begin{small}
\begin{table} [ht]
\centering
\begin{math}
\begin{array}{|c|c|c||c|c|c|}
\hline
 \multicolumn{6}{|c|}{\text{Fit result at the electroweak scale $\mu=M_Z$} }\\
\hline
 &  \text{fit} &  \text{pull} &   &  \text{fit} &  \text{pull} \\ \hline
 m_d(\text{MeV}) &3.44 & -2.4 	&\Delta_{12}(\text{eV$^2$})&7.39 \times 10^{-5} & 0.63 \\
 m_s(\text{MeV}) &50.4 & 1.4		&\Delta_{13}(\text{eV$^2$})&-0.76 \times
10^{-3} & -0.19\\
 m_b(\text{GeV}) & 2.85 & 0.27				& \sin  \theta _{12}^q & 0.225 & 0.56 \\
 m_u(\text{MeV}) & 1.32 & -0.08				& \sin  \theta _{23}^q & 0.0414 & 0.1 \\
 m_c(\text{GeV}) & 0.63 & -0.07 		& \sin  \theta _{13}^q & 0.0035& 1.1 \\
 m_t(\text{GeV}) &171.58 & 0.08				& \sin ^2 \theta _{12}^l & 0.302 & 0.37 \\
 m_e(\text{MeV}) &0.486& 0.15 		&\sin ^2 \theta _{23}^l&0.405 & 1.5  \\
 m_{\mu }(\text{MeV})&102.76 & -0.61 		& \sin ^2\theta _{13}^l & 0.022 & -0.26 \\
 m_{\tau }(\text{GeV})&1.746 & -0.04	&\delta_{\rm CKM}&1.13 & 1.5\\
\hline
\end{array}
\end{math}
\caption{Result of the fitting procedure, as described in the text. The pull of a fit value ${\cal O}^{\rm fit}_i$ is defined as $\text{pull}({\cal O}^{\rm fit}_i)=\left( {\cal O}^{\rm exp}_i-{\cal O}^{\rm fit}_i \right)/\sigma^{\rm exp}_i$, where $\sigma^{\rm exp}_i$ is the corresponding experimental error and ${\cal O}^{\rm exp}_i$ the experimental value as given in Table~\ref{tab:smmasses}. } \label{tab:fitresults}
\end{table}
\end{small}
Using the above fit parameters, we can also make predictions for the neutrino Dirac phase, Majorana phases and neutrino mass observables. Experiments that are sensitive to the absolute neutrino mass scale, like the KATRIN \cite{Osipowicz:2001sq},  MARE \cite{Monfardini:2005dk} , Project 8 \cite{Monreal:2009za},
or ECHo \cite{Blaum:2013pfu} experiments, measure the effective mass $m_\beta$ defined by
\begin{equation} \label{eq:mbeta}
m_\beta = \sqrt{\sum |U_{ei}|^2 \, m_i^2} \, .
\end{equation}\\
In contrast, cosmology probes the sum of neutrino masses $\Sigma = \sum m_i$ and neutrinoless double beta decay experiments, like, for example, the GERDA \cite{Agostini:2013mzu}, EXO-200 \cite{Albert:2014awa} or KamLAND-Zen \cite{Gando:2012zm} experiments, tests the ``effective Majorana mass"
\begin{equation} \label{eq:meff}
m_{\beta \beta} = \left| \sum U_{ei}^2 \, m_i \right|  \, .
\end{equation}
To give an estimate for the robustness of these predictions in our model, we  numerically considered perturbations around the best fit point that reproduce the standard model fermion observables with $\chi^2/{\rm dof} \lesssim 10$. Our predictions and the resulting ranges for the above mass observables and Dirac and Majorana phases are summarized in Table~\ref{tab:predictionsandboundsneutrinomasses}. While the mass observables are all far below current and future sensitivity, we obtain a quite narrow range for the Dirac phase $\delta \in \left[ 154, 157 \right]^\circ$, which might be verified or excluded with upcoming data coming from neutrino oscillations, for example at Hyper-Kamiokande~\cite{HK2} or DUNE~\cite{Dune}.
\begin{table}[]
\centering
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
                       & $m_\beta$ {[}meV{]} & $\Sigma$ {[}meV{]} & $m_{\beta \beta}$ {[}meV{]} &$ \delta$ {[}$ ^\circ ${]}& $\varphi_1$ {[}$^\circ${]} & $\varphi_2$ {[}$^\circ${]} \\ \hline & & & & & & \\[-1em]
Prediction &  $8.8 \pm 0.5   $  &   $ 59 \pm 3  $        &   $ 1.8 \pm 0.1 $       & $157 \pm 3 $  & $187 \pm 4$  &  $159 \pm 5 $      \\ \hline
Current bound  & $\lesssim 2000 $~\cite{Patrignani:2016xqp}      &$\lesssim 230$~\cite{Patrignani:2016xqp, Ade:2015xua}    & $200$~\cite{Capozzi:2017ipn, KamLAND-Zen:2016pfg}     & - &  - &  - \\ \hline
\end{tabular}
\caption{Predicted values and current bounds for the neutrino observables. The current bounds were taken from Ref. \cite{Pas:2015eia}. As explained in the text, the ranges shown here correspond to perturbations of the best fit point with $\chi^2/{\rm dof} \lesssim 10$.}
\label{tab:predictionsandboundsneutrinomasses}
\end{table}

Finally we comment on the remaining free parameters that are left undetermined by the fit to masses and and mixings. From 12 VEVs (see Eq.~\eqref{vevdef}) six are determined by the fit and one by the electroweak scale ($v^2 = v_{u1}^2 + v_{d1}^2 + v_{u2}^2 + v_{d2}^2$). From the remaining 5 VEVs, $V_{10}^\prime$ does not affect the neutrino sector given the hierarchy $V_{10}^\prime \sim V_{10} \ll \tilde{V}_6 $, so for simplicity we set $V_{10}^\prime = V_{10} = M_\nu = v_{d2}/r_\epsilon \sim 10^{11} {\, \rm GeV}$ without any impact on the spectrum.  We are then left with four VEVs that are free parameters, which we take as $v_{d1}, |V^c_{10}|, \tilde{V}_{6}, \tilde{V}_{5} $. As the two latter VEVs control the mass of heavy gauge bosons, they are bounded from below by proton decay constraints, and we take $\tilde{V}_{6} = \tilde{V}_{5} \equiv M_{\rm GUT} \sim 5 \cdot 10^{16} {\, \rm GeV}$. The VEV
$v_{d1}$ is mainly bounded by requiring perturbative Yukawa couplings and does not have a big impact on the spectrum, and for the sake of explicitness we fix  $v_{d1} = 70 {\, \rm GeV}$. The remaining scale $M$ is bounded from above by neutron EDM constraints, which require that the loop corrections to the effective $\overline{\theta}$ parameter remain sufficiently small. As we will discuss in the next section, these higher-loop corrections are sufficiently suppressed if $M \sim 10^9 {\, \rm GeV}$.

\section{Loop Contributions to $\overline{\theta}$}

In Nelson-Barr models $\overline{\theta}$ vanishes at tree-level by construction, but is generated at loop-level due to higher order corrections to the effective Yukawa couplings. Therefore care has to be taken to ensure that such corrections are sufficiently small in order to have $\overline{\theta} < 10^{-10}$. The form of these (finite) corrections has already been discussed to large extent in the literature for the original Nelson model~\cite{Nelson2} and in more general setups~\cite{Vecchi}. It turns out that such corrections are in general suppressed by loop factors and small Yukawa couplings and/or small mass ratios. While the contributions suppressed by Yukawas are always negligibly small in Nelson-Barr type models where only the RH down quarks mix with heavy fields~\cite{Vecchi}, the contributions sensitive to UV physics are suppressed by ratios of the heavy RH down quark masses over heavy gauge boson or heavy scalar masses~\cite{Nelson2, Branco1}. Thus they can be made sufficiently small by lowering the mass scale of RH down quarks $M$, which in our setup is a free parameter. In this section we (conservatively) estimate the leading corrections involving heavy gauge bosons and scalars using a spurion analysis, showing that $M \sim 10^{9}$ is enough to render $\overline{\theta} \lesssim 10^{-10}$.

In this spirit we work with a simplified Lagrangian before going  to the light-heavy mass basis, cf. Eq.~\eqref{eq:fermionmasses}
\begin{align}
{\cal L} = q^T \lambda_u u \, h + q^T \lambda_d d \, \tilde{h} + d^T m_{dD} \overline{D} + d^T \kappa_{10} \overline{D} S_{10} + d^T \kappa_{5} \overline{D} S_{5} + D^T M_D \overline{D} + {\rm h.c.}
\end{align}
where we also included scalar couplings $\kappa_{10}, \kappa_5$ and all masses and couplings are real symmetric $3 \times 3$ matrices except $m_{dD}$ that is complex symmetric
\begin{align}
\lambda_u & = \frac{1}{v} \left( H r_{\beta 1} + F r_{\beta 2} \right) \, , &
\lambda_d & = \frac{1}{v} \left( H  + F   \right) \, , \nonumber \\
m_{dD} & = \frac{V_{10}^c}{v_{d1}} \left( H + F c_{5,10} \right) \, , &
M_{D} & = \frac{|V_{10}^c|}{v_{d1} r_{10,6}} \left( H + F r_{5,6} \right) \, , \nonumber \\
\kappa_{10} & = \frac{H}{v_{d1} \sqrt2} \, , & \kappa_{5} & = \frac{F}{v_{d2} \sqrt2} \, .
\end{align}
 We are now interested in loop corrections to the Yukawa couplings $\lambda_{u,d}$ that we write as
\begin{align}
\lambda_u^{\rm tot} & = \lambda_u + \Delta \lambda_{u} \, , & \lambda_d^{\rm tot} & = \lambda_d + \Delta \lambda_{d} \, .
\end{align}
The effective SM Yukawa couplings $y_{u,d}$ are given by (cf. Eq.~\eqref{eq:quarkandleptonmasses})
\begin{align}
y_u & = \lambda_u + \Delta \lambda_{u} = \lambda_u \left[1 + \lambda_u^{-1} \Delta \lambda_{u}  \right]\, , \nonumber \\
 y_d  & = \left( \lambda_d   +  \Delta \lambda_{d} \right) a_d =  \lambda_d a_d \left[ 1 + a_d^{-1} \lambda_d^{-1} \Delta \lambda_{d} a_d \right] \, .
\end{align}
Therefore the effective $\theta$ parameter is
\begin{align}
\overline{\theta} & = \arg \det y_u  y_d  =   { \rm Im} \,  {\rm tr} \log y_u  +  { \rm Im} \,  {\rm tr} \log y_d  \, , \nonumber \\
& =  { \rm Im} \,  {\rm tr} \log  \left[1 + \lambda_u^{-1} \Delta \lambda_{u}  \right] + { \rm Im} \,  {\rm tr} \log  \left[1 + a_{d}^{-1} \lambda_d^{-1} \Delta \lambda_{d} a_{d} \right] \, ,
\end{align}
where have used  that $\lambda_{u}, \lambda_{d}$ are real and $a_d$ is hermitian. Expanding the logarithms we finally get
\begin{align}
\overline{\theta} & =   \sum_n  \frac{1}{n}  \left[ { \rm Im} \,  {\rm tr}\left(  \lambda_u^{-1} \Delta \lambda_{u}  \right)^n +  { \rm Im} \,  {\rm tr}\left(  \lambda_d^{-1} \Delta \lambda_{d}  \right)^n  \right] =  { \rm Im} \,  {\rm tr}\left(  \lambda_u^{-1} \Delta \lambda_{u}  + \lambda_d^{-1} \Delta \lambda_{d}  \right) + \hdots
\end{align}
We can now estimate the corrections $\Delta  \lambda_{u,d}$ using a spurion analysis. Under unitary field redefinitions $f \to V_f f$ with $f= q,u,d,D,\overline{D}$,  the Lagrangian parameters transform as
\begin{align}
\lambda_u & \to V_q^T \lambda_u V_u \, , & \lambda_d & \to V_q^T \lambda_d V_d \, , \nonumber \\
m_{dD} & \to V_d^T m_{dD} V_{\overline{D}} \, , & M_{D} & \to V_D^T M_{D} V_{\overline{D}}  \, , \nonumber \\
\kappa_{10} & \to V_d^T \kappa_{10} V_{\overline{D}} \, , & \kappa_{5} & \to V_d^T \kappa_{5} V_{\overline{D}} \, , &
\end{align}
Since we can treat the masses $m_{dD}$ as insertions, the covariant expressions involving $m_{dD}$ and $M_D$ that will enter the contributions to $\Delta_{\lambda_u,d}$ can only be of the form
\begin{gather}
\xi_{\rm IR}  \equiv  (m_{dD})^* (M_D^{-1})^* (M_D^{-1})^T (m_{dD})^T = Z_d^\dagger Z_d\, , \nonumber \\
\xi_{\rm V}   \equiv m_{dD}^* m_{dD}^T/M_V^2 \, , \qquad \qquad \xi_{\rm S}   \equiv \kappa_i^*  m_{dD}^T \kappa_i^* m_{dD}^T/M_S^2 \, ,
\end{gather}
where $M_V, M_S$ are the heavy gauge boson and scalar masses. These expressions transform as
\begin{align}
\xi_{\rm IR,V,S} & \to V_q^\dagger \xi_{\rm IR,V,S} V_q \, ,
\end{align}
and are the only quantities that carry complex phases. The heaviest particle in the loop diagram then determines the form of $\xi$, i.e. diagrams with only Higgs scalars, the ``IR" contributions, will involve $\xi_{\rm IR}$, diagrams with heavy vectors $\xi_{\rm V}$ and diagrams with heavy scalars $\xi_{\rm S}$.

\subsection{IR Contributions}

For IR diagrams $\xi_{\rm IR} \sim {\cal O}(1)$, so one has to sum up all insertions leading effectively to a field redefinition $d \to a_d d$, and thus $\lambda_d \to \lambda_d a_d = y_d$ which is the SM down Yukawa coupling. The spurion analysis is then quite involved, since one has to take into account that the light quark propagators can involve hermitian functions of $y_u y_u^\dagger (y_d y_d^\dagger)^{-1}$ arising from the integration over loop momenta. In Ref.~\cite{Vecchi} it was shown that the leading contribution arises at three loop and is given by
\begin{align}
\Delta_{\rm IR} \overline{\theta} \sim \frac{1}{(4 \pi^2)^3} { \rm Im} \,  {\rm tr} \left[ f_1 y_d^\dagger y_u y_u^\dagger y_d f_2 y_d^\dagger y_d \right] \sim 10^{-16} \, ,
\end{align}
where the  functions $f_1 \ne f_2$ were taken to as ${\cal O}(1)$ hermitian matrices. Note that the strong suppression is due to the fact that there is no mixing with heavy fields in the up and the LH down sector.

\subsection{Gauge Contributions}
The most dangerous contributions involve the U(1)$_5$ gauge boson, since all heavy gauge fields live at $M_{\rm GUT}$. The spurion analysis is greatly simplified, because now the heavy gauge boson dominates the loop momentum integration, and thus strongly suppresses the contributions from propagators with non-trivial flavor structure. One can show that all one-loop contributions vanish, and that the leading contribution arises from two-diagrams like Fig.~\ref{2loopgauge} that involve additional Higgs loops.
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.9]{./2loopgauge.pdf}
\caption{\label{2loopgauge} Example of 2-loop diagram with heavy gauge fields.}
\end{center}
\end{figure}
An estimate gives
\begin{align}
\Delta_{\rm V} \overline{\theta} \sim \frac{ \log{M_f^2/M_V^2}}{(4 \pi^2)^2} { \rm Im} \,  {\rm tr} \left[ \lambda_d^{-1}g_{qq}  \lambda_u \lambda_u^\dagger \lambda_d \xi_{\rm V} g_{dd} \right]  \, ,
\end{align}
where $g_{qq} = g$ and $g_{dd} = -3 g$ are the couplings of the U(1)$_5$ gauge boson to quarks, $M_V$ is its mass and $M_f$ denotes the heaviest   of the heavy vectorlike down quarks. All numerical values depend only on $M$ (fixing $v_{d1} = 70 {\, \rm GeV}$). Taking $M = 10^{9} {\, \rm GeV}$ implies $M_V = 2 \cdot 10^{12} {\, \rm GeV}$ and $M_f = 10^9 {\, \rm GeV}$, and taking for simplicity the GUT value of the U(1)$_5$ gauge coupling $g \sim  \sqrt{4 \pi \alpha_{\rm GUT}} \sim \sqrt{4 \pi/24}  \approx 0.7$, one finds
\begin{align}
\Delta_{\rm V} \overline{\theta} \sim  3 \cdot 10^{-11} \, .
\end{align}
\subsection{Scalar Contributions}
Analogously,  all one loop diagrams with heavy scalars in the loop vanish, and the leading contribution comes from a 2-loop diagram involving a U(1)$_Y$ and scalar loop, shown in Fig.~\ref{2loopscalar}.
\begin{figure}[h]
\begin{center}
\includegraphics[scale=0.9]{./2loopscalar.pdf}
\caption{\label{2loopscalar} Example of 2-loop diagram with heavy scalar fields.}
\end{center}
\end{figure}
This gives
\begin{align}
\Delta_{\rm S} \overline{\theta} \sim \frac{ \log{M_f^2/M_S^2}}{(4 \pi^2)^2} { \rm Im} \,  {\rm tr} \left[ \lambda_d^{-1} g_{qq}^Y \lambda_d \xi_{\rm S} g_{dd}^Y \right]  \, ,
\end{align}
where $g_{qq}^Y = g_Y/6$ and $g_{dd}^Y = g_Y/3$. Note that this term is simply proportional to the imaginary part of the trace of $\xi_S$, which is in general not a hermitian matrix, and arises because we assume an ${\cal  O}(1)$ splitting between the masses of the scalar and pseudoscalar components of the complex fields $S_5$ and $S_{10}$. For degenerate $S_5$ and $S_{10}$, the $S_5$ contribution dominates since it has larger couplings to the heavy fermions, and for $M= 10^9 {\, \rm GeV}$, $M_S = M_\nu = 3 \cdot 10^{11} {\, \rm GeV}$ and $g_Y (10^9 {\, \rm GeV}) \sim 0.4$ one gets
\begin{align}
\Delta_{\rm S} \overline{\theta} \sim  4 \cdot 10^{-11} \, .
\end{align}

\section{Summary and Conclusions}

To summarize, we have shown that the Nelson-Barr mechanism can be naturally realized in the context of an $E_6$ GUT. The SM fermions are embedded in three generations of E$_6$ fundamentals together with the Nelson-Barr fields (vectorlike RH down quarks), a vectorlike pair of LH lepton doublets  and two RH neutrinos. All heavy mass terms arise from VEVs of scalar fields in E$_6$ representations, whose couplings to fermions are given by two $3 \times 3$ symmetric matrices. CP is imposed on the Lagrangian, and therefore all Yukawa couplings are real. CP is broken spontaneously by two scalar VEVs that mix the chiral SM fermions with the Nelson-Barr fields, through which CP violation is mediated to the low-energy theory. By integrating out the heavy down-quarks, lepton doublets and neutrinos, we have derived analytic formulas for all SM fermion mass matrices, including Majorana neutrino masses. The resulting SM quark mass matrices are real (up sector) and the product of a real and a hermitian matrix (down sector), thus implying that  $\overline{\theta}$ vanishes at tree-level.

Besides solving the strong CP problem with the Nelson-Barr mechanism, the main benefit of the GUT setup is the predictivity in the fermion sector. The fundamental Yukawa matrices contain just 9 parameters, which together with 6 real VEV ratios and a single complex phase determine the complete SM fermion sector including neutrinos (17 real observables + 1 CKM phase). Surprisingly, we nevertheless obtain a perfect fit with $\chi^2/{\rm dof} \approx 0.9$, implying that there are two relations among SM observables that hold to good precision, but unfortunately we were not able to derive them in closed form due to the complexity of the analytical expressions. Since all low-energy parameters of the model are fixed, we obtain definite predictions for the neutrino sector that makes this model testable in the near future, as shown in Table~\ref{tab:predictionsandboundsneutrinomasses}. Particularly interesting is the prediction of the Dirac CP phase $\delta_{\rm CP} = 157 \pm 3  ^\circ $, which is directly correlated with the CKM phase, and will be verified or excluded by future experiments like  Hyper-Kamiokande~\cite{HK2} or DUNE~\cite{Dune}.

The fit to the fermion sector determines the absolute mass scales only in the neutrino sector, fixing the mass of RH neutrinos at about $M_\nu \sim 10^{11} {\, \rm GeV}$ (there is another SM singlet around the GUT scale $M_{\rm GUT} \sim 5 \cdot 10^{16} {\, \rm GeV}$). The overall mass scale in the heavy RH down and LH lepton sector $M$ is left undetermined, but bounded from above to keep loop corrections to $\overline{\theta}$ sufficiently small. The leading loop contributions from diagrams involving heavy gauge bosons and heavy scalars are suppressed by mass ratios $M^2/M_{V,S}^2$, and we have (conservatively) estimated that $M = 10^9 {\, \rm GeV}$ is enough to render $\overline{\theta} < 10^{-10}$. This essentially fixes all heavy mass scales in our model, as sketched in Fig.~\ref{scales}.

\section*{Acknowledgements}
We thank L.~di Luzio, U.~Nierste and L.~Vecchi for helpful discussions, and L.~di Luzio for useful comments on the manuscript. J.S. and P.T. acknowledge support from the DFG-funded doctoral school KSETA. The Feynman diagrams were drawn using Ti$k$Z-Feynman~\cite{Ellis:2016jkw}.

redpajama_set_name: RedPajamaArXiv


Learn More – opens in a new window or tab International shipping and import charges paid to Pitney Bowes Inc. Report item – opens in a new window or tab. Sign in to check out Check out as guest. Free shipping on all eligible items from dalbanicorporation, when you use the cart to make your purchase. This seller offers shipping discounts when you purchase two or more eligible items using the cart.
If you'd like to get d1854 additional items you've selected to qualify for this offer, close this window and add these items to your cart. This item will ship to United Statesbut the seller has not specified shipping options. The item may have some signs of cosmetic wear, but is fully operational and functions as intended. Be the first to write a review.
Any international shipping and import charges are paid in part to Pitney Bowes Inc. If you use choose PayPal as a payment option, your billing and shipping address must be identical.
Seller information dalbanicorporation This amount trasnistor subject to change until you make payment. Learn More – opens in a new window or tab International shipping and import charges paid to Pitney Bowes Inc. Email to friends Share on Facebook – opens in a new window or tab Share on Twitter – opens in a new window or tab Share on Pinterest – opens in a new window or tab Add to watch list. See terms – opens in a new window or tab.
Watch list is transiwtor. See all condition definitions – opens in a new window or tab. Seller information speedyracing Report item – opens in a new window or tab.
Make Offer – Loading United States and many other countries See details. The prices advertised are for one lot or one piece only. See the seller's listing for full details. People who viewed this item also viewed.
The item you've selected was not added to your cart. Learn More – opens in a new window or tab Any international shipping and import charges are paid in part to Pitney Bowes Inc. A brand-new, unused, unopened, undamaged item in its original packaging where packaging is applicable.


Craps proposition bets are craps center bets located in the center of the table. Craps proposition bets covers this group of bets which are similar.
This is a name that covers a group of bets. Proposition bets are bets that are made on a specific outcome of a roll of the dice. Craps proposition bets are craps center bets, so named because of their location on the craps table. While each side of the table is a mirror image, the center bets are not and are used by both sides of the table.
Except for the hardways bets, all the proposition bets are one roll bets, meaning that the bet is placed, the dice are thrown, and if the bet wins, the players take their money, and if it loses, the money goes directly to the dealer.
Craps proposition bets can be placed at any time during the game. The bets are placed by the stickman. The player should gently toss their chips to the center of the table and tell the stickman what they would like their bet to be place on. It is, however, appropriate to give the stickman the bet before the dice have been given to the shooter. It is irritating to other players, and also bad etiquette for a player to be tossing their chips into the middle of the table just before the shooter throws the dice.
Any Craps - Craps numbers are 2, 3 and 12. The player is betting that the next number thrown will be one of these numbers.
Snake Eyes - The throw that lands with two ones showing is called snake eyes.The player is betting that the next number to be bet will be a 2.
Craps Three - The player is betting that the next number to be thrown will be a 3.
Any Seven - The player is betting that the next number to be thrown will be a 7.
Yo - Eleven - The player is betting that the next number to be thrown will be 11. The reason players call it yo - eleven is because seven and eleven sound quite similar and this helps to avoid any confusion that could arise.
Craps 12 - The player is betting that the next number to be thrown will be a 12.
Horn - This is a bet on a few proposition numbers together. Each of the four numbers need to have at least the minimum bet placed on them. If the minimum bet is $1, then at least $4 needs to be placed on this bet. The four numbers are: 2, 3, 11 and 12. When winning, the player will receive chips according to the odds on the specific number that won, minus the portion of the bets placed on the numbers that did not win.
Hardways - These bets are placed on doubles - 4, 6, 8 and 10. These are all doubles which can be made in other ways as well. For this reason, the 12 is excluded from the list because it can only be made with two sixes, and in no other way. If the number is made as as double, the bet wins. If the number chosen is made in a different way, for example 3 and 1 for 4, or a 7 is rolled before the chosen number is rolled, the bet is lost.


text:
Toyota India car sales dip 22% in November
Bengaluru: Japanese car maker's joint venture Toyota Kirloskar Motor (TKM) on Monday said it sold 8,312 units in November, registering a 22 per cent annual decline from 10,721 units in the same month a year ago in the domestic market.
"Exports, however, grew 39 per cent annually to 929 units of Etios model last month from 669 units in the like month a year ago," said the city-based company in a statement here.
As a result, total sales for the month under review declined 19 per cent year-on-year to 9,241 units from 11,390 units in November 2018.
"We have lowered the volume of vehicles to dealers to have lean inventory and adjusted production to ensure we do not burden them before the shift to BS 6 in April 2020," said TKM deputy Managing Director N. Raja in the statement.
During the festive month of October, the company's domestic sales declined 6 per cent annually to 11,866 units as against 12,606 units in the same month a year ago as demand spiked during the Dassehra, Danteras and Diwali festivals.
"We are correcting inventory levels to liquidate stocks by December and make a smooth transition to Bharat Standard (BS)-6," Raja added.
Cities Price (10g)
Gold Rate in Chennai Rs. 38280.00 (0.42%)
Gold Rate in Mumbai Rs. 39000.00 (0.23%)
Gold Rate in Delhi Rs. 39421.00 (1.19%)
Gold Rate in Kolkata Rs. 38820.00 (0.13%)
Gold Rate in Kerala Rs. 37737.00 (0.3%)
Gold Rate in Bangalore Rs. 37500.00 (-0.49%)
Gold Rate in Hyderabad Rs. 38276.00 (0.69%)
Cities Price (1 kg)
Silver Rate in Chennai Rs. 50400.00 (0.4%)
Silver Rate in Mumbai Rs. 50400.00 (0.4%)
Silver Rate in Delhi Rs. 50400.00 (0.4%)
Silver Rate in Kolkata Rs. 50400.00 (0.4%)
Silver Rate in Kerala Rs. 50400.00 (0.4%)
talking point on sify finance

redpajama_set_name: RedPajamaCommonCrawl


text:
Бакалов — фамилия (женская форма — Бакалова):

Известные носители
 Бакалов, Валерий Пантелеевич (1940—2021) — ректор СибГУТИ.
 Бакалов, Василий Иванович (1929—2020) — советский конструктор.
 Бакалов, Георги (1873—1939) — болгарский литературный критик, историк и публицист.
 Бакалов, Евгений Васильевич (род. 1963) — российский актёр.
 Бакалов, Игорь Григорьевич (1939—1992) — советский спортивный стрелок, многократный чемпион мира, Европы и СССР.
 Бакалов, Леонид Ованесович (1908—1982) — советский композитор.
 Бакалов, Луис Энрикес (1933—2017) — аргентинский и итальянский композитор.
 Бакалов, Михаил Ильич (1920—1944) — Герой Советского Союза.
 Бакалов, Петр (1879—1964) — болгарский геолог и палеонтолог.
 Бакалов, Юрий Михайлович (род. 1966) — советский и украинский футболист.
Бакалов, Димо (род. 1988) — болгарский футболист

См. также
 Бакалова, Мария — болгарская киноактриса.

redpajama_set_name: RedPajamaWikipedia


text: Q: Automating daily import task in MongoDB Currently, I am exploring MongoDB and I have a very basic scenario related to automating an import job in MongoDB. I have a text file placed daily at a particular location(FTP) and I need to import .txt file into MongoDB on a daily basis. My question is what is the mechanism available in MongoDB to do this without manually doing this. Is there any kind of job scheduler available in MongoDB?

redpajama_set_name: RedPajamaStackExchange


text:
package br.com.transmetais.dao.impl;

import java.lang.reflect.ParameterizedType;
import java.util.List;

import javax.persistence.EntityManager;
import javax.persistence.EntityManagerFactory;
import javax.persistence.Persistence;

import br.com.transmetais.dao.ComboDAO;
import br.com.transmetais.dao.commons.DAOException;

public abstract class ComboDaoImpl<T> implements ComboDAO<T>{

	private Class<T> classEntity;
	protected static final EntityManagerFactory factory = Persistence.createEntityManagerFactory("unit");

	@SuppressWarnings("unchecked")
	public ComboDaoImpl() {
		this.classEntity = (Class<T>) ((ParameterizedType) getClass()
                .getGenericSuperclass()).getActualTypeArguments()[0];
	}

	public EntityManager createEntityManager() {
		EntityManager manager = factory.createEntityManager();
		return manager;
	}

	@SuppressWarnings("unchecked")
	public List<T> retrieveCombo() throws DAOException{
		EntityManager manager = factory.createEntityManager();
		try {
			String query = "select new br.com.transmetais.bean.Combo(id, CONCAT(codigo,CONCAT(' - ',descricao))) from " + classEntity.getSimpleName();
			return manager.createQuery(query).getResultList();
		} catch (Exception e) {
		    throw new DAOException(e);
		} finally {
			if (manager != null) {
				manager.close();
			}
		}
	}

}

redpajama_set_name: RedPajamaGithub


text:
Centennial Celebrations: Herald of Holiness and NNU
Engaging the Church for God's Mission
Home / Women in Ministry: Conviction or Culture
Women in Ministry: Conviction or Culture
The mission statement of Nazarene Theological Seminary in Kansas City includes the intentional phrase "to prepare men and women for the practice of Christian ministry." At NTS this academic year, 63 women are preparing for ministry. The majority of these women are preparing for pastoral ministry in answer to God's call in their lives. They are committed Christians. They are actively pursuing the preparation process prescribed by the Manual of the Church of the Nazarene.
Many of them heard the call while they were teenagers, and they have never thought of doing anything else with their lives. They are not interested in making a statement about their civil rights for equal employment. They are not on a campaign to 'challenge the system.' Their only desire is to do the will of God. The Church of the Nazarene, through its educational institutions and district ministerial boards, has been cheering them on! And God continues to call women to ministry.
Yet the critical question that must be asked is: Will there be a place for them to serve? The challenge for our Nazarene colleges, universities, and seminaries is not only to educate women for ministry but also to encourage their placement in pastoral ministry assignments. Our cooperative process of calling and assigning pastors to local churches requires that both the district superintendent and the local church membership agree on the pastoral call. For several years now, the placement process has been difficult for women.
A district superintendent recently confided to me, "I would like to place some women as pastors on my district, but when I suggest the possibility, I face some stiff opposition from church boards, especially the women." Unfortunately, this district superintendent's experience is not unique. Yet even in the face of this opposition, God continues to call women to ministry in the Church of the Nazarene.
The arguments for restricting the role of women in ministry to certain age-level or gender-specific assignments are almost as old as the history of the Christian church. For centuries, certain denominational groups have struggled with the issue of the ordination of women, arguing over biblical passages that speak directly to the issue of women and authority in the church. Primarily from the apostle Paul, these passages include those that place qualifications on a woman's opportunity to pray and prophesy in a church meeting (1 Corinthians 11:3-12), call for women not to speak in public without authority (1 Corinthians 14:33-35), or restrict the teaching roles of women to exclude any influence over men by appealing to the order of creation (1 Timothy 2:9-15).
In each of these cases, Paul is speaking to a specific circumstance in the midst of a specific culture. The question for the church has been: Are these texts to be interpreted as specific instructions for those local first-century congregations, or should they be taken as universal commandments regardless of the century? There has not been agreement on this question.
On the other side of the issue, the apostle Paul also wrote, "There is neither Jew nor Greek, slave nor free, male nor female, for you are all one in Christ Jesus" (Galatians 3:28). Is Paul simply referring to the absence of distinction we share in salvation, or was he arguing for an equalitarian view of men and women, Jew and Greek, slave and free for ministry as well as for salvation? Are we to assume that some of the gifts of the Spirit usually associated with church leadership and pastoral ministry (e.g., 1 Corinthians 12 and Ephesians 4) are gender specific? Again, there has been much debate about how this passage is to be interpreted. Yet in the midst of all these questions of interpretation, God continues to call women to ministry in the Church of the Nazarene.
The arguments for restricting the role of women in ministry have appealed to historical particularity and precedence. Jesus was a man and chose male disciples. Throughout the majority of the church's history, it has been men who have been assigned to positions of church leadership and authority. Women historically have not had the cultural respect and appropriate education to be qualified for ministry.
Yet how does one deal with the fact that women were baptized equally with men or with the prevalence of New Testament women whom Paul often described as "fellow workers" in Christ, especially in light of the assumed cultural roles and place of women? How does one deal with the thousands of women throughout the centuries who have been at the front of significant spiritual movements only to be replaced by men as the movements became institutionalized? How does one deal with the absence of any statement about gender hierarchy in any of the early Christian confessions or creeds? Even in the heat of historical controversy, God continues to call women to ministry in the Church of the Nazarene.
While all of these biblical and historical controversies are alive in the broader Christian Church, they are not at the heart of the issue for the Church of the Nazarene.
We have, for the entirety of our history, believed in and practiced the ordination of women. It is embedded in our theology. We are among those who have chosen to recognize the call of God on women to serve as leaders in Christ's Church. Our official documents (e.g., the Manual) do not merely make allowance for women in ministry; we state our position in such a way as to expect that God will call men and women to ministry.
We are among those who see Paul's restriction upon women in spiritual authority as culturally appropriate for the pagan culture of those first-century communities but not normative for women ministering in the need pagan cultures of the 20th and 21st centuries. Our history is resplendent with the contributions of great women preachers and pastors like Mary Lee Cagle, Agnes Diffee, Estelle Crutcher, and Bessie Luisa Tsambe, who currently is pastor of one of the largest Nazarene churches in the world, in Maputo, Mozambique. Thanks be to God, He continues to call women to ministry in the Church of the Nazarene. We need them as much now as we ever have.
Despite these foundations, however, Nazarene history also is marked by the decline of women in pastoral ministry and church leadership. We have followed the pattern of institutionalization so that authoritative women at the front of our dynamic movement have been slowly but surely replaced by men in organizational positions of authority, including the pastorate. Our biblical and theological convictions didn't demand this shift. The shift was sociological and cultural. And our present hesitance and opposition to women in pastoral and church leadership roles aren't biblical or theological, but cultural, pure and simple.
It's time for our culture to live up to our convictions. Otherwise, God may start calling women to somebody else's movement.
Ed Robinson is director of Leadership Studies and Servant Leadership at Northwest Nazarene University's Wesley Center.
Catholic Protestant theology


Morotai Island is located at the northern tip of North Halmahera District and is part of the North Maluku province. Morotai Island is geographically situated between 200-240 degrees North latitude and longitude degrees 12815-12848. Morotai Island is bordered by the Pacific Ocean in the North Sea in the east of Halmahera, Morotai Strait to the south and the Celebes Sea to the west.
Morotai Island area of 2474.94 square kilometers is, or 10 percent of the land area of North Maluku Regency. Administratively, the island of Morotai since 2002 belong to the district administration with the capital of North Halmahera regency in Tobelo.
Soil texture on the island of Morotai in general, with smooth and textured areas are on the east. Most of Daruba City area is agricultural land or plantations of coconut plantation folk and garden mix. While the use of land for the physical (residential, office and economic facilities) only covering 79.64 hectares or 3.92 per cent of the total area of the city. Other land-use airfield area is 15 acres, ponds, protected areas, and so on. Like most cities located in coastal areas, the land use pattern in the City Daruba tend to follow the pattern of linear shoreline. In the coastal section is dominated mainly by the physical structure. While agricultural activities tend toward the hills to the east and north of the city.
The population of the island of Morotai as a whole as much as 58,720 people scattered in 47 villages. Livelihoods mostly as farmers and fishermen (more than 60 per cent), while the other is the livelihood of traders, civil servants and the military / police.
Type of food crop production on the island of Morotai including paddy rice, dry rice, maize, cassava, sweet potato, peanut, mung bean, soybean, fruits and vegetables. To go to Morotai Island can only be reached by means of sea transport to the City Daruba. Travel to Morotai taken by speedboat drive from Ternate to Sidangoli with 1-hour travel time. Next by ground vehicles to Tobelo with travel time of 3 hours and Tobelo by speedboat to Morotai with 1.5 hours of travel time.
Infrastructure and land transportation facilities to the villages and inter-district existing and in good condition. Public passenger terminal located in the City Daruba with some land transport fleet serving passengers.
Marine transportation infrastructure in the port category that is not cultivated there Daruba City, the capital of South Morotai sub-district. Volume loading and unloading of goods in the domestic shipping for inter-island trade in the Port of Daruba dismantled in 2002 and 6525 tons of 33,718 tons loaded.
Although the island of Morotai a former airfield from World War II, which has 7 lines long runway with each 3 km, but the air transportation of passenger transportation, especially public until now not been able to operate on a regular basis. This is due to the lack of general aviation serving permanently flight path to and from the island of Morotai. The existing airport is currently managed as a military air base by the AU and landed several times the general aircraft to and from the Ternate more widely used for commercial transportation. Hopefully in the future, the island of Morotai increasingly the desire for all tourists to vacation there.


The company's in-house spice expert, Joy, focuses on new spice introductions and seasonal spices from the Pereg pantry.
The experts at Pereg, a leading producer of all-natural spices from around the world, offers more than 60 spices and spice blends sourced from the best places on earth. Every once in a while, their in-house spice expert, Joy, focuses on new spice introductions and seasonal spices from the Pereg pantry, explaining their unique properties and offering up creative ideas to help cooks and consumers make the most of them in recipes.
The fourth most consumed spice in the world, paprika often appears in rubs, marinades, stews, chilies, and as a garnish. It's a key ingredient in numerous cuisines, from Mexican rices to classic Hungarian goulash to Italian sausages.
All paprika starts life as a type of red Caspicum annum, otherwise known as the bell pepper. Paprika can be smoked, sweet, hot, Hungarian, or Spanish style, depending on the variety of the peppers used and how they are processed. They range in color from bright red to brown, each with its own flavor profile, from mild to spicy. Along with new Spanish paprika, Pereg Natural Foods offers five other varieties: hot, hot oil, smoked, sweet, and sweet oil paprika.
With Spanish cuisine being a huge trend these days, you may have come across Spanish paprika on a recipe's ingredient list. Also known as pimentón, this spice is becoming very popular in the United States. But what exactly is Spanish paprika and what makes it so special?
Whether smoked or non-smoked, Spanish paprika is available in three varieties: sweet (dulce), semi-sweet (agridulce), and spicy (picante). The levels of heat and sweetness vary based on the blend of peppers used. Spanish paprika is generally less intense than Hungarian paprika, so it can be used in a multitude of ways.
"Spanish paprika can be your best secret ingredient!" says Joy. "It has just enough spiciness to be interesting, and its array of flavors—from sweet to spicy—gives depth to a variety of recipes. We use it in baked eggs, potato casseroles, sprinkled on roasted tomatoes, and in beef stews. Sometimes we use just a hint—not so much that it defines a dish, but just enough to give it a smoky or sweet note in the background.
Poppy seeds come in three different colors: white, blue, and black. There are no distinct differences between these types aside from their color, with the choice mainly depending on the color preference of the baker or the cook and its availability. Though they vary in color, they all come from the same European poppy plant.
Poppy seeds on their own are generally tasteless. When using them uncooked in foods such as salads, it is advisable to roast them lightly, as this enhances their flavor and aroma.
Ground poppy seeds are widely used in poppy seed cakes and pastries.
PEREG GOURMET produces more than 60 varieties of spices, spice blends and herbs. The spices are pure, fresh and natural with no additives, no preservatives, no added volume and no food coloring.


Chimay 150 / Spéciale Cent Cinquante 10° - 3/4L - delivery worldwide - discount following quantities purchased.
Fiona K. from bought this product recently.
To celebrate the 150 years spent at the Abbey Of Scourmont, the Chimay Trappist brewery has developed this exceptional anniversary beer brewed specially for the occasion.
Pours hazy orange with a small white head. Aroma is slightly tart with citrus, orange peel, some toffee and hints of caramel. Notes of spices like pepper andcoriander with hop. The taste has spices, sweet fruits and hop bitters. the aftertaste is a little sweet with nice bitter and spices. This is a treasure!
Date of valididy 2015 But can still be consumed several years later.


text:
Sentinel Staff Writer 05-18-2009
Olive Garden diners may be eligible for $9 voucher
By Sandra Pedicini
Did you eat at Olive Garden and pay with plastic a couple of years ago? If so, the restaurant chain may owe you a free appetizer.
Olive Garden could be the latest restaurant to fork over payment — in the form of $9 appetizer vouchers — in settling a federal lawsuit over credit-card privacy.
The deal already has received preliminary approval in the Northern District of Illinois, with a final hearing set for July. It stems from a lawsuit in 2007 that accused Olive Garden of printing the last six digits of customers' credit-card numbers on receipts. The limit under the Fair and Accurate Credit Transactions Act is five.
Already, several thousand people have submitted voucher claims, said Chicago attorney Thomas Zimmerman, who represented the plaintiffs in the class-action lawsuit against the chain, part of Orlando-based Darden Restaurants. Zimmerman maintains that the glitch put patrons at risk of identity theft. But he could not cite anyone whose identity was stolen.
"This requirement to truncate the credit card numbers was widely publicized and was well known for years and the merchants had three years to comply before the law went into effect," said Zimmerman, who files class-action lawsuits on a variety of claims. "We don't know why the Olive Garden failed to comply."
The chain said in a statement that "Olive Garden takes its guests' data and its legal obligations very seriously." The statement said the problem was caused by a vendor, and that problematic slips "were provided only to the individual Olive Garden guests. Unfortunately, this mistake initially went unnoticed, but the problem was promptly remedied when it was brought to our attention. There is no indication that anyone has been harmed in any way by this error."
Diners who used debit or credit cards between Dec. 4, 2006, and Aug. 10, 2007, are eligible for vouchers.
The 2003 Fair and Accurate Credit Transactions Act covers a range of issues, such as mandating annual free credit reports for anyone who wants them. It also puts limits on how much debit- or credit-card information can be printed on receipts. Those limits went into effect in December 2006.
When restaurants and other establishments have printed more than the limits, lawsuits have arisen.
"It is something where both very large and seemingly sophisticated and small and unsophisticated businesses both get caught," said Walter Olson, a senior fellow at the Manhattan Institute, who has a blog called Overlawyered.
Critics of such suits describe them as opportunistic, pointing out that no one generally reports any identity theft as a result of the breaches.
"It's like reckless driving in which no one had an accident and except for the lawyers, no one even noticed the car speeding," Olson said.
The lead plaintiff in the case was Mary Dudzienski of Illinois. Records show that Zimmerman represented Dudzienski in three other similar lawsuits. "A friend of hers had her identity stolen, so that's what made her interested in these types of cases," Zimmerman said.
Dudzienski could not be reached for comment.
According to the notice on Zimmerman's Web site, Dudzienski will be applying for an "incentive award" of $2,500, which Darden has agreed to pay separately. Under the proposal, according to the notice, the company also has agreed to pay about $130,000 to Zimmerman and $5,000 to charity.
Who's eligible
Customers who ate at an Olive Garden in the United States and paid with a debit or credit card between Dec. 4, 2006 and Aug. 10, 2007, can fill out a form available at www.attorneyzim.com requesting a voucher. The PDF form is available under the heading "Class Action Notices." You can also call 1-866-890-4862. You don't have to provide proof of purchase but do have to sign a document certifying, under penalty of perjury, that you made the purchase. The voucher forms must be postmarked by June 4.


text:
William A. Ekwall
Title: William A. Ekwall
Subject: United States congressional delegations from Oregon, United States House of Representatives elections, 1936, United States House of Representatives elections, 1934, 74th United States Congress, Charles Martin (Oregon politician), List of United States Representatives from Oregon, Oregon's 3rd congressional district, University of Oregon School of Law, Nan Wood Honeyman, List of Oregon judges
William Alexander Ekwall
Judge of the United States Customs Court
February 9, 1942 – October 16, 1956
Walter Howard Evans
Scovel Richardson
Member of the U.S. House of Representatives
from Oregon's 3rd district
January 3, 1935 – January 3, 1937
Charles H. Martin
Nan Wood Honeyman
(1887-06-14)June 14, 1887
Ludington, Michigan
University of Oregon School of Law LL.B.
William Alexander Ekwall (June 14, 1887 - October 16, 1956) was a U.S. Representative from Oregon and a Judge for the United States Customs Court.
2 Congressional career
3 Federal Judicial Service
Born in Ludington, Michigan to Alexander and Emilie Ekwall,[1] Ekwall moved to Klamathon, California with his parents in 1893.[2] In 1902, the town of Klamathon was destroyed in a massive fire,[3] and the Ekwalls eventually made their way to Portland, Oregon in 1906.[2]
He attended the public schools and then the University of Oregon School of Law, then located in Portland, graduating in 1912.[2] He was admitted to the bar the same year and commenced practice in Portland in the firm Senn, Ekwall, and Recken.[1][2] During World War I, Ekwall served in the United States Army as a private in the Infantry, attending the Central Officers Training School in 1918. After his Army service, he worked in Portland as a municipal judge from 1922 through 1927, and as judge of the circuit court, fourth judicial district (Multnomah County), department 8 until 1935.[2]
Congressional career
In 1934, Democrat Charles H. Martin, the incumbent U. S. Representative for Oregon's 3rd congressional district in Portland, announced that he would run for Governor of Oregon. Ekwall ran for Martin's congressional seat as a Republican, winning the May primary election and facing Walter B. Gleason, who two years earlier, had lost the 1932 U.S. Senate election to Frederick Steiwer.[4] With several third-party candidates in the race, Ekwall earned a narrow 41%–38% plurality over Gleason and a seat in the 74th United States Congress.[5]
In Congress, Ekwall was known for a somewhat belligerent style.[6] He once referred to Representative Wright Patman as a "stool pigeon"[7] and Representative Marion Zioncheck as a "jackass."[8]
Ekwall sought re-election in 1936. He was challenged by Nan Wood Honeyman, a Portland community activist and family friend of President and Mrs. Roosevelt.[9] Honeyman's aggressive door-to-door campaign, coupled with Roosevelt's landslide re-election, helped her defeat Ekwall, earning 51% of the vote to Ekwall's 33%.[9][10] Following his loss, Ekwall returned to his Portland law practice, serving as a delegate to the Republican National Convention in 1940.[2]
Federal Judicial Service
On January 19, 1942, President Roosevelt nominated Ekwall to serve as a Judge for the United States Customs Court, to the seat vacated by Judge Walter Howard Evans. He was confirmed by the Senate on February 9, 1942 and received his commission on February 13, 1942. He served upon the court until his death and was succeeded by Judge Scovel Richardson.[11]
Ekwall died while on vacation in Portland on October 16, 1956.[12] Ekwall and his wife Lina and the couple had two daughters.[12] He was interred in Portland Memorial Cemetery.[13]
Template:CongBio
Biographical Directory of the United States Congress.
Name Ekwall, William Alexander
Short description American politician
Date of birth June 14, 1887
Place of birth Ludington, Michigan
Date of death October 16, 1956
Place of death Portland, Oregon
Mason County, Michigan, Michigan, Wisconsin, Marriage, SS Badger
Oregon, Multnomah County, Oregon, The Oregonian, Washington County, Oregon, Clackamas County, Oregon
United States congressional delegations from Oregon
Oregon's 1st congressional district, Oregon's 2nd congressional district, 35th United States Congress, 113th United States Congress, Ron Wyden
Socialist Party of America, United States House of Representatives elections, 1932, United States House of Representatives elections, 1934, Communist Party USA, United States Hous...
Socialist Party of America, United States House of Representatives elections, 1932, Communist Party USA, United States House of Representatives elections, 1930, United States Hous...
74th United States Congress
Democratic Party (United States), United States Statutes at Large, 73rd United States Congress, 75th United States Congress, Wisconsin Progressive Party


Family and friends of Kathleen Fowler are raising money for the nonprofit Help Hope Live to fund uninsured medical expenses associated with Catastrophic Illness.
Kathleen has chosen to fundraise for Help Hope Live in part because Help Hope Live assures fiscal accountability of funds raised and tax deductibility for contributors. Contributors can be sure donations will be used to pay or reimburse medical and related expenses. To make a tax-deductible donation to this fundraising campaign, click on the Give button.
Have a Merry Christmas and a Blessed New Yeary!!


text:
Roberto Ercilla
MUSIC SCHOOL IN BILBAO
Photos by César San Millán Agüera
César San Millán Agüera
The new Conservatory of Bilbao is located on an exempt city block in the neighbourhood of Deusto, where it coexists with an important Metro station whose glass shell stands out ostensibly.
Because of the possibility of an intervention on all of the surrounding space, the proposed building is limited to a close relationship with the topography of the lot, looking more towards urban integration and consolidation of the area, with a singular prominence.
This is precisely because we are dealing with an educational centre, where a wide programme of classrooms, workshops, rehearsal areas, etc., much be structured, all of this including an auditorium to hold 400 people.
Once the linear location of the project to the back of the lot was decided, the main issue became the manifestation of the natural slope of the plaza by means of the roof; in this way the building accompanies the urban space in its inclined gestures.
To reduce impact of the resulting volume, the building is sunken under the land and surrounded by separating crevices on its long sides.
On the outside, it appears as an elementary glass volume that holds a second body inside, fractured by narrow transversal patios that let in natural light to classrooms and other areas, reducing possible acoustic impact from outside.
In this way, all areas receive natural light, a sensation that is perceived when passing through the common areas of the building.
Spain - BILBAO
Patxi Galarraga, Laura Angulo
Additional Notes Finalist Prizes COAVN (Architects' school Basque - Navarrese) 2010 Building category
Music Schools and Art Academies


text:
Кенигсфельден - это бывший двойной монастырь клариссинок и францисканцев в муниципалитете Виндиш в швейцарском кантоне Аргау . Он был основан Габсбургами в 1309 году и секуляризован после Реформации в 1528 году. После секуляризации комплекс зданий служил резиденцией бернских губернаторов, а с 1868 года здесь располагалась психиатрическая клиника. Церковь с витражами  14 века является частью  музея Аргау с 2009 года.

История
Монастырь был построен по инициативе Габсбургов, родовой замок которых находится примерно в двух километрах к юго-западу от Виндиша. 1-го мая 1308 года король Альбрехт I был убит своим племянником, герцогом Иоганном Швабским.  В память об этой семейной трагедии вдова короля Элизабет фон Герц-Тироль основала монастырь клариссинок который был назван Кёнигсфельден. С самого начала к монастырю клариссинок был прикреплен небольшой францисканский монастырь, который отвечал за пастырское попечение. Первые братья францисканцы переехали в 1311 году, а в следующем году - монахини. Кёнигсфельдская хроника сообщает, что при строительстве монастыря было сделано много находок из времён Римской Империи . Позже выяснилось, что здесь когда-то располагался лагерь легионеров Виндонисса .

Дочь Альбрехта Агнес Венгерская, вдова венгерского короля Андреаса III,  с 1317 года жила в Кенигсфельдене. Благодаря приобретённым ей  землям  и  умелому ведению хозяйства монастырь процветал. 22  Августа 1344 года  папа Климент VI. подарил Агнес привилегию свободного входа в монастырь  для неё даже был выстроен дом на территории монастыря.  После ее смерти в 1364 году начался постепенный упадок. В 1397 году  Габсбурги предоставили монастырю самостоятельность .

После введения Реформации в 1528 году монастырь был закрыт. Инициатива роспуска принадлежала монахиням монастыря.

Комплекс зданий подвергся многочисленным реконструкциям и служил официальной резиденцией бернских губернаторов . В 1804 году бывший монастырь перешел во владение кантона Аргау, основанного годом ранее. С 1868 по 1872 год он был преобразован в кантональный санаторий, психиатрическую лечебницу. Большая часть францисканского монастыря была снесена.

Известные игуменьи
 около 1313 г .: Хедвига фон Кунцлау
 1318–1324: Гута фон Бахенштейн
 1329: Бенинья фон Бахенштейн
 около 1330–1340: Агнес  фон Брандис? (Это не могла быть Агнес Венгерская, как принято считать, поскольку, по словам Герберт, она сама никогда не вступала в орден  ).  Возможно, что настоятельница женского монастыря Зекинген временами была также настоятельницей женского монастыря Кенигсфельден. В то же время Агнес фон Брандис была аббатисой Зекинген. Как и его предшественник, дворянство Улинген именовалось здесь до 1330 года.
 около 1334 г .: Адельхейд I.
 около 1355 г .: Елизавета I из Лейнингена? (Либенау видит в этом путаницу 1455 года)
 ок. 1371: Анна I. фон Гольденберг
 1374–1383: Ирменгард фон Хоэнберг
 около 1405: Адельхайд II фон Халльвиль
 1406–1408: Маргарета I из Вахингена
 1411–1415: Маргарета II фон Грюненберг
 1416–1456: Елизавета II Лейнингенская
 1456–1459: Урсула фон Мюлинен
 около 1459: Ева фон Эрпах
 ок. 1471: Осанна Ягер
 1472–1492: Аполлония фон Гогенберг
 1497–1506: Анна II фон Штайн
 1511–1513: леденцы Emerita
 1516–1528: Катерина фон Вальдбург

Монастырский комплекс

Первоначально церковь была обрамлена монастырем с двух сторон: к северу находился францисканский монастырь, из которого к 1870 году уцелело только так называемое архивное хранилище - истинное назначение помещения до сих пор неизвестно. В нем можно увидеть настенные росписи с изображением рыцарей , павших в битве при Земпахе в 1386 году. Контуры остальных строений францисканского монастыря отмечены каменными плитами .

К югу сохранились части женского монастыря, например, клуатр . Уцелевшие строения в их нынешнем виде дают лишь приблизительное представление о былом величии. Сохранился также бывший фермерский двор с многочисленными хозяйственными постройками.

Монастырский амбар

Монастырский амбар, построен в 1744 году и является самым мощным в своем роде в кантоне, напоминает о прежнем экономическом статусе Кенигсфельдена как самого богатого хозяйства этих мест. Несмотря на то, что потребовалась некоторая модернизация, он по сути сохранил свой первоначальный вид.

Примечания

Католические монастыри Швейцарии
Виндиш
Здания и сооружения Аргау


text:
Pronto Digital
Customer orientation
Caring to identify, understand and exceed customer needs in every transaction, to build enduring relationships for mutual benefit.
People orientation
Creating and managing an environment that encourages and inspires people to actively participate in growing the business by and performing willingly, efficiently and effectively.
Visionary conduct that builds trust, stretches capabilities, and inspires commitment in people for achieving challenging goals by working as a team.
Working together by playing on each other's strengths to achieve shared goals.
Ambition to grow the business by continuously developing personal and professional. Capability to lead, manage and innovate for building greater value.
Our mission is to focus on our customer's satisfaction and value. We passionately pursue excellence in all that we do and are committed to attaining world-class standing in every sphere of our operations – technical and managerial. By valuing and respecting differences, we thrive in diversity and rely on each other to achieve exciting, meaningful and challenging goals.
Pronto Digital was established in 2003 and is an IT services provider and now specializes in digital analytics, digital marketing, and online platform development. We strive to stay on the cutting edge of technology and business and utilize tried and true methods to get our clients the results they require.
Our people are empowered and display initiative, share ideas and enjoy performing tasks, keeping the interests of all stakeholders in mind, with self-discipline and a sense of ownership, in a free & open culture. We care for our internal and external customer needs with a commitment to delighting them by exceeding their expectations. We passionately pursue excellence in all that we do and are committed to attaining world-class standing in every sphere of our operations – technical and managerial. By valuing and respecting differences, we thrive in diversity and rely on each other to achieve exciting, meaningful and challenging goals.


text:
Графство Гана́у-Ли́хтенберг () — территория в составе Священной Римской империи.

История

Образование графства Ганау-Бабенхаузен
В 1451 году скончался правивший в графстве Ганау Рейнхард II, а год спустя скончался также его сын и наследник Рейнхард III. Филиппу — сыну Рейнхарда III — было тогда всего четыре года, и не было уверенности в том, что он сможет прожить достаточно долго, чтобы произвести наследника мужского пола. Единственным оставшимся мужчиной в роду был другой Филипп — брат Рейнхарда III. Так как ещё в 1375 году в роду Ганау был принят принцип первородства, то разразился конфликт: пфальцграфиня Маргарет Мосбахская (мать младшего Филиппа) и её отец Оттон I (пфальцграф Мосбаха) настаивали на сохранении принципа первородства, в то время как старший Филипп, на стороне которого было большинство влиятельных людей в графстве, хотел стать графом сам. В 1457 году Маргарет скончалась, и в 1458 году лежавший южнее реки Майн амт Бабенхаузен был отделён от графства и отдан старшему Филиппу, ставшему Филиппом Бабенхаузенским, а оставшуюся севернее реки Майн часть графства стали впоследствии называть Ганау-Мюнценберг.

Наследование Лихтенберга
В том же 1458 году Филипп Бабенхаузенский женился на  — одной из двух дочерей . В 1471 году Людвиг V скончался, и сеньором Лихтенберга стал его брат . В 1480 году умер и он, и Филипп, получивший права на наследство от своей скончавшейся в 1474 году супруги, унаследовал половину его владений в нижнем Эльзасе вместе с его столицей Буксвиллером. В результате его владения выросли с крошечного клочка до земель, по площади не уступавшим графству Ганау-Мюнценберг, и их стали называть графством Ганау-Лихтенберг.

Наследование Цвейбрюккена
Другая дочь Людвига V — Элизабет — вышла за Симона IV Векера, графа Цвейбрюккен-Битшского, который и унаследовал вторую половину лихтенбергских владений. В 1570 году скончался Якоб — последний граф Цвейбрюккен-Битшский, и женатый на его дочери Лудовике Маргарет граф Филипп V Ганау-Лихтенбергский унаследовал остаток лихтенбергских владений, а также графство Цвейбрюккен-Битш и баронство Оксенштейн. Однако наследство оспорил Филипп I Лейнинген-Вестербургский, женатый на дочери предыдущего графа Цвейбрюккен-Битшского: дело в том, что Битш формально относился к герцогству Лотарингия, и теоретически, в соответствии с законами герцогства, мог наследоваться только по мужской линии.

Поначалу Филиппу V удалось взять верх. Однако распространение лютеранства вызвало неудовольствие лотарингского герцога Карла III, и он на правах сюзерена отнял феодальное владение. В 1572 году лотарингские войска оккупировали графство и остановили Реформацию. Так как Филипп V не мог соперничать с герцогством Лотарингия в военной области, то он перенёс спор в юридическую плоскость. В итоге, в 1606 году было решено, что Битш возвращается Лотарингии, а амт Лемберг, являвшийся аллодом
Цвейбрюккенских графов, отходит графству Ганау-Лихтенберг.

Воссоединение графства Ганау

В 1642 году скончался Иоганн Эрнст — последний из мужчин ветви, правившей в Ганау-Мюнценберге. Ближайшим родственником мужского пола был Фридрих Казимир Ганау-Лихтенбергский, который в то время был ещё мал и находился под опекой Георга II Флекенштайн-Дагштульского. В это время шла Тридцатилетняя война, и если в Ганау-Мюнценберге большинство населения поддерживало кальвинистов, то жители Ганау-Лихтенберга были лютеранами. Чтобы обеспечить наследство Фридриха Казимира, Георгу II пришлось объявить кальвинизм государственной религией на землях Ганау-Мюнценберга, сохранив право на совершение лютеранских обрядов лишь для себя и членов своего двора. В 1643 году ему пришлось заключить договор с Амалией Елизаветой Ганау-Мюнценбергской (которая к тому времени была регентом Гессен-Касселя при несовершеннолетнем сыне Вильгельме VI), по условиям которого она предоставляла военную и дипломатическую поддержку против тех, кто препятствовал вступлению Фридриха Казимира в наследство, однако взамен на это в случае пресечения мужской линии дома Ганау права на графство отходили потомкам Амалии Елизаветы.

В 1638 году после смерти Филиппа Морица Ганау-Мюнценбергского, его вдова Сибилла Кристина Ангальт-Дессауская получила в качестве вдовьей доли замок Штайнау. Чтобы избежать её возможных претензий на графство, было решено женить на ней Фридриха Казимира. Из-за двадцатилетней разницы в возрасте (вдове было уже 44 года) брак оказался бездетным. В 1680 году французский король Людовик XIV, проводивший «политику присоединений», занял Лотарингию, и графство Ганау лишилось собственно исторического Лихтенберга.

Второе создание Ганау-Лихтенберга
Фридрих Казимир умер в 1685 году, и графство Ганау вновь разделилось на две части, унаследованные его племянниками: в Ганау-Мюнценберге стал править Филипп Рейнхард, а в Ганау-Лихтенберге — Иоганн Рейнхард III. В 1712 году Филипп Рейнхард скончался, и графство Ганау объединилось вновь.

Исчезновение графства Ганау с карты
Иоганн Рейнхард III был последним мужчиной из рода Ганау, и после его смерти в 1736 году в соответствии с договором 1643 года земли графства Ганау-Мюнценберг отошли ландграфству Гессен-Кассель. Земли графства Ганау-Лихтенберг отошли ландграфству Гессен-Дармштадт, так как Шарлотта Кристина Ганау-Лихтенбергская (дочь Иоганна Рейнхарда III) была супругой Людвиг VIII Гессен-Дармштадтского. При этом вопрос об административной принадлежности амта Бабенхаузен чуть не привёл к войне между двумя ландграфствами. Дело было передано в Имперский камеральный суд, и после долгого разбирательства спорная территория была в 1771 году примерно поровну разделена между Гессен-Касселем и Гессен-Дармштадтом.

Графства Священной Римской империи


text:
Q: call a vb.net class function from javascript I want to make a call to a function of vb.net class from javascript. I mean I would call something which doesnot have extention as .aspx but rather .vb only. Is is possible? how?
Thanks and regards,
Tanmay.

A: If you add
<System.Web.Services.WebMethod()>

To your function signature then you can use PageMethods to call that function from JavaScript
<System.Web.Services.WebMethod()>_
Public Shared Function DisplayDate()
    Label1.Text = DateTime.Now()
End Function

So now add a ScriptManager to your page and in the ScriptManager do this
<script language="javascript" type="text/javascript">
function ShowDate()
{
    PageMethods.DisplayDate();
}


text:
Follow me @dJcybersonique on Instagram
Teejay sent word that there's a new radio station (still unnamed) in town that's currently going through its paces over 92.0FM in the Klang Valley. It took me a while to figure out what kind of stuff they're playing until I realized that they're playing nothing but local music be it in Malay, English, Mandarin or Tamil. Most of the stuff that they have got on their playlist are pretty urban stuff from the likes of local hip hop groups (Ruffedge, Da Joint, Muchachaz, Chakrasonic) to pop (Ning Baizura, Nur Fatima, Ferhad, Victor Wong, etc.) to alternative rock (OAG, Butterfingers, Exist, Black Maria). Since this is coming fromAMP Radio Networks, the very same people that brought you Hitz.FM, Era.FM, My.FM, etc. you can pretty much expect it to be a format radio station like its other siblings.
Ex-Boilermakers' Wedding Weekend
Two ex-Boilermakers had their wedding receptions today. First up was Part II of Firdaus and Fawzana's wedding at the groom's place in Penang (their picture page has been updated with pictures taken today). I was joined by other ex-Boilers Md. Zin, Bart and Jahang there. Immediately after that, I was off to Ipoh for Eijatt and Fara's reception (pictures below). I was joined by ex-Boilers Ustad, Hanif, Jimmy, Salleh and Asroll. I've already made it back home to KL at this time of writing and I'm really high on nasi kandar and obviously nasi minyak right now. Curiously, only the guys made their appearances at both events today. Whatever happened to them ex-Boiler gals, lah? Heheh! :P Anyways, Selamat Pengantin Baru to both couples! Here's wishing a good life ahead for the four of you!
Dedicating: Alice Peacock (feat. John Mayer) - Bliss
Songs And Movies For Mother's Day
Songs: Hey Mamma (Black Eyed Peas), Song For Mama (Boyz II Men), Mama (Spice Girls), Good Mother (Jann Arden), Mother (Tori Amos), Untukmu Ibu (Exist)
Movies: Stepmom, Freaky Friday, Anywhere But Here, My Stepmother Is An Alien, Ibu Mertuaku
Those Idiotic, Inconsiderate, Numbnutted Nitwits
There are just too many idiotic, inconsiderate, numbnutted nitwits out there going about doing things without even the slightest hint in the world on how their actions affect other people around them. How would your family being passengers in your car were to react if I were to recklessly overtake your vehicle by squeezing in at an impossible angle between two lanes on the highway? How would you feel if I were to come around disposing my waste in the corridor of your home? What if I were to swing by your house and relief myself by spraying all over the toilet and just leave without even bothering to flush? Would you mind if I were to cut queue right in front of you just as you're about to reach the counter after spending a long time queueing? There are times when I feel like retaliating by doing the same. After all, do unto others what others have done unto you. Then again, why even bother. I'd be no different than those idiotic, inconsiderate numbnutted, nitwits themselves if I were to do so.
Selamat Pengantin Baru: Firdaus & Fawzana
Firdaus a.k.a. Penang tied the knot with his sweetheart Fawzana noon today. Most of us who stayed together in the same apartment/house with him during our uni days were there to accompany him and his family to the bride's place at Damansara for the akad nikah ceremony. Both looked every bit the happy couple, as is evident from the pictures! Here's wishing all the joy and bliss for the couple in the years to come!
Next posts >>


text:
First Look at Anthony Mackie in 'Abraham Lincoln: Vampire Hunter' (Photos)
Posted on May 29, 2012 /Film
Here's an exclusive look at Anthony Mackie in the Tim Burton-produced Abraham Lincoln: Vampire Hunter.
The film, directed by Timur Bekmambetov and adapted from Seth Grahame-Smith's best selling novel, blends history and fiction in a cool story about US president Abraham Lincoln fighting for mankind by freeing slaves and killing vampire oppressors trying to take over the world. Mackie plays William Johnson, the President's personal valet and gun-toting right hand man.
In the new pics, we see Mackie getting in on all of the gory action while dressed in 19th century garb. The actor also appears to be captured by killer vamps in a behind-the-scenes image from the editing room.
Vampire Hunter also stars Benjamin Walker as Abraham Lincoln with Dominic Cooper as Henry Sturgess, Alan Tudyk as Stephen A. Douglas, and Jaqueline Fleming as Harriet Tubman.
Abraham Lincoln: Vampire Hunter opens in theaters on June 22nd.
(Photo credit: 20th Century Fox/Jim Lemley)
Anthony Mackie in talks to play FBI agent in 'Runner Runner'
Anthony Mackie appears in 'Gangster Squad' promo poster, trailer
'Abraham Lincoln: Vampire Hunter' star Jaqueline Fleming talks Harriet Tubman role
New posters for Abraham Lincoln: Vampire Hunter ( Co-Starring Anthony Mackie, Jaqueline Fleming)