As is well-known, spontaneous CP-violation in the strong interaction is possible at theta = pi, which is commonly referred to as Dashen's phenomenon. This phenomenon has been studied extensively using chiral Lagrangians. Here the two-flavor NJL model at theta = pi is discussed. It turns out that the occurrence of spontaneous CP-violation depends on the strength of the 't Hooft determinant interaction, which describes the effect of instanton interactions. The dependence of the phase structure, and in particular of the CP-violating phase, on the quark masses, temperature, baryon and isospin chemical potential is examined in detail. The latter dependence shows a modification of the charged pion condensed phase first discussed by Son and Stephanov.
The CP-restoring phase transition at theta = pi and high temperature is investigated using two related models that aim to describe the low-energy phenomenology of QCD, the NJL model and the linear sigma model coupled to quarks. Despite many similarities between the models, different predictions for the order of the phase transition result. Using the Landau-Ginzburg formalism, the origin of this difference is traced back to a non-analytic vacuum term at zero temperature that is present in the NJL model, but usually not included in the linear sigma model. Due to the absence of explicit CP violat…
With the help of the functional integration method, the formation of scalar, pseudoscalar condensates, and dynamical symmetry breaking in the U(3) four-fermion model has been investigated. We show the possibility of spontaneous CP symmetry violation in the model under consideration. The bosonization procedures of the model are performed; the propagators of quarks, scalar and pseudoscalar fields are calculated in one loop approximation. The masses of the scalar and pseudoscalar mesons are evaluated.
In this talk we discuss the role of inhomogeneous phases in the phase diagram of the Nambu-Jona-Lasinio (NJL) and the quark meson (QM) model. By means of a generalized Ginzburg-Landau (GL) expansion it is concluded that the critical point in the mean-field phase diagram of the NJL model is in fact a Lifshitz point where homogeneous spontaneously broken, inhomogeneous and restored phases meet. This picture is confirmed by a mean-field calculation for inhomogeneous phases with a one-dimensional modulation. For the latter it is shown that recent results within lower dimensional models can be exte…
Spontaneous CP-violation in the strong interaction is analyzed at theta = pi within the framework of the two-flavor NJL model. It is found that the occurrence of spontaneous CP-violation at theta = pi depends on the strength of the 't Hooft determinant interaction, which describes the effect of instanton interactions. The dependence of the phase structure, and in particular of the CP-violating phase, on the quark masses, temperature, baryon and isospin chemical potential is examined in detail. When available a comparison to earlier results from chiral perturbation theory is made. From our resu…
According to the Ideal Walking Technicolor paradigm large mass anomalous dimensions arise in gauged Nambu--Jona-Lasinio (NJL) models when the four-fermion coupling is sufficiently strong to induce spontaneous symmetry breaking in an otherwise conformal gauge theory. We therefore study the $SU(2)$ gauged NJL model with two adjoint fermions using lattice simulations. The model is in an infrared conformal phase at small NJL coupling while it displays a chirally broken phase at large NJL couplings. In the infrared conformal phase we find that the mass anomalous dimension varies with the NJL coupli…
This work proposes a stringent concept of matter mass generation and Theta vacuum in the context of local gauge theory for the strong force under the constraint of the flat universe. The matter mass is generated as the consequence of dynamical spontaneous symmetry breaking (DSSB) of gauge symmetry and discrete symmetries, which is motivated by the parameter Theta representing the surface term. Matter mass generation introduces the typical features of constituent particle mass, dual Meissner effect, and hyperfine structure. The Theta term plays important roles on the DSSB of the gauge group and…
In this paper we explore the chiral phase transition in QCD within the three-flavor Nambu-Jona-Lasinio (NJL) model with a negative coupling constant in the isoscalar axial-vector channel, which is associated with a polarized instanton--anti-instanton molecule background. The QCD phase diagram described in this scenario shows a new first order phase transition around the transition temperature $T_c$ toward a phase without chiral condensates, but with nontrivial dynamic chiral chemical potentials for the light quarks, spontaneously giving rise to local $\mathcal {CP}$ violation and local chirali…
We consider QCD at Theta ~ Pi with two, one and zero light flavours Nf, using the Di Vecchia-Veneziano-Witten effective lagrangian. For Nf=2, we show that CP is spontaneously broken at Theta = Pi for finite quark mass splittings, z= Md/Mu \not= 1. In the z-Theta plane, there is a line of first order transitions at Theta = Pi with two critical endpoints, z1* < z < z2*. We compute the tension of the domain walls relating the two CP violating vacua. For Mu=Md the tension of the family of equivalent domain walls agrees with the expression derived by Smilga from chiral perturbation theory at next-t…
The description of baryons as chiral solitons of the Nambu--Jona--Lasinio (NJL) model is reviewed. A motivation for the soliton description of baryons is provided from large $N_C$ QCD. Rigorous results on the spontaneous breaking of chiral symmetry in QCD are discussed. It is then argued that the NJL model provides a fair description of low--energy hadron physics. The NJL model is therefore employed to mimic the low--energy chiral flavor dynamics of QCD. The model is bosonized by functional integral techniques and the physical content of the emerging effective meson theory is discussed. In par…
We explore the physical consequences of a scenario when the standard Hermitian Nambu--Jona-Lasinio (NJL) model spontaneously develops a non-Hermitian PT-symmetric ground state via dynamical generation of an anti-Hermitian Yukawa coupling. We demonstrate the emergence of a noncompact non-Hermitian (NH) symmetry group which characterizes the NH ground state. We show that the NH group is spontaneously broken both in weak- and strong-coupling regimes. In the chiral limit at strong coupling, the NH ground state develops inhomogeneity, which breaks the translational symmetry. At weak coupling, the N…
We consider massive $SU(N)$ gauge theory with fermions. Gauge bosons become massive due to the interaction with the scalar field, whose vacuum average provides the spontaneous breakdown of gauge symmetry. We investigate Dyson - Schwinger equation for the fermion propagator written in ladder approximation and in Landau gauge. Our analysis demonstrates that the chiral symmetry breaking in the considered theory is the strong coupling phenomenon. There are the indications that there appears the second order phase transition between chirally broken and symmetric phases of the theory at the value of…
This study proposes that the longstanding problems of quantum chromodynamics (QCD) as an SU(3)_C gauge theory, the confinement mechanism and Θvacuum, can be resolved by dynamical spontaneous symmetry breaking (DSSB) through the condensation of singlet gluons and quantum nucleardynamics (QND) as an SU(2)_N x U(1)_Z gauge theory is produced. The confinement mechanism is the result of massive gluons and the Yukawa potential provides hadron formation. The evidences for the breaking of discrete symmetries (C, P, T, CP) during DSSB appear explicitly: baryons and mesons without their parity partners,…
Charge conjugation (C) and Parity (P) are exact symmetries at theta =pi and Theta = mu/(iT)=pi, where theta is the parameter of the so-called theta-vacuum, mu is the imaginary quark-number chemical potential and T is the temperature. Spontaneous breakings of these discrete symmetries are investigated by the the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. At zero T, P symmetry is spontaneously broken while C symmetry is conserved. As T increases, P symmetry is restored just after C symmetry is spontaneously broken, so that either P or C symmetry or both the symmetries are spontaneo…
We consider an extended Nambu--Jona-Lasinio model including both (q \bar q)- and (qq)-interactions with two light-quark flavors in the presence of a single (quark density) chemical potential. In the color superconducting phase of the quark matter the color SU(3) symmetry is spontaneously broken down to SU(2). If the usual counting of Goldstone bosons would apply, five Nambu-Goldstone (NG) bosons corresponding to the five broken color generators should appear in the mass spectrum. Unlike that expectation, we find only three gapless diquark excitations of quark matter. One of them is an SU(2)-si…
We formulate the covariant equations for quark-antiquark bound states in Minkowski space in the framework of the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We show that these equations are charge-conjugation invariant, and that in the chiral limit of vanishing bare quark mass, a massless pseudoscalar bound state is produced in a Nambu-Jona-Lasinio (NJL) mechanism, which is associated with the Goldstone boson of spontaneous chiral symmetry breaking. In this introductory paper, we test the formalism …
We propose a supersymmetric SU(5) GUT model with an A_4 family symmetry - including a full flavon- and messenger sector - which realises the relation theta_13^PMNS \simeq theta_C / sqrt(2). The neutrino sector features tri-bimaximal mixing, and theta_13^PMNS \simeq theta_C / sqrt(2) emerges from the charged lepton contribution to the PMNS matrix, which in turn is linked to quark mixing via specific GUT relations. These GUT relations arise after GUT symmetry breaking from a novel combination of group theoretical Clebsch-Gordan factors, which in addition to large theta_13^PMNS lead to promising …
We study the magnetic properties of quark matter in the NJL model with the tensor interaction. The spin-polarized phase given by the tensor interaction remains even when the quark mass is zero, while the phase given by the axial vector interaction disappears. There are two kinds of spin-polarized phases: one appears in the chiral-broken phase, and the other appears in the chiral-restored phase where the quark mass is zero. The latter phase can appear independently of the strength of the tensor interaction.
We construct a supersymmeterized version of the model presented by Grimus and Lavoura (GL) in [1] which predicts theta_{23} maximal and theta_{13}=0 in the lepton sector. For this purpose, we extend the flavor group, which is D4 x Z2^{(aux)} in the original model, to D4 x Z5. An additional difference is the absence of right-handed neutrinos. Despite these changes the model is the same as the GL model, since theta_{23} maximal and theta_{13}=0 arise through the same mismatch of D4 subgroups, D2 in the charged lepton and Z2 in the neutrino sector. In our setup D4 is solely broken by gauge single…
Nambu-Jona-Lasinio-type models are frequently employed as low-energy models in various research fields. With respect to the theory of the strong interaction, this class of models is indeed often used to analyze the structure of the phase diagram at finite temperature and quark chemical potential. The predictions from such models for the phase structure at finite quark chemical potential are of particular interest as this regime is difficult to access with lattice Monte Carlo approaches. In this work, we consider a Fierz-complete version of a Nambu-Jona-Lasinio model. By studying its renormaliz…
In [1] it has been shown that the Cabibbo angle theta_C might arise from a dihedral flavor symmetry which is broken to different (directions of) subgroups in the up and the down quark sector. This leads to a prediction of theta_C in terms of group theoretical quantities only, i.e. the index n of the dihedral group D_n, the index j of the fermion representation 2_j and the preserved subgroups indicated by m_u and m_d. Here we construct a low energy model which incorporates this idea. The gauge group is the one of the Standard Model and D_7 x Z_2 ^(aux) serves as flavor symmetry. The additional …
We briefly review the cases of forced and spontaneous chiral symmetry breaking. In particular the chiral condensate of q anti-q pairs is parametrized with two angles, phi which measures the chiral condensation, and theta which measures the chiral rotation. The strong CP problem arises when it is assumed that the current quark masses of the Standard Model, have a theta phase that differs from the phase induced by the instanton term wich is originated in the QCD sector of the Standard Model. We show how chiral symmetry breaking may solve the strong CP problem at the BCS level. We show variationa…
We construct a supersymmetric model with the flavor symmetry D14 in which the CKM matrix element |V_{ud}| can take the value |V_{ud}| =cos (pi/14) = 0.97493 implying that the Cabibbo angle theta_C is sin (theta_C) = |V_{us}| = sin (pi/14) = 0.2225. These values are very close to those observed in experiments. The value of |V_{ud}| (theta_C) is based on the fact that different Z2 subgroups of D14 are conserved in the up and down quark sector. In order to achieve this, D14 is accompanied by a Z3 symmetry. The spontaneous breaking of D14 is induced by flavons, which are scalar gauge singlets. The…
Quantum weakdynamics (QWD) as an SU(3)_I gauge theory with the Theta vacuum term is considered to be the unification of the electroweak interaction as an SU(2)_L x U(1)_Y gauge theory. The grand unification of SU(3)_I x SU(3)_C beyond the standard model SU(3)_C x SU(2)_L x U(1)_Y is established by the group SU(3)_I. The grand unified interactions break down to weak and strong interactions at a new grand unification scale 10^{3} GeV, through dynamical spontaneous symmetry breaking (DSSB); the weak and strong coupling constants are the same, alpha_i = alpha_s ~ 0.12, at this scale. DSSB is reali…
NJL-type effective models represent a low-energy realization of QCD and incorporate pertinent aspects such as chiral symmetry and its spontaneous breaking, the center symmetry in the heavy-quark limit as well as the axial anomaly. One such model, the Polyakov-quark-meson model for three light quark flavors, is introduced in order to study the phase structure of strongly-interacting matter. With recent high-statistics lattice QCD simulations of the finite-temperature equation of state, a detailed comparison with model results becomes accessible. Such comparisons allow to estimate volume and tru…
A non-zero CP-violating $θ$ parameter is treated in the domain model which assumes a cluster-like vacuum structure whose units are characterised in particular by a topological charge which is not necessarily an integer number. In the present paper we restrict consideration to rational values of the charge. The model has previously been shown to manifest confinement, spontaneous chiral symmetry breaking and the absence of an axial U(1) Goldstone boson. We find that the specific structure of the minima of the free energy density of the domain ensemble forces a $2π$-periodicity of observables in …
We recently proposed a spontaneous A$_{4}$ flavor symmetry breaking scheme implemented in a warped extra dimensional setup to explain the observed pattern of quark and lepton masses and mixings. The main features of this choice are the explanation of fermion mass hierarchies by wave function overlaps, the emergence of tribimaximal (TBM) neutrino mixing and zero quark mixing at the leading order and the absence of tree-level gauge mediated flavor violation. Quark mixing and deviations from TBM neutrino mixing are induced by the presence of bulk A$_4$ flavons, which allow for "cross-brane" inter…
We propose a model of spontaneous CP violation to address the strong CP problem in warped extra dimensions that relies on sequestering flavor and CP violation. We assume that brane-localized Higgs Yukawa interactions respect a U(3) flavor symmetry that is broken only by bulk fermion mass and Yukawa terms. All CP violation arises from the vev of a CP-odd scalar field localized in the bulk. To suppress radiative corrections to theta-bar, the doublet quarks in this model are localized on the IR brane. We calculate constraints from flavor-changing neutral currents (FCNCs), precision electroweak me…
