Chiral symmetry and supersymmetry in the Nambu-Jona-Lasinio model

The connection between chiral symmetry and supersymmetry is investigated in the context of a supersymmetric extension of the Nambu-Jona-Lasinio model. A supersymmetric gap equation is found and it is shown that no solution exists which breaks chiral symmetry. A simple physical argument for this phenomenon is given and possible implications for the dynamics of composite models are discussed.     

Chiral symmetry restoration in hadron spectra

The evidence and the theoretical justification of chiral symmetry restoration in high-lying hadrons is presented.     

Chiral symmetry restoration in baryon rich environments

Chiral symmetry restoration in an environment rich in baryons is studied by computer simulation methods in SU(2) and SU(3) gauge theories in the quenched approximation. The basic theory of symmetry restoration as a function of chemical potential is illusstrated and the implementation of the ideas on a lattice is made explicit. A simple mean field model is presented to guide one's expectations. The second order conjugate-gradient iterative method and the pseudo-fermion Monte Carlo procedure are convergent methods of calculating the fermion propagator in an environment rich in baryons. Computer simulations of SU(3) gauge theory show an abrupt chiral symmetry restoring transition and the critical chemical potential and induced baryon density are estimated crudely. A smoother transition is observed for the color group SU(2).     

Chiral symmetry restoration and parity mixing

We derive the expressions of the vector and axial current from a chiral Lagrangian restricted to nucleons and pions. They display mixing terms between the axial and vector currents. We study the modifications in the nuclear medium of the coupling constants of the axial current, namely the pion decay constant and the nucleonic axial one due to the requirements of chiral symmetry. We express the renormalizations in terms of the local scalar pion density. The latter also governs the quark condensate evolution and we discuss the link between this evolution and the renormalizations. In the case of the nucleon axial coupling constant this renormalization corresponds to a new type of pion exchange currents, with two exchanged pions. We give an estimate for the resulting quenching. Although moderate it helps explaining the quenching experimentally observed.     

Chiral symmetry restoration in excited hadrons and dense matter

We overview two interconnected topics: possible effective restoration of chiral symmetry in highly excited hadrons and possible existence of confined but chirally symmetric matter at low temperatures and high densities.     

Chiral symmetry restoration in excited hadrons and dense matter

We overview two interconnected topics： possible effective restoration of chiral symmetry in highly excited hadrons and possible existence of confined but chirally symmetric matter at low temperatures and high densities.     

Chiral anomaly and nucleon properties in the Nambu-Jona-Lasinio model with vector mesons

We consider the extended SU(3) Nambu and Jona-Lasinio model with explicit vector couplings in the presence of external fields. We study the chiral anomaly in this model and its implications on the properties of the nucleon described as a chiral soliton of three valence quarks bounded in mesonic background fields. For the model to reproduce the QCD anomaly it is necessary to subtract suitable local and polynomial counterterms in the external and dynamical vector and axial-vector fields. We compute the counterterms explicitly in a vector-gauge-invariant regularization, and obtain modifications to the total effective action and vector and axial currents. We study the numerical influence of those counterterms in the two-flavour version of model with dynamical σ, π, , A and ω mesons. We find that, for time-independent hedgehog configurations, the numerical effects in the nucleon mass, the isoscalar nucleon radius and the axial coupling constant are negligibly small.     

Chiral symmetry breaking in the colour dielectric model

Approximating the long-distance gluon dynamics ofSU(3)_colour by colour-dielectric block-spin variables, we obtain an effective QCD theory of a scalar colour-dielectric field and a massive colour-bleached gluon field coupled to light quarks. The massive vector field produces a strong attraction betweenq \(\bar q\) pairs, which leads toq \(\bar q\) condensation when the colour-dielectric field becomes small. We calculate \(\left\langle {\bar \psi \psi } \right\rangle\) and the pion decay constantf _n as a function of the dielectric field expectation value, by evaluating the fermion determinant in a derivative expansion, and integrating out the bosonic variables. We find that the effective quark-gluon coupling,α _s ^eff , including quark effects, is large on the surface of bags, where \(\left\langle {\bar \psi \psi } \right\rangle\) ±0, but decreases inside hadronic bags, where | \(\left\langle {\bar \psi \psi } \right\rangle\) | is decreasing.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

Chiral symmetry restoration and deconfinement in the contact interaction model of quarks with parallel electric and magnetic fields

We study the impact of steady,homogeneous,and external parallel electric and magnetic field strengths(eE ‖ eB) on the chiral symmetry breaking-restoration and confinement-deconfinement phase transition.We also sketch the phase diagram of quantum chromodynamics(QCD) at a finite temperature T and in the presence of background fields.The unified formalism for this study is based on the Schwinger-Dyson equations,symmetry preserving vector-vector contact interaction model of quarks,and an optimal time regularization scheme.At T=0,in the purely magnetic case(i.e.,eE→0),we observe the well-known magnetic catalysis effect.However,in a pure electric field background(eB→0),the electric field tends to restore the chiral symmetry and deconfinement above the pseudo-critical electric field eE_c~(χ,C).In the presence of both eE and eB,we determine the magnetic catalysis effect in the particular region where eB dominates over eE,whereas we observe the chiral inhibition(or electric chiral rotation) effect when eE overshadows eB.At finite T,in the pure electric field case,the phenomenon of inverse electric catalysis appears to exist in the proposed model.Conversely,for a pure magnetic field background,we observe the magnetic catalysis effect in the mean-field approximation and inverse magnetic catalysis with eB-dependent coupling.The combined effects of eE and eB on the pseudo-critical T_c~(χ,C) yields an inverse electromagnetic catalysis,with and without an eB-dependent effective coupling of the model.The findings of this study agree well with the already predicted results obtained via lattice simulations and other reliable effective models of QCD.     

The Nambu-Jona-Lasinio mechanism of symmetry breaking in a U(5)-invariant model

We study dynamical symmetry breaking and mass generation in a U(5) four-fermion model with two coupling constants. We show that the consistency conditions result in a connection between the dynamical masses of the fermion quintuplet. The masses of fermions and of collective states are expressed through two independent quantities only. We find the propagator of the collective fields, from which it follows that there are goldstone fields as well as fields of massive particles. The mass formulas are obtained on the basis of dimensional regularization of divergent integrals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 30–35, March, 1988.     

Chiral symmetry restoration and properties of Goldstone bosons at finite temperature

We study chiral symmetry restoration by analyzing thermal properties of QCD's(pseudo-) Goldstone bosons, especially the pion. The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions. To obtain the correlation functions, we solve the Dyson-Schwinger equations and the inhomogeneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation. In chiral limit, the pion and its partner sigma degenerate at the critical temperature begin{document}$T_{rm c}$end{document}. At begin{document}$T gtrsim T_{rm c}$end{document}, it was found that the pion rapidly dissociates, which signals deconfinement phase transition. Beyond the chiral limit, the pion dissociation temperature can be used to define the pseudo-critical temperature of the chiral phase crossover, which is consistent with that obtained by the maximum point of chiral susceptibility. A parallel analysis for kaon and pseudoscalar begin{document}$ sbar{s} $end{document} suggests that heavy mesons may survive above begin{document}$T_{rm c}$end{document}.     

Spontaneous symmetry breakdown and symmetry restoration in the statistical mechanics of a many-boson model

We study the statistical mechanics of a many-boson system with constant two-body potential energy g/N (g > 0, N is the number of bosons). The grand canonical partition function can be computed exactly by functional integration which allows for a simple discussion of spontaneous symmetry breakdown. It turns out to be possible to exhibit the healing of the broken symmetry.     

Heavy mesons in the Nambu-Jona-Lasinio model

We propose an extended Nambu-Jona-Lasinio model to include heavy mesons with heavy quark symmetry.The quark current-current interaction is generalized to include the heavy quark currents. In order to comply with the heavy quark spin symmetry at the heavy quark limit,the dependence of the quark mass on the interaction strength is introduced. The light and heavy pseudo-scalar and vector mesons,their masses and the weak decay constants are calculated in the unified frame.