The influence of strong magnetic fields and instantons on the phase structure of the two-flavor NJL model

Both in heavy-ion collisions as in magnetars very strong magnetic fields are produced, which has its influence on the phases of matter involved. In this paper we investigate the effect of strong magnetic fields (B = 5 m_pi^2 /e = 1.7 x 10^19 G) on the chiral symmetry restoring phase transition using the Nambu-Jona-Lasinio model. It is observed that the pattern of phase transitions depends on the relative magnitude of the magnetic field and the instanton interaction strength. We study two specific regimes in the phase diagram, high chemical potential and zero temperature and vice versa, which are of relevance for neutron stars and heavy-ion collisions respectively. In order to shed light on the behavior of the phase transitions we study the dependence of the minima of the effective potential on the occupation of Landau levels. We observe a near-degeneracy of multiple minima with differing occupation numbers, of which some become the global minimum upon changing the magnetic field or the chemical potential. These minima differ considerably in the amount of chiral symmetry breaking and in some cases also of isospin breaking.Comment: 11 pages, 8 figures, references added and some minor change

The high temperature CP-restoring phase transition at theta = pi

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 violation, this term always alters the qualitative aspects of the high temperature phase transition at theta = pi, just as for theta = 0 in the chiral limit.Comment: 11 pages, 1 eps figure; corrected various typos, added missing term in Eq. (13), conclusions unchanged, minor revisions to Sec. IA and II

Spontaneous CP-violation in the strong interaction at theta = pi

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 results we conclude that spontaneous CP-violation in the strong interaction is an inherently low-energy phenomenon. In all cases we find agreement with the Vafa-Witten theorem, also at nonzero density and temperature. Meson masses and mixing in the CP-violating phase display some unusual features as a function of instanton interaction strength. A modification of the condition for charged pion condensation at nonzero isospin chemical potential and a novel phase of charged a_0 mesons are discussed.Comment: 15 pages, 11 eps figures; matches version published in Phys. Rev. D, reference added, corrected Eq. 16, modified discussion Ref.

The box diagram in Yukawa theory

We present a light-front calculation of the box diagram in Yukawa theory. The covariant box diagram is finite for the case of spin-1/2 constituents exchanging spin-0 particles. In light-front dynamics, however, individual time-ordered diagrams are divergent. We analyze the corresponding light-front singularities and show the equivalence between the light-front and covariant results by taming the singularities.Comment: 21 pages, 17 figures. submittes to Phys. Rev.

Spontaneous CP violation in the NJL model at theta = pi

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.Comment: 5 pages, 7 figures; talk given at the 8th Conference "Quark Confinement and the Hadron Spectrum", Mainz, Germany, 1-6 September 200