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 ∼ 5m 2 π /e = 1.7 × 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.

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The CP-restoring phase transition at θ = π 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 θ = π, just as for θ = 0 in the chiral limit.PACS numbers: 12.39. 11.30.Er,11.30.Rd It is well known that there is a possibility of CP violation in the strong interaction due to instanton contributions. These contributions are incorporated in the QCD Lagrangian through the topological θg 2 32π 2 FF -term, where θ is the QCD vacuum angle. This term violates CP, unless θ = 0 mod π. The case θ = π is special, because then Dashen's phenomenon can occur, i.e., spontaneous CP violation atFrom experiments it is known that in nature θ is very small [2,3,4,5]. The reason for this is unknown and is commonly referred to as the strong CP problem. However, it has been argued that in heavy-ion collisions meta-stable CP-violating states could be created corresponding to states with an effective θ [6,7,8,9,10,11,12,13]. Studying the behavior of the strong interactions at nonzero θ is therefore of interest and has been done quite extensively using chiral Lagrangians, see for example Refs [14,15,16,17,18,19,20].Recently the θ-dependence of two models describing the chiral dynamics of low energy QCD have been studied, the NJL model [21] and the linear sigma model coupled to quarks (LSMq) [22]. In both models the effects of instantons are included through an additional interaction, the 't Hooft determinant interaction [23,24]. It was found that both models exhibit Dashen's phenomenon, which turns out to be temperature dependent. This is to be expected, since at high temperature the effects of instantons, which are needed for the CP violation, are exponentially suppressed [25]. In both models the spontaneous CP violation at θ = π disappears at a critical temperature between 100 and 200 MeV, however, the order of the phase transition differs. In case of the NJL model the transition is of second order, whereas in the LSMq model it is of first order. Clearly this difference is important, because a first order transition allows meta-stable phases, in contrast to a second order transition.Although the NJL and LSMq model are not the same, they are closely related. Eguchi [26] has shown that when the NJL model is bosonized, a linear sigma model is obtained (see also [27]). However, the effects of quarks are treated differently in both models, which was already discussed in Ref. [28] for θ = 0. In the case of the LSMq model the effects of the quarks are usual...

Spontaneous CP-violation in the strong interaction is analyzed at θ = π within the framework of the two-flavor NJL model. It is found that the occurrence of spontaneous CP-violation at θ = π 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 lowenergy 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 a0 mesons are discussed.

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.