We consider the low energy realization of QCD in terms of mesons when an axial chemical potential is present; a situation that may be relevant in heavy ion collisions. We shall demonstrate that the presence of an axial charge has profound consequences on meson physics. The most notorious effect is the appearance of an explicit source of parity breaking. The eigenstates of strong interactions do not have a definite parity and interactions that would otherwise be forbidden compete with the familiar ones. In this work we focus on scalars and pseudoscalars that are described by a generalized linear sigma model. We comment briefly on the screening role of axial vectors in formation of effective axial charge and on the possible experimental relevance of our results, whose consequences may have been already seen at RHIC.

We propose that local parity breaking induced by a large-scale fluctuation of topological charge at large temperatures and/or condensation of pseudoscalar mesons in the isotriplet channel for large baryon densities may be responsible for the substantial dilepton excess that is found for low invariant masses and moderate values of $p_T$ in central heavy ions collisions. This insofar unexplained enhancement could be understood by a combination of two effects leading both to an excess of $e^+e^-$ and $\mu^+ \mu^-$ pairs with respect to theoretical predictions based on conventional hadronic processes: (a) a modification of the dispersion relation of photons and vector mesons propagating in such a nuclear medium due to local parity breaking; (b) the appearance of new decay channels, forbidden by parity conservation in QCD in the usual vacuum. Possible signatures of this effect and perspectives for its detection are discussed.Comment: 11 pages, refs corrected, PLB versio

We consider the 'two flavour' Nambu-JonaLasinio model in the presence of a vector and an axial external chemical potential and study the phase structure of the model at zero temperature. The Nambu-Jona-Lasinio model is often used as a toy replica of QCD and it is therefore interesting to explore the consequences of adding external vector and axial chemical potentials in this model, mostly motivated by claims that such external drivers could trigger a phase where parity could be broken in QCD. We are also motivated by some lattice analysis that attempt to understand the nature of the so-called Aoki phase using this simplified model. Analogies and differences with the expected behaviour in QCD are discussed and the limitations of the model are pointed out. MotivationIn the last years, the possibility that parity breaks in QCD at high temperatures and/or densities has received a lot of attention [1][2][3][4][5][6][7][8]. Although parity is well known to be a symmetry of strong interactions, there are reasons to believe that it may be broken under extreme conditions. On the one hand, theoretical work using effective meson Lagrangians satisfying the QCD symmetries at low energies suggest that for some values of the vector chemical potential μ a new phase with an isotriplet pseudoscalar condensate may arise [7,8]. On the other hand, thermal fluctuations in a finite volume may lead to large topological fluctuations that induce a non-trivial axial quark charge that could be described in a quasi-equilibrium situation by an axial chemical potential μ 5 [1][2][3][4][5][6][9][10][11][12][13].Checking these claims in QCD is unfortunately very difficult. For one thing, finite density numerical simulations in the lattice present serious difficulties [14][15][16][17][18][19]. A vector chemical potential in gauge theories like QCD cannot easily be a e-mail: xumeu@icc.ub.edu treated and therefore simpler models hopefully reproducing the main features of the theory may be useful. Needless to say, non-equilibrium effects are also notoriously difficult to study non-perturbatively. However, an axial chemical potential is tractable on the lattice [20,21] and with other methods [22,23].In the present paper we shall consider the Nambu-JonaLasinio model (NJL) [24][25][26][27][28][29][30], which shares interesting features with QCD such as the appearance of chiral symmetry breaking. In the NJL modelisation, QCD gluon interactions among fermions are assumed to be replaced by some effective four-fermion couplings. Confinement is absent in the NJL model, but global symmetries can be arranged to be identical in both theories.However, NJL is definitely not QCD and the present work does not attempt to draw definite conclusions on the latter theory; just to point out possible phases requiring further analysis.Previously some authors have studied the effect of a vector chemical potential μ with three flavours [31] in the NJL model, but the consequences of including both a vector and an axial chemical potentials have not been considered so...

We investigate how local parity breaking due to large topological fluctuations may affect hadron physics. A modified dispersion relation is derived for the lightest vector mesons ρ and ω. They exhibit a mass splitting depending on their polarization. We present a detailed analysis of the angular distribution associated to the lepton pairs created from these mesons searching for polarization dependencies. We propose two angular variables that carry information related to the parity breaking effect. Possible signatures for experimental detection of local parity breaking that could potentially be seen by the PHENIX and STAR collaborations are discussed.

At finite density parity can be spontaneously broken in strong interactions with far reaching implications. In particular, a time-dependent pseudoscalar background would modify QED by adding a Chern-Simons term to the lagrangian. As a striking consequence we propose a novel explanation for the dilepton excess observed in heavy ion collisions at low invariant masses. The presence of local parity breaking due to a time-dependent pseudoscalar condensate substantially modifies the dispersion relation of photons and vector mesons propagating in such a medium, changing the $\rho$ spectral function and resulting in a potentially large excess of dileptons with respect to the predictions based in a `cocktail' of known processes.Comment: 3 pages, 2 figures. Contributed to the International Conference on Quark Confinement and the Hadron Spectrum IX, Madrid, August 2010, to appear in the proceeding