Matter-induced hadronic processes

Two examples of ``exotic'' phenomena which become possible and important in the presence of nuclear matter are discussed: omega -> pi pi decay, and rho-omega mixing. Significance of these processes for the low-mass dilepton production in relativistic heavy-ion collisions is indicated.Comment: 8 pages, uses aipproc.cls, talk presented by W. Florkowski at the International Workshop on Hadron Physics "Effective Theories of Low Energy QCD", Coimbra, Portugal, September 10-15, 199

Role of current quark mass dependent multi-quark interactions in low lying meson mass spectra

We call attention to a class of current-quark mass dependent multi-quark interaction terms which break explicitly the chiral $SU(3)_L\times SU(3)_R$ and $U_A(1)$ symmetries. They complete the set of effective quark interactions that contribute at the same order in $N_c$ as the 't Hooft flavor determinant interaction and the eight quark interactions in the phase of spontaneously broken chiral symmetry. The $N_c$ classification scheme matches the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. Together with the leading in $N_c$ four quark Nambu-Jona-Lasinio Lagrangian and current quark mass matrix, the model is apt to account for the correct empirical ordering and magnitude of the splitting of states in the low lying mass spectra of spin zero mesons. The new terms turn out to be essential for the ordering $m_K < m_\eta$ in the pseudoscalar sector and $m_{\kappa_0} < m_{a_0}\sim m_{f0}$ for the scalars.Comment: 6 pages, 1 figure, prepared for the proceedings of the workshop "Excited QCD 2013", 03-09 February 2013 in Bjelasnica Mountain, Sarajevo, Bosni

Light quark mass differences in the π0−η−η′\pi^0 - \eta - \eta' system

A generalized 3 flavor Nambu-Jona--Lasinio Lagrangian including the explicit chiral symmetry breaking interactions which contribute at the same order in the large $1/N_c$ counting as the $U_A(1)$ 't Hooft flavor determinant is considered to obtain the mixing angles in the $\pi^0-\eta-\eta'$ system and related current quark mass ratios in close agreement with phenomenological values. At the same time an accurate ordering and magnitude of the splitting of states in the low lying pseudoscalar nonet is obtained.Comment: 6 pages, 4 tables, presented at the workshop "Excited QCD 2016", 05-12 March 2016, Costa da Caparica, Portugal. Submitted to Acta Phys. Pol.

Subtleties in the beta function calculation of N=1 supersymmetric gauge theories

We investigate some peculiarities in the calculation of the two-loop beta-function of $N=1$ supersymmetric models which are intimately related to the so-called "Anomaly Puzzle". There is an apparent paradox when the computation is performed in the framework of the covariant derivative background field method. In this formalism, it is obtained a finite two-loop effective action, although a non-null coefficient for the beta-function is achieved by means of the renormalized two-point function in the background field. We show that if the standard background field method is used, this two-point function has a divergent part which allows for the calculation of the beta-function via the renormalization constants, as usual. Therefore, we conjecture that this paradox has its origin in the covariant supergraph formalism itself, possibly being an artifact of the rescaling anomaly.Comment: Few misprintings corrected and comments added. To meet the version to be published at European Physical Journal

Quark mass effects in the thermodynamical properties of an extended (P)NJL model

We analyze the thermodynamical properties of a system of strongly interacting particles at vanishing quark chemical potential in the framework of a recently developed extension of the Polyakov-Nambu-Jona-Lasinio Model. In addition to eight quark interactions terms, non-canonical terms which explicitly break chiral symmetry up to the same order in a $1/N_c$ expansion ($N_c$ number of colors) are included. A recently proposed Polyakov potential is considered and the results are compared to lattice QCD data resulting in a favorable scenario for the recent model variants.Comment: To appear in the proceedings of "8th International Conference on Quarks and Nuclear Physics (QNP2018)

Effective multi-quark interactions with explicit breaking of chiral symmetry

In a long distance Lagrangian approach to the low lying meson phenomenology we present and discuss the most general spin zero multi-quark interaction vertices of non-derivative type which include a set of effective interactions proportional to the current quark masses, breaking explicitely the chiral SU(3)_L X SU(3)_R and U_A(1) symmetries. These vertices are of the sameorder in Nc counting as the 't Hooft flavor determinant interaction and the 8 quark interactions which extend the original leading in Nc four quark interaction Lagrangian of Nambu and Jona-Lasinio. The Nc assignements match the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. With path integral bosonization techniques which take appropriately into account the quark mass differences we derive the mesonic Lagrangian up to 3-point mesonic vertices. We demonstrate that explicit symmetry breaking effects in interactions are essential to obtain the correct empirical ordering and magnitude of the splitting of certain states such as m_K < m_eta for the pseudoscalars and m{kappa(800)} < m{a0(980)} m{f0(980)} in the scalar sector, and achieve total agreement with the empirical low lying meson mass spectra. With all parameters of the model fixed by the spectra we analyze further a bulk of two body decays at tree level of the bosonic Lagrangian: the strong decays of the scalars sigma->pi pi, f0->pi pi, kappa->pi K, a0(980)->pi eta, as well as the two photon decays of a0, f0 and sigma mesons and the anomalous decays of the pseudoscalars {pi,eta,eta'}-> 2 photons. Our results for the strong decays are within the current expectations and the pseudoscalar radiative decays are in very good agreement with data. The radiative decays of the scalars are smaller than the observed values for the f0 and the sigma, but reasonable for the a0. A detailed discussion accompanies all the results.Comment: 18 pages, 2 figures, 8 table