A. Gomez Nicola

Meson meson scattering within one loop chiral perturbation theory and its unitarization

We present a complete one-loop calculation of all the two-meson scattering amplitudes within the framework of SU(3) chiral perturbation theory, which includes pions, kaons, and the eta. In addition, we have unitarized these amplitudes with the coupled channel inverse amplitude method, which simultaneously ensures the good low energy properties of chiral perturbation theory and unitarity. We show how this method provides a remarkable description of meson-meson scattering data up to 1.2 GeV including the scattering lengths and the generation of seven light resonances, which is consistent with previous determinations of the chiral parameters. Particular attention is paid to discussing the differences and similarities of this work with previous analyses in the literature.

Bulk Viscosity and the Conformal Anomaly in the Pion Gas

We calculate the bulk viscosity of the massive pion gas within unitarized chiral perturbation theory. We obtain a low-temperature peak arising from explicit conformal breaking due to the pion mass and another peak near the critical temperature, dominated by the conformal anomaly through gluon condensate terms. The correlation between bulk viscosity and conformal breaking supports a recent QCD proposal. We discuss the role of resonances, heavier states, and large-N_(c) counting.

Transport coefficients and resonances for a meson gas in chiral perturbation theory

We present recent results on a systematic method to calculate transport coefficients for a meson gas (in particular, we analyze a pion gas) at low temperatures in the context of Chiral Perturbation Theory (ChPT). Our method is based on the study of Feynman diagrams taking into account collisions in the plasma by means of the non-zero particle width. This implies a modification of the standard ChPT power counting scheme. We discuss the importance of unitarity, which allows for an accurate high-energy description of scattering amplitudes, generating dynamically the ρ(770) and f0(600) mesons. Our results are compatible with analyses of kinetic theory, both in the non-relativistic very low-T regime and near the transition. We show the behavior with temperature of the electrical and thermal conductivities as well as of the shear and bulk viscosities. We obtain the result that the bulk viscosity is negligible against the shear viscosity, except near the chiral phase transition where the conformal anomaly might induce larger bulk effects. Various asymptotic limits for transport coefficients, large-Nc scaling and some applications to heavy-ion collisions are studied.We present recent results on a systematic method to calculate transport coefficients for a meson gas (in particular, we analyze a pion gas) at low temperatures in the context of Chiral Perturbation Theory (ChPT). Our method is based on the study of Feynman diagrams taking into account collisions in the plasma by means of the non-zero particle width. This implies a modification of the standard ChPT power counting scheme. We discuss the importance of unitarity, which allows for an accurate high-energy description of scattering amplitudes, generating dynamically the ρ(770) and f0(600) mesons. Our results are compatible with analyses of kinetic theory, both in the non-relativistic very low-T regime and near the transition. We show the behavior with temperature of the electrical and thermal conductivities as well as of the shear and bulk viscosities. We obtain the result that the bulk viscosity is negligible against the shear viscosity, except near the chiral phase transition where the conformal anomaly might induce larger bulk effects. Various asymptotic limits for transport coefficients, large-Nc scaling and some applications to heavy-ion collisions are studied.

Inverse amplitude method and Adler zeros

The inverse amplitude method is a powerful unitarization technique to enlarge the energy applicability region of effective Lagrangians. It has been widely used to describe resonances in hadronic physics, combined with chiral perturbation theory, as well as in the strongly interacting symmetry breaking sector. In this work we show how it can be slightly modified to also account for the subthreshold region, incorporating correctly the Adler zeros required by chiral symmetry and eliminating spurious poles. These improvements produce negligible effects on the physical region.

Electrical conductivity of a pion gas

The electrical conductivity of a pion gas at low temperatures is studied in the framework of linear response and chiral perturbation theory. The standard ChPT power counting has to be modified to include pion propagator lines with a nonzero thermal width in order to properly account for collision effects typical of kinetic theory. With this modification, we discuss the relevant chiral power counting to be used in the calculation of transport coefficients. The leading order contribution is found and we show that the dominant higher order ladder diagrams can be treated as perturbative corrections at low temperatures. We find that the DC conductivity sigma(T) is a decreasing function of T, behaving for very low T as sigma(T)similar to e(2)m(pi) root m pi/T, consistently with nonrelativistic kinetic theory. When unitarization effects are included, sigma(T) increases slowly as T approaches the chiral phase transition. We compare with related works and discuss some physical consequences, especially in the context of the low-energy hadronic photon spectrum in relativistic heavy ion collisions.

Improved unitarized heavy baryon chiral perturbation theory for pi N scattering

Abstract We show how the unitarized description of pion nucleon scattering within Heavy Baryon Chiral Perturbation Theory can be considerably improved, by a suitable reordering of the expansion over the nucleon mass. Within this framework, the Δ resonance and its associated pole can be recovered from the chiral parameters obtained from low-energy determinations. In addition, we can obtain a good description of the six S and P wave phase shifts in terms of chiral parameters with a natural size and compatible with the Resonance Saturation Hypothesis.

Transport coefficients in Chiral Perturbation Theory

Abstract.We present recent results on the calculation of transport coefficients for a pion gas at zero chemical potential in Chiral Perturbation Theory (ChPT) using the Linear Response Theory (LRT). More precisely, we show the behavior of DC conductivity and shear viscosity at low temperatures. To compute transport coefficients, the standard power counting of ChPT has to be modified. The effects derived from imposing unitarity are also analyzed. As physical applications in relativistic heavy-ion collisions, we show the relation of the DC conductivity to soft-photon production and phenomenological effects related to a non-zero shear viscosity. In addition, our values for the shear viscosity to entropy ratio satisfy the KSS bound.

Scalar susceptibilities and four-quark condensates in the meson gas within chiral perturbation theory

We analyze the properties of four-quark condensates and scalar susceptibilities in the meson gas, within finite temperature chiral perturbation theory (ChPT). The breaking of the factorization hypothesis does not allow for a finite four-quark condensate and its use as an order parameter, except in the chiral limit. This is rigorously obtained within ChPT and is therefore a model-independent result. Factorization only holds formally in the large N-c limit and breaks up at finite temperature even in the chiral limit. Nevertheless, the factorization breaking terms are precisely those needed to yield a finite scalar susceptibility, deeply connected to chiral symmetry restoration. Actually, we provide the full result for the SU(3) quark condensate to next-to-next-to- leading order in ChPT, thus extending previous results to include kaon and eta interactions. This allows us to check the effect of those corrections compared to previous approaches and the uncertainties due to low-energy constants. We provide a detailed analysis of scalar susceptibilities in the SU(3) meson gas, including a comparison between the pure ChPT approach and the virial expansion, where the unitarization of pion scattering is crucial to achieve a more reliable prediction. Through the analysis of the interactions within this approach, we have found that the role of the sigma resonance is largely canceled with the scalar isospin two-channel interaction, leaving the rho(770) as the main contribution. Special attention is paid to the evolution towards chiral restoration, as well as to the comparison with recent lattice analysis. DOI: 10.1103/PhysRevD.87.016001

Nonfactorization of four-quark condensates at low energies within chiral perturbation theory

Four-quark correlators and the factorization hypothesis are analyzed in the meson sector within chiral perturbation theory. We define the four-quark condensate as lim(x -> 0) , which is equivalent to other definitions commonly used in the literature. Factorization of the four-quark condensate holds to leading and next to leading order. However, at next to next to leading order, a term with a nontrivial space-time dependence in the four-quark correlator yields a divergent four-quark condensate, whereas the two-quark condensate and the scalar susceptibility are finite. Such a nonfactorization term vanishes only in the chiral limit. We also comment on how factorization still holds in the large N-c limit, provided such a limit is taken before renormalization.

Unitarized pion-nucleon scattering within Heavy Baryon Chiral Perturbation Theory

By means of the inverse amplitude method we unitarize the elastic pion-nucleon scattering amplitudes obtained from heavy baryon chiral perturbation theory to O(q(3)). Within this approach we can enlarge their applicability range and generate the Delta(1232) resonance. We can find a reasonable description of the pion nucleon phase shifts with O(q(2)) parameters in agreement with the resonance saturation hypothesis. However, the uncertainties in the analysis of the low energy data as well as the large number of chiral parameters, which can have strong correlations, allow us to obtain very good fits with rather different sets of chiral constants.