arXiv subjects

A. Gomez Nicola

Publications and source records attributed to A. Gomez Nicola.

At least 19 recordsLinked to original sources

arXiv2018

Patterns and partners for chiral symmetry restoration

We present and analyze a new set of Ward Identities which shed light on the distinction between different patterns of chiral symmetry restoration in QCD, namely $O(4)$ vs $O(4)\times U(1)_A$. The degeneracy of chiral partners for all scalar and pseudoscalar meson nonet members are studied through their corresponding correlators. Around chiral symmetry degeneration of $O(4)$ partners, our analysis predicts that $U(1)_A$ partners are also degenerated. Our analysis also leads to $I=1/2$ scalar-pseudoscalar partner degeneration at exact chiral restoration, and supports ideal mixing between the $η$-$η^\prime$ and the $f_0(500)$-$f_0(980)$ mesons at $O(4)\times U(1)_A$ restoration, with a possible range where the pseudoscalar mixing vanishes if the two transitions are well separated. We test our results with lattice data and provide further relevant observables regarding chiral and $U(1)_A$ restoration for future lattice and model analyses.

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arXiv2016

Pseudoscalar susceptibilities and quark condensates: chiral restoration and lattice screening masses

We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the $η$-$η'$ sector and the $U_A(1)$ anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard $SU(3)$ framework for the octet case and combining the use of the $U(3)$ framework and the large-$N_c$ expansion of QCD to account properly for the nonet sector and anomalous contributions. The analysis is performed including finite temperature corrections as well as the calculation of $U(3)$ quark condensates and all pseudoscalar susceptibilities, which together with the full set of Ward identities, are new results of this work. Finally, the Ward identities are used to derive scaling relations for pseudoscalar masses, which explain the behavior with temperature of lattice screening masses near chiral symmetry restoration.

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arXiv2014

Electromagnetic effects in the pion dispersion relation at finite temperature

We investigate the charged-neutral pion self-energy difference at finite temperature. Within Chiral Perturbation Theory we extend previous analysis in the chiral and soft pion limits. Our analysis with physical masses leads to additional contributions for temperatures typical of a meson gas, including a momentum-dependent function for the self energy. In addition, a nonzero imaginary part arises, which we define consistently in the Coulomb gauge and comes from an infrared enhanced contribution due to thermal bath photons. For distributions typical of a heavy-ion meson gas, the charged and neutral pion masses and their difference depend on temperature through slowly increasing functions. Chiral symmetry restoration is ultimately responsible for keeping the corrections smooth and compatible with observed pion spectra. We study phenomenological effects related to the electromagnetic damping leading to corrections for transport coefficients and neutral-charged mean free times differences. An important aspect is the connection with chiral symmetry restoration through the relation of the pion mass difference with the vector-axial spectral function difference, which holds at $T=0$ due to a sum rule in the chiral and soft pion limits. We analyze the modifications of that sum rule including nonzero pion masses and temperature, up to order $T^2$ and $M_π^2$. Both effects produce terms making the pion mass difference grow against chiral-restoring decreasing contributions. Finally, we analyze the corrections to the previous ChPT and sum rule results within the resonance saturation framework at finite temperature, including explicitly $ρ$ and $a_1$ exchanges. Our results show that the ChPT result is robust at low and intermediate temperatures, the leading corrections being of order $T^2 M_π^2/M_R^2$ with $M_R$ the involved resonance masses.

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arXiv2013

Chiral Symmetry Restoration and Scalar-Pseudoscalar partners in QCD

We describe Scalar-Pseudoscalar partner degeneration at the QCD chiral transition in terms of the dominant low-energy physical states for the light quark sector. First, we obtain within model-independent one-loop Chiral Perturbation Theory (ChPT) that the QCD pseudoscalar susceptibility is proportional to the quark condensate at low $T$. Next, we show that this chiral-restoring behaviour for $χ_P$ is compatible with recent lattice results for screening masses and gives rise to degeneration between the scalar and pseudoscalar susceptibilities ($χ_S$, $χ_P$) around the transition point, consistently with an O(4)-like current restoration pattern. This scenario is clearly confirmed by lattice data when we compare $χ_S(T)$ with the quark condensate, expected to scale as $χ_P(T)$. Finally, we show that saturating $χ_S$ with the $σ/f_0(500)$ broad resonance observed in pion scattering and including its finite temperature dependence, allows to describe the peak structure of $χ_S(T)$ in lattice data and the associated critical temperature. This is carried out within a unitarized ChPT scheme which generates the resonant state dynamically and is also consistent with partner degeneration.

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arXiv2013

Pion masses at finite temperature

We present preliminary results on a study about the thermal variation of the charged and neutral pion masses to one loop, analyzing their electromagnetic difference, in the context of Chiral Perturbation Theory with two flavours, as well as using a light resonance model. We find that the pion mass difference increases for, at least, low and intermediate temperatures, unlike the chiral limit decreasing result. The axial-vector mixing arising from chiral restoration smooths the Debye-screening temperature increase. Taking into account further corrections due to axial and vector resonances, dominated by a1 and rho particles respectively, does not change significantly the ChPT prediction.

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arXiv2013

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 NNLO in ChPT, thus extending previous results to include kaon and eta interactions. This allows 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 $σ$ resonance is largely canceled with the scalar isospin two channel interaction, leaving the $ρ(770)$ as the main contribution. Special attention is paid to the evolution towards chiral restoration, as well as to the comparison with recent lattice analysis.

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arXiv2011

Scalar susceptibilities and Electromagnetic thermal mass differences in Chiral Perturbation Theory

We make a thermal analysis of the light scalar susceptibilities using SU(3)-Chiral Perturbation Theory to one loop taking into account the QCD source of isospin breaking (IB), i.e corrections coming from $m_u\neq m_d$. The value of the connected scalar susceptibility in the infrared regime, the one relevant when approaching chiral symmetry restoration, and below the critical temperature is found to be entirely dominated by the $π^0-η$ mixing, which leads to model-independent $\mathcal{O}(ε^0)$ corrections, where $ε\sim m_d-m_u$, in the combination $χ_{uu}-χ_{ud}$ of flavour breaking susceptibilities. We also present preliminary results for the corrections to the real part of the pion self-energy at nexst-to-leading order in SU(2)-Chiral Perturbation Theory taking into account electromagnetic interaction. The zero and finite temperature results for the charged and neutral pions are given in terms of the three-momentum of the external pion; and their difference is calculated to this order stressing the fact that, at low and moderate temperature, the mass splitting $M_{π^\pm}-M_{π^0}$ grows with temperature for, at least, non-zero charged pion mass running inside the loops.

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arXiv2011

Isospin-Breaking quark condensates in Chiral Perturbation Theory

We analyze the isospin-breaking corrections to quark condensates within one-loop SU(2) and SU(3) Chiral Perturbation Theory including $m_u\neq m_d$ as well as electromagnetic (EM) contributions. The explicit expressions are given and several phenomenological aspects are studied. We analyze the sensitivity of recent condensate determinations to the EM low-energy constants (LEC). If the explicit chiral symmetry breaking induced by EM terms generates a ferromagnetic-like response of the vacuum, as in the case of quark masses, the increasing of the order parameter implies constraints for the EM LEC, which we check with different estimates in the literature. In addition, we extend the sum rule relating quark condensate ratios in SU(3) to include EM corrections, which are of the same order as the $m_u\neq m_d$ ones, and we use that sum rule to estimate the vacuum asymmetry within ChPT. We also discuss the matching conditions between the SU(2) and SU(3) LEC involved in the condensates, when both isospin-breaking sources are taken into account.

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arXiv2011

Isospin Breaking and chiral symmetry restoration

We analyze quark condensates and chiral (scalar) susceptibilities including isospin breaking effects at finite temperature $T$. These include $m_u\neq m_d$ contributions as well as electromagnetic ($e\neq 0$) corrections, both treated in a consistent chiral lagrangian framework to leading order in SU(2) and SU(3) Chiral Perturbation Theory, so that our predictions are model independent. The chiral restoration temperature extracted from $<\bar q q>= <\bar u u + \bar d d >$ is almost unaffected, while the isospin breaking order parameter $<\bar u u - \bar d d >$ grows with $T$ for the three-flavour case SU(3). We derive a sum rule relating the condensate ratio $<\bar q q>(e\neq 0)/<\bar q q>(e=0)$ with the scalar susceptibility difference $χ(T)-χ(0)$, directly measurable on the lattice. This sum rule is useful also for estimating condensate errors in staggered lattice analysis. Keeping $m_u\neq m_d$ allows to obtain the connected and disconnected contributions to the susceptibility, even in the isospin limit, whose temperature, mass and isospin breaking dependence we analyze in detail. The disconnected part grows linearly, diverging in the chiral (infrared) limit as $T/M_π$, while the connected part shows a quadratic behaviour, infrared regular as $T^2/M_η^2$ and coming from $π^0η$ mixing terms. This smooth connected behaviour suggests that isospin breaking correlations are weaker than critical chiral ones near the transition temperature. We explore some consequences in connection with lattice data and their scaling properties, for which our present analysis for physical masses, i.e. beyond the chiral limit, provides a useful model-independent description for low and moderate temperatures.

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arXiv2011

Light scalar susceptibilities and the $π^0-η$ mixing

We have performed a thermal analysis of the light scalar susceptibilities in the context of SU(3)-Chiral Perturbation Theory to one loop taking into account the QCD source of isospin breaking (IB), i.e corrections coming from $m_u\neq m_d$. We find that the value of the connected scalar susceptibility in the infrared regime and below the critical temperature is entirely dominated by the $π^0-η$ mixing, which leads to model-independent $\mathcal{O}(ε^0)$ corrections, where $ε\sim m_d-m_u$, in the combination $χ_{uu}-χ_{ud}$ of flavour breaking susceptibilities.

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arXiv2010

Chiral symmetry and mesons in hot and dense matter: recent developments

We review recent results on properties of the meson gas relevant for Heavy Ion Collision and Nuclear Matter experiments, within the framework of chiral lagrangians. In particular, we describe the temperature and density evolution of the $σ$ and $ρ$ poles and its connection with chiral symmetry restoration, as well as the chemical nonequilibrated phase and transport coefficients.

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arXiv2010

Non-factorization 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. 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 non-factorization 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.

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arXiv2009

Transport coefficients of a massive pion gas

We review or main results concerning the transport coefficients of a light meson gas, in particular we focus on the case of a massive pion gas. Leading order results according to the chiral power-counting are presented for the DC electrical conductivity, thermal conductivity, shear viscosity, and bulk viscosity. We also comment on the possible correlation between the bulk viscosity and the trace anomaly in QCD, as well as the relation between unitarity and a minimum of the quotient $η/s$ near the phase transition.

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arXiv2009

Chemical nonequilibrium for interacting bosons: applications to the pion gas

We consider an interacting pion gas in the regime where thermal but not chemical equilibrium has been reached. Approximate particle number conservation is implemented by a nonvanishing pion chemical potential $μ_π$ within a diagrammatic thermal field theory approach, valid in principle for any bosonic field theory in this regime. The resulting Feynman rules are then applied within the context of Chiral Perturbation Theory to discuss thermodynamical quantities of interest for the pion gas such as the free energy, the quark condensate and thermal self-energy. In particular, we derive the $μ_π\neq 0$ generalization of Luscher and Gell-Mann-Oakes-Renner type relations. We pay special attention to the comparison with the conventional kinetic theory approach in the dilute regime, which allows for a check of consistency of our approach. Several phenomenological applications are discussed, concerning chiral symmetry restoration, freeze-out conditions and Bose-Einstein pion condensation.

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arXiv2009

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.

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arXiv2009

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 $f_0(600)$ 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 that bulk viscosity is negligible against shear viscosity, except near the chiral phase transition where the conformal anomaly might induce larger bulk effects. Different asymptotic limits for transport coefficients, large-$N_c$ scaling and some applications to heavy-ion collisions are studied.

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arXiv2008

Chiral Symmetry and light resonances in hot and dense matter

We present a study of the $ππ$ scattering amplitude in the $σ$ and $ρ$ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear density effects associated to a renormalization of the pion decay constant, and complementarily (c) by extending our calculation of the scalar-isoscalar channel to account for finite nuclear density and temperature effects in a microscopic many-body implementation of pion dynamics. Our results are discussed in connection with several phenomenological aspects relevant for nuclear matter and Heavy-Ion Collision experiments, such as $ρ$ mass scaling vs broadening from dilepton spectra and chiral restoration signals in the $σ$ channel. We also elaborate on the molecular nature of $ππ$ resonances.

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arXiv2007

The 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 from Chiral Perturbation Theory as well as for the Strongly Interacting Symmetry Breaking Sector. In this work we show how it can be slightly modified to account also for the sub-threshold region, incorporating correctly the Adler zeros required by chiral symmetry and eliminating spurious poles. These improvements produce negligible effects on the physical region.

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