arXiv subjects

A. Gómez Nicola

Publications and source records attributed to A. Gómez Nicola.

8 recordsLinked to original sources

arXiv2026

Pion scattering in finite volume within the Inverse Amplitude Method

We study the effect of a finite volume for pion-pion scattering within Chiral Perturbation Theory (ChPT) and the Inverse Amplitude Method (IAM) in a $L^3$ box (rest frame). Our full ChPT calculation takes into account the discretization not only in the $s$-channel loops but also in the $t,u$- channels and tadpole contributions. Hence, not only the unitarity right-hand cut but also the left-hand one continuum contributions are calculated in the finite volume. A proper extension of the standard Veltman-Pasarino identities is needed, as well as a suitable projection on the internal space spanned by the irreducible representations (irreps) of the octahedral group, based on either a finite set of cubic harmonics or the matrices which represent the irreps properly. From the ChPT we construct the IAM in the internal space, which provides the full volume dependence of the interacting energy levels of two-pions scattering in the finite volume. Our results for various low-energy constants sets show sizable corrections with respect to previous analyses in the literature for $ m_πL \lesssim 2$, being compatible with energy levels lattice data. We expect that our analysis and results will help to optimize the process of determination of energy levels and phase-shifts with higher accuracy.

hep-lat↗

arXiv2019

Chiral and $U(1)_A$ restoration: Ward Identities and effective theories

We discuss our recent results regarding chiral and $U(1)_A$ restoration, both from the formal point of view of QCD Ward Identities (WI) and from an Effective Theory analysis provided by $U(3)$ Chiral Perturbation Theory (ChPT) at finite temperature. Our results lead to relevant conclusions regarding the behavior of chiral partners (in terms of susceptibilities) in the limit of exact restoration and provide useful results for lattice analysis. In addition, it helps to understand the temperature dependence of lattice screening masses in terms of quark condensate combinations. The U(3) ChPT calculation supports the conclusions obtained within the WI analysis. Finally, the role of the thermal $f_0(500)$ state in chiral symmetry restoration, regarding the scalar susceptibility, is also discussed.

hep-ph↗

arXiv2019

The role of the thermal $f_0(500)$ in chiral symmetry restoration

We show that the $σ/f_0(500)$ state with finite-temperature $T$ corrections to its spectral properties included, plays an essential role for the description of the scalar susceptibility $χ_S$, signaling chiral symmetry restoration. First, we use the $O(4)$ Linear Sigma Model as a testbed to derive the connection between $χ_S$ and the $σ$ propagator and to check the validity and reliability of the approach where $χ_S$ is saturated by the $σ/f_0(500)$ inverse self-energy, which we calculate at finite $T$ to one loop. A more accurate phenomenological description is achieved by considering the saturation approach as given by the thermal $f_0(500)$ state generated in Unitarized Chiral Perturbation Theory. Such approach allows to describe fairly well recent lattice data within the uncertainty range given by the UChPT parameters. Finally, we compare the UChPT saturated description with one based on the Hadron Resonance Gas, for which the hadron mass dependences are extracted from recent theoretical analysis. Several fits to lattice data are performed, which confirm the validity of the thermal $f_0(500)$ saturated approach and hence the importance of that thermal state for chiral symmetry restoration.

hep-ph↗

arXiv2018

The role of the thermal $f_0(500)$ or sigma in chiral symmetry restoration

We analyze the $f_0(500)$ state generated as a pole of $ππ$ scattering within unitarized low-energy effective theories at finite temperature. First, we report on the $σ$ self-energy in the LSM, which is used as a benchmark in order to test the hypotheses carried out. The relation of that thermal pole with the scalar susceptibility is studied within a scalar saturation approach, which yields results complying with lattice data. The robustness and predictability of this method are studied in terms of the low-energy constants involved and the unitarization method. Our analysis highlights the importance of this thermal state to describe the main qualitative features of the scalar susceptibility around the chiral transition.

hep-ph↗

arXiv2018

Chiral and $U(1)_A$ restoration for the scalar/pseudoscalar meson nonets

We analyze the restoration pattern of the members of the scalar and pseudoscalar meson nonets under chiral $O(4)$ and $U(1)_A$ symmetries. For that purpose, we exploit QCD Ward Identities (WI), which allow one to relate susceptibilities with quark condensates, as well as susceptibility differences with meson vertices. In addition, we consider the low-energy realization of QCD provided by $U(3)$ Chiral Perturbation Theory (ChPT) at finite temperature to perform a full analysis of the different correlators involved. Our analysis suggests $U(1)_A$ partner restoration if chiral symmetry partners are also degenerated. This is also confirmed by the ChPT analysis when the light chiral limit is reached. Partner degeneration for the $I=1/2$ sector, the behavior of $I=0$ mixing and the temperature scaling of meson masses predicted by WI are also studied. Special attention is paid to the connection of our results with recent lattice analyses.

hep-ph↗

arXiv2008

Chiral extrapolation of the sigma and rho mesons from dispersion relations and Chiral Perturbation Theory

We review our recent study of the pion mass dependence of the rho and sigma resonances, generated from one-loop SU(2) Chiral Perturbation Theory (ChPT) with the Inverse Amplitude Method (IAM). In order to properly account for the Adler zero region, we also review the recently obtained modified version of the IAM; which is based on analyticity, elastic unitarity and ChPT at low energies, thus yielding the correct pion mass dependence of the resonance pole positions up to next-to-leading order in ChPT. As main results we find that the rho-pi-pi coupling constant is almost pion mass independent and that the rho mass shows a smooth pion mass dependence while that of the sigma shows a strong non-analyticity. These findings are important for studies of the meson spectrum on the lattice.

hep-ph↗

arXiv2000

Chiral Perturbation Theory and Unitarization

We review our recent work on unitarization and chiral perturbation theory both in the $ππ$ and the $πN$ sectors. We pay particular attention to the Bethe-Salpeter and Inverse Amplitude unitarization methods and their recent applications to $ππ$ and $πN$ scattering.

hep-ph↗

arXiv2000

Improved Unitarized Heavy Baryon Chiral Perturbation Theory for $πN $ Scattering

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.

hep-ph↗