Searcharxiv⌕ Search

arXiv subjects

J. R. Pelaez

Publications and source records attributed to J. R. Pelaez.

At least 37 records · Page 2Linked to original sources
arXiv2013

Determination of SU(2) Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters

We determine the values of the one- and two-loop low energy constants appearing in the SU(2) Chiral Perturbation Theory calculation of pion-pion scattering. For this we use a recent and precise sum rule determination of some scattering lengths and slopes that appear in the effective range expansion. In addition we provide sum rules for these coefficients up to third order in the expansion. Our results when using only the scattering lengths and slopes of the S, P, D and F waves are consistent with previous determinations, but seem to require higher order contributions if they are to accommodate the third order coefficients of the effective range expansion.

hep-ph↗
arXiv2013

Properties and composition of the $f_0(500)$ resonance

In this talk we review our recent developments on the understanding of the nature of the f_0(500) resonance---or sigma meson---coming from the N_c expansion, dispersion relations with Chiral Perturbation Theory, as well as finite energy sum rules and semi-local duality.

hep-ph↗
arXiv2013

Present status of light flavoured scalar resonances

This talk is a brief account of recent developments on light scalar meson spectroscopy. I mostly focus on the major revision of the $σ$ or $f_0(500)$ meson in the Review of Particle Physics, driven by new data and the accummulation of rigorous dispersive studies, but I also comment on recent updates of other scalars and future progress.

hep-ph↗
arXiv2013

Recent progress on light scalars: from confusion to precision using dispersion theory

In this talk I briefly review the recent developments on light scalar meson spectroscopy, paying particular attention to the causes of major revision of the $σ$ or $f_0(500)$ meson in the Review of Particle Phsycis. This resonance, despite playing a central role in the nucleon-nucleon attraction as well as the QCD chiral symmetry breaking, has suffered a longstanding controversy which has been acknowledged to be finally settled. The combination of new and precise data together with rigorous dispersive approaches has turned the old confusing situation about the properties of these mesons, and even thir existence in some cases, into a field which now aims at precision studies.

hep-ph↗
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.

hep-ph↗
arXiv2012

Precise determination of the f0(500) and f0(980) parameters in dispersive analysis of the pipi data

We review the use of new and precise dispersive equations, which also implement crossing symmetry, in order to shed further light on the long-standing puzzle in the parameters of the f0(500), as well as the f0(980). This puzzle is finally being settled thanks to several analyses carried out during the last years. In this talk we show how our very recent dispersive data analysis allowed for a precise and model independent determination of the amplitudes for the S,P,D and F waves. In particular, we show how the analytic continuation of once subtracted dispersion relations for the S0 wave to the complex energy plane leads to very precise results for the f0(500) pole: sqrt(s)_pole = 457^(+14)_(-13) - i 279^(+11)_(-7) MeV and for the f0(980) pole: sqrt(s)_pole = 996+/-7 - i 25^(+10)_(-6) MeV. We also comment on how these results have been already used for other practical applications, including a refit of a previous model to the pipi S-wave amplitudes below 1000 MeV, which improves its consistency with the poles found with the dispersive approach.

hep-ph↗
arXiv2011

Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory

We calculate the pion-pion elastic scattering phase shifts for pion masses from the chiral limit to values of interest for lattice studies. At low energies, we use the standard Chiral Perturbation Theory expressions to one and two loops. In addition, we study the phase shifts mass dependence in the resonance region by means of dispersion theory in the form of unitarized Chiral Perturbation Theory and the Inverse Amplitude Method. We pay particular attention to the case when resonances are close to threshold, illustrating the different behavior between scalar and vector resonances. We also provide the estimation of uncertainties, which are dominated by those of the O(p^6) chiral parameters.

hep-ph↗
arXiv2011

Enhanced non-quark-antiquark and non-glueball Nc behavior of light scalar mesons

We show that the latest and very precise dispersive data analyses require a large and very unnat- ural fine-tuning of the 1/Nc expansion at Nc = 3 if the f_0(600) and K(800) light scalar mesons are to be considered predominantly quark-antiquark states, which is not needed for light vector mesons. For this, we use scattering observables whose 1/Nc corrections are suppressed further than one power of 1/Nc for quark-antiquark or glueball states, thus enhancing contributions of other nature. This is achieved without using unitarized ChPT, but if it is used we can also show that it is not just that the coefficients of the 1/Nc expansion are unnatural, but that the expansion itself does not even follow the expected 1/Nc scaling of a glueball or a quark-antiquark meson.

hep-ph↗
arXiv2011

Mass dependence of pion-pion phase shifts within standard and unitarized ChPT versus Lattice results

We report on our recent results in the study of the chiral extrapolation of the phase-shifts in elastic pion-pion scattering, using both standard and unitarized ChPT to one and two loops. In the standard ChPT approach, limited to low momenta, we study the S, P and D waves. Unitarization extends the analysis to energies of around 1 GeV, being compatible with standard ChPT at low energies for the S and P waves. We then compare with lattice results and find a good agreement of standard ChPT below p \sim 200 MeV for the I=2, J=0 and I=1, J=1 channels and up to p \sim 500 MeV for the I=2, J=2 channel. Unitarized ChPT improves the agreement in the scalar and vector channels at higher energies. We have also performed a Montecarlo analysis to provide an estimation of the uncertainties.

hep-ph↗
arXiv2011

Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis

We use our latest dispersive analysis of pion-pion scattering data and the very recent Kl4 experimental results to obtain the mass, width and couplings of the two lightest scalar-isoscalar resonances. These parameters are defined from their associated poles in the complex plane. The analytic continuation to the complex plane is made in a model independent way by means of once and twice subtracted dispersion relations for the partial waves, without any other theoretical assumption. We find the f0(600) pole at (457^{+14}_{-13})-i(279^{+11}_{-7}) MeV and that of the f0(980) at (996\pm7)-i(25^{+10}_{-6}) MeV, whereas their respective couplings to two pions are 3.59^{+0.11}_{-0.13} GeV and 2.3\pm0.2 GeV.

hep-ph↗
arXiv2011

N_c and m_pi dependence of rho and sigma mesons from unitarized Chiral Perturbation Theory

We review our work on the rho and sigma resonances derived from the Inverse Amplitude Method. In particular, we study the leading 1/N_c behavior of the resonances masses and widths and their evolution with changing m_pi. The 1/N_c expansion gives a clear definition of quark-antiquark states, which is neatly satisfied by the rho but not by the sigma, showing that its dominant component is not quark-antiquark. The m_pi dependence of the resonance properties is relevant to connect with lattice studies. We show that our predictions compare well with some lattice results and we find that the rho-pi-pi coupling constant is m_pi independent, in contrast with the sigma-pi-pi coupling, that shows a strong m_pi dependence.

hep-ph↗
arXiv2010

Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results

We study the pion mass dependence of the rho(770) and f_0(600) masses and widths from one and two-loop unitarized Chiral Perturbation Theory. We show the consistency of one-loop calculations with lattice results for the M_rho, f_pi and the isospin 2 scattering length a_20.Then, we develop and apply the modified Inverse Amplitude Method formalism for two-loop ChPT. In contrast to the f_0(600), the rho(770) is rather sensitive to the two-loop ChPT parameters --our main source of systematic uncertainty. We thus provide two-loop unitarized fits constrained by lattice information on M_rho, f_pi, by the qqbar leading 1/N_c behavior of the rho and by existing estimates of low energy constants. These fits yield relatively stable predictions up to m_pi\simeq 300-350 MeV for the rho coupling and width as well as for all the f_0(600) parameters. We confirm, to two-loops, the weak m_pi dependence of the rho coupling and the KSRF relation, and the existence of two virtual f_0(600) poles for sufficiently high m_pi. At two loops one of these poles becomes a bound state when m_pi is somewhat larger than 300 MeV.

hep-ph↗
arXiv2010

m_pi and N_c dependence of resonances from Unitarized Chiral Perturbation Theory

We review our studies on the rho and sigma resonances properties derived from the Inverse Amplitude Method. In particular, we study the leading $1/N_c$ behavior of the resonances masses and widths and their evolution with changing $m_π$. The $1/N_c$ expansion gives a clear definition of $\bar qq$ states, which is neatly satisfied by the $ρ$ but not by the sigma, showing that its dominant component is not $\bar qq$. The $m_π$ dependence of the resonance properties is relevant to connect with lattice studies. We show that our predictions compare well with some lattice results and we find that the rho-pi-pi coupling constant is $m_π$ independent, in contrast with the sigma-pi-pi$ coupling, that shows a strong $m_π$ dependence.

hep-ph↗
arXiv2010

Dependence on the quark masses of elastic phase shifts and light resonances within standard and unitarized Chiral Perturbation Theory

We study the dependence of the pion-pion scattering phase shifts on the light quark mass in both standard and unitarized SU(2) Chiral Perturbation Theory (ChPT) to one and two loops. We then use unitarized SU(3) ChPT to study the elastic f_0(600), kappa(800), rho(770) and K*(892) resonances. The quark masses are varied up to values of interest for lattice studies. We find a very soft dependence on the light quark mass of the pion-pion phase shifts at one loop and slightly stronger at two loops and a good agreement with lattice results. The SU(3) analysis shows that the properties of the rho(770) and K*(892) depend smoothly on the quark mass whereas the scalar resonances present a non-analyticity at high quark masses. We also confirm the lattice assumption of quark mass independence of the vector two-meson coupling that, however, is violated for scalars.

hep-ph↗
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.

hep-ph↗
arXiv2010

f_0(600), kappa(800), rho(770) and K*(892), quark mass dependence from unitarized SU(3) Chiral Perturbation Theory

We study the strange and non-strange quark mass dependence of the parameters of the f_0(600), kappa(800), rho(770) and K*(892) resonances generated from elastic meson-meson scattering using unitarized one-loop Chiral Perturbation Theory. We fit simultaneously all experimental scattering data up to 0.8-1 GeV together with lattice results on decay constants and scattering lengths up to a pion mass of 440 MeV. Then, the strange and non-strange quark masses are varied from the chiral limit up to values of interest for lattice studies. In these amplitudes, the mass and width of the rho(770) and K*(892) present a similar and smooth quark mass dependence. In contrast, both scalars present a similar non-analyticity at high quark masses. Nevertheless the f_0(600) dependence on both quark masses is stronger than for the kappa(800) and the vectors. We also confirm the lattice assumption of quark mass independence of the vector two-meson coupling that, in contrast, is violated for scalars.

hep-ph↗
arXiv2010

Structure of the lightest scalar meson from the 1/Nc expansion of Unitarized Chiral Perturbation Theory and Regge Theory

One-loop unitarized Chiral Perturbation Theory (UChPT) calculations, suggest a different Nc behaviour for the sigma or f_0(600) and rho(770) mesons: while the rho meson becomes narrower with Nc, as is expected for a q-qbar meson, the sigma becomes broader, and its contribution to the total cross section is less and less important. On the other hand, local duality requires a cancellation between the sigma and rho amplitudes, but if there is a different Nc behaviour for them, there is a possible contradiction between the Inverse Amplitude Method (IAM) and local duality for large Nc. However, next to next to leading order UChPT calculations suggested a subdominant q-qbar component for the sigma with a mass around 1.2 GeV. In this work, we show that this subdominant q-qbar component is indeed needed to ensure local duality.

hep-ph↗