arXiv subjects

J. R. Peláez

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

26 records · Page 2Linked to original sources

arXiv2011

Chiral Perturbation Theory, the ${1/N_c}$ expansion and Regge behaviour determine the structure of the lightest scalar meson

The leading $1/N_c$ behaviour of Unitarised Chiral Perturbation Theory distinguishes the nature of the $ρ$ and the $σ$. At one loop order the $ρ$ is a ${\bar q}q$ meson, while the $σ$ is not. However, semi-local duality between resonances and Regge behaviour cannot be satisfied for larger $N_c$, if such a distinction holds. While the $σ$ at $N_c=3$ is inevitably dominated by its di-pion component, Unitarised Chiral Perturbation Theory beyond one loop order reveals that as $N_c$ increases above 6-8, the $σ$ has a sub-dominant ${\bar q}q$ fraction up at 1.2 GeV. Remarkably this ensures semi-local duality is fulfilled for the range of $N_c \lesssim 15$, where the unitarisation procedure adopted applies.

hep-ph↗

arXiv2011

The nature of the lightest scalar meson, its Nc behaviour and semi-local duality

One-loop unitarized Chiral Perturbation Theory (UChPT) calculations, suggest a different Nc behaviour for the sigma or f0(600) and rho(770) mesons: while the rho meson becomes narrower with Nc, as expected for a qqbar meson, the f0(600) contribution to the total cross section below 1 GeV becomes less and less important. Here we review our recent work where we have shown, by means of finite energy sum rules, that a different Nc behaviour for these resonances may lead to a conflict with semi-local duality for large Nc, since local duality requires a cancellation between the f0(600) and rho(770) amplitudes. However, UChPT calculations also suggest a subdominant qqbar component for the f0(600) with a mass above 1 GeV and this can restore semi-local duality, as we show.

hep-ph↗

arXiv2011

The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV

We improve our description of pion-pion scattering data by imposing additional requirements to our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of Forward Dispersion Relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy Kl4 decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost all disagreement with previous Chiral Perturbation Theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.

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↗

arXiv2007

Scalar mesons from Unitarized Chiral Perturbation Theory: N_c and quark mass dependences

We review recent studies of light scalar meson properties by means of unitarization techniques, obtained from dispersion theory, and applied to the Chiral Perturbation Theory expansion. In particular, light scalars do not follow the N_c dependence of $\bar q q$ states although a subdominant quark-antiquark component may be observed to arise for the f_0(600) around 1 GeV, where another quark-antiquark multiplet is believed to exist. Finally, we present our preliminary results on the quark mass dependence of the f_0(600) and rho(770) resonances.

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.

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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↗

arXiv1998

A coupled channel unitary chiral approach to the meson-meson interaction and pion-pion scattering in a nuclear medium

A new tool which combines chiral perturbation theory and unitarity in coupled channels is applied with success to the study of the meson-meson interaction, extending the theoretical predictions up to sqrt{s} = 1.2 GeV, hence improving considerably the convergence radius of conventional chiral perturbation theory. The method is applied to obtain the meson-meson phase shifts and inelasticities as well as the isoscalar pion-pion scattering amplitude inside a nuclear medium.

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