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Title: Nature of the f{sub 0}(600) Scalar Meson from its N{sub c} Dependence at Two Loops in Unitarized Chiral Perturbation Theory

Abstract

By using unitarized two-loop chiral perturbation theory partial waves to describe pion-pion scattering we find that the dominant component of the lightest scalar meson does not follow the qq dependence on the number of colors that, in contrast, is obeyed by the lightest vectors. The method suggests that a subdominant qq component of the f{sub 0}(600) possibly originates around 1 GeV.

Authors:
;  [1]
  1. Departamento de Fisica Teorica II, Universidad Complutense de Madrid, 28040 Madrid (Spain)
Publication Date:
OSTI Identifier:
20861472
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 97; Journal Issue: 24; Other Information: DOI: 10.1103/PhysRevLett.97.242002; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRALITY; GEV RANGE 01-10; PARTIAL WAVES; PARTICLE IDENTIFICATION; PERTURBATION THEORY; PION-PION INTERACTIONS; SCALAR MESONS

Citation Formats

Pelaez, J. R., and Rios, G. Nature of the f{sub 0}(600) Scalar Meson from its N{sub c} Dependence at Two Loops in Unitarized Chiral Perturbation Theory. United States: N. p., 2006. Web. doi:10.1103/PHYSREVLETT.97.242002.
Pelaez, J. R., & Rios, G. Nature of the f{sub 0}(600) Scalar Meson from its N{sub c} Dependence at Two Loops in Unitarized Chiral Perturbation Theory. United States. doi:10.1103/PHYSREVLETT.97.242002.
Pelaez, J. R., and Rios, G. Fri . "Nature of the f{sub 0}(600) Scalar Meson from its N{sub c} Dependence at Two Loops in Unitarized Chiral Perturbation Theory". United States. doi:10.1103/PHYSREVLETT.97.242002.
@article{osti_20861472,
title = {Nature of the f{sub 0}(600) Scalar Meson from its N{sub c} Dependence at Two Loops in Unitarized Chiral Perturbation Theory},
author = {Pelaez, J. R. and Rios, G.},
abstractNote = {By using unitarized two-loop chiral perturbation theory partial waves to describe pion-pion scattering we find that the dominant component of the lightest scalar meson does not follow the qq dependence on the number of colors that, in contrast, is obeyed by the lightest vectors. The method suggests that a subdominant qq component of the f{sub 0}(600) possibly originates around 1 GeV.},
doi = {10.1103/PHYSREVLETT.97.242002},
journal = {Physical Review Letters},
number = 24,
volume = 97,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2006},
month = {Fri Dec 15 00:00:00 EST 2006}
}
  • We study the strange and non-strange quark mass dependence of the parameters of the f{sub 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 massmore » dependence. In contrast, both scalars present a similar non-analyticity at high quark masses. Nevertheless the f{sub 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.« less
  • One-loop unitarized Chiral Perturbation Theory (UChPT) calculations, suggest a different Nc behaviour for the {sigma} or f{sub 0}(600) and {rho}(770) mesons: while the {rho} meson becomes narrower with Nc, as is expected for a q-barq 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 tomore » leading order UChPT calculations suggested a subdominant q-barq component for the {sigma} with a mass around 1.2 GeV. In this work, we show that this subdominant q-barq component is indeed needed to ensure local duality.« less
  • We review our work on the {rho} and {sigma} resonances derived from the Inverse Amplitude Method. In particular, we study the leading 1/N{sub c} behavior of the resonances masses and widths and their evolution with changing m{sub {pi}}. The 1/N{sub c} expansion gives a clear definition of q-barq states, which is neatly satisfied by the {rho} but not by the {sigma}, showing that its dominant component is not q-barq. The m{sub {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 themore » {rho}{pi}{pi} coupling constant is m{sub {pi}} independent, in contrast with the {sigma}{pi}{pi} coupling, that shows a strong m{sub {pi}} dependence.« less
  • We review the N{sub c} and m{sub {pi}} dependence of the {rho}(770) and {sigma}(or f{sub 0}(600)) resonances generated with the Inverse Amplitude Method. The {sigma}N{sub c} behavior is at odds with being dominantly a q-barq state, but there is a hint of a subdominant q-barq component with a mass above 1 GeV. We find fair agreement with lattice results for the chiral extrapolation of the {rho} mass, and that the {rho}{pi}{pi} coupling is almost m{sub {pi}} independent whereas the {sigma}{pi}{pi} coupling depends strongly on m{sub {pi}}.
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