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Title: Vanishing chiral couplings in the large-N{sub C} resonance theory

Abstract

The construction of a resonance theory involving hadrons requires implementing the information from higher scales into the couplings of the effective Lagrangian. We consider the large-N{sub C} chiral resonance theory incorporating scalars and pseudoscalars, and we find that, by imposing LO short-distance constraints on form factors of QCD currents constructed within this theory, the chiral low-energy constants satisfy resonance saturation at NLO in the 1/N{sub C} expansion.

Authors:
;  [1];  [2]
  1. IFIC, Universitat de Valencia-CSIC, Apartat de Correus 22085, E-46071 Valencia (Spain)
  2. Max-Planck-Institut fuer Physik (Werner-Heisenberg Institut), Foehringer Ring 6, 80805 Munich (Germany)
Publication Date:
OSTI Identifier:
20929550
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevD.75.114011; (c) 2007 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; FORM FACTORS; LAGRANGIAN FUNCTION; PSEUDOSCALARS; QUANTUM CHROMODYNAMICS; RESONANCE; SCALARS

Citation Formats

Portoles, Jorge, Rosell, Ignasi, and Ruiz-Femenia, Pedro. Vanishing chiral couplings in the large-N{sub C} resonance theory. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.114011.
Portoles, Jorge, Rosell, Ignasi, & Ruiz-Femenia, Pedro. Vanishing chiral couplings in the large-N{sub C} resonance theory. United States. doi:10.1103/PHYSREVD.75.114011.
Portoles, Jorge, Rosell, Ignasi, and Ruiz-Femenia, Pedro. Fri . "Vanishing chiral couplings in the large-N{sub C} resonance theory". United States. doi:10.1103/PHYSREVD.75.114011.
@article{osti_20929550,
title = {Vanishing chiral couplings in the large-N{sub C} resonance theory},
author = {Portoles, Jorge and Rosell, Ignasi and Ruiz-Femenia, Pedro},
abstractNote = {The construction of a resonance theory involving hadrons requires implementing the information from higher scales into the couplings of the effective Lagrangian. We consider the large-N{sub C} chiral resonance theory incorporating scalars and pseudoscalars, and we find that, by imposing LO short-distance constraints on form factors of QCD currents constructed within this theory, the chiral low-energy constants satisfy resonance saturation at NLO in the 1/N{sub C} expansion.},
doi = {10.1103/PHYSREVD.75.114011},
journal = {Physical Review. D, Particles Fields},
number = 11,
volume = 75,
place = {United States},
year = {Fri Jun 01 00:00:00 EDT 2007},
month = {Fri Jun 01 00:00:00 EDT 2007}
}
  • The precision obtainable in phenomenological applications of chiral perturbation theory is currently limited by our lack of knowledge on the low-energy constants (LECs). The assumption that the most important contributions to the LECs come from the dynamics of the low-lying resonances, often referred to as the resonance saturation hypothesis, has stimulated the use of large-N{sub C} resonance Lagrangians in order to obtain explicit values for the LECs. We study the validity of the resonance saturation assumption at the next-to-leading order in the 1/N{sub C} expansion within the framework of resonance chiral theory. We find that, by imposing QCD short-distance constraints,more » the chiral couplings can be written in terms of the resonance masses and couplings and do not depend explicitly on the coefficients of the chiral operators in the Goldstone boson sector of resonance chiral theory. As we argue, this is the counterpart formulation of the resonance saturation statement in the context of the resonance Lagrangian. Going beyond leading order in the 1/N{sub C} counting allows us to keep full control of the renormalization scale dependence of the LEC estimates.« less
  • We construct {pi}{pi} amplitudes that fulfill exact elastic unitarity, account for one-loop chiral perturbation theory contributions and include all 1/N{sub C} leading terms, with the only limitation of considering just the lowest-lying nonet of exchanged resonances. Within such a scheme, the N{sub C} dependence of {sigma} and {rho} masses and widths is discussed. Robust conclusions are drawn in the case of the {rho} resonance, confirming that it is a stable meson in the limit of a large number of QCD colors, N{sub C}. Less definitive conclusions are reached in the scalar-isoscalar sector. With the present quality of data, we cannotmore » firmly conclude whether or not the N{sub C}=3 f{sub 0}(600) resonance completely disappears at large N{sub C} or if it has a subdominant component in its structure, which would become dominant for a number of quark colors sufficiently large.« less
  • By using a dynamical model of chiral-symmetry breaking, we demonstrate that the chiral perturbation expansion around the SU{sub {ital f}}(3)-symmetric vacuum does not converge in the large-{ital N}{sub {ital c}} limit. The convergence radius of the expansion in the strange-quark mass {ital m}{sub {ital s}} is shown to be 30--50 MeV, which means that higher-order terms become larger as one increases the order of the expansion in the physical region ({ital m}{sub {ital s}}{similar to}150 MeV). The first-order mass formula for the Nambu-Goldstone bosons turns out to be accidentally valid in the physical region.
  • Interactions of two baryons are considered in large {ital N}{sub {ital C}} chiral perturbation theory and compared to the interactions derived from the Skyrme model. Special attention is given to a toruslike configuration known to be present in the Skyrme model.
  • The magnetic and transition magnetic moments of the ground-state baryons are computed in heavy baryon chiral perturbation theory in the large-N{sub c} limit, where N{sub c} is the number of colors. SU(3) symmetry breaking is systematically studied twofold: On the one hand, one-loop nonanalytic corrections of orders m{sub q}{sup 1/2} and m{sub q} ln m{sub q} are included, with contributions of baryon intermediate states from both flavor octet and flavor decuplet multiplets, assuming degeneracy between baryon states within a given flavor multiplet but nondegeneracy between baryons of different multiplets. On the other hand, perturbative SU(3) symmetry breaking is also analyzedmore » by including all relevant leading-order operators that explicitly break SU(3) at linear order. The resultant expressions are compared with the available experimental data and with other determinations in the context of conventional heavy baryon chiral perturbation theory for three flavors of light quarks and at the physical value N{sub c}=3. The agreement reached is quite impressive.« less