1997/07/01 by S. P. Klevansky, Klevansky, S. P., R. H. Lemmer +1 · 1 citation
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph
paper · pdf · doi:10.48550/arxiv.hep-ph/9707206
100 Pages Revtex, Figures available upon request
arxiv created 1997/07/01 · arxiv updated 2009/11/30
The validity of Weinberg's two sum rules for massless QCD, as well as the six additional sum rules introduced into chiral perturbation theory by Gasser and Leutwyler, are investigated for the extended Nambu-Jona-Lasinio chiral model that includes vector and axial vector degrees of freedom. A detailed analysis of the vector, axial vector and coupled pion plus longitudinal axial vector modes is given. We show that, under Pauli-Villars regularization of the meson polarization amplitudes that determine the spectral density functions, all of the sum rules involving inverse moments higher than zero are automatically obeyed by the model spectral densities. By contrast, the zero moment sum rules acquire a non-vanishing right hand side that is proportional to the quark condensate density of the non-perturbative groundstate. We use selected sum rules in conjunction with other calculations to obtain explicit expressions for the scale-independent coupling constants li of chiral perturbation theory in the combination li+ln(m2π/μ2), to evaluate the Das-Guralnik-Mathur-Low-Young current algebra expression for the electromagnetic mass difference of the pion, and to compute the pion electrical polarizability αE. The sum rule calculations %of αE set an upper limit of αE≤ α/(8π2mπf2π) ≈ 6×10-4fm3 on this quantity, that is independent of the quark mass up to \cal O(m2π/m2), and only depends on the fundamental constants: pion mass mπ and pion decay constant fπ, in addition to fine structure constant α≈ 1/137.