Evaluation of the Axial Vector Commutator Sum Rule for Pion-Pion Scattering
Abstract
We consider the sum rule proposed by one of us (SLA), obtained by taking the expectation value of an axial vector commutator in a state with one pion. The sum rule relates the pion decay constant to integrals of pion-pion cross sections, with one pion off the mass shell. We remark that recent data on pion-pion scattering allow a precise evaluation of the sum rule. We also discuss the related Adler--Weisberger sum rule (obtained by taking the expectation value of the same commutator in a state with one nucleon), especially in connection with the problem of extrapolation of the pion momentum off its mass shell. We find, with current data, that both the pion-pion and pion-nucleon sum rules are satisfied to better than six percent, and we give detailed estimates of the experimental and extrapolation errors in the closure discrepancies.
Keywords
Cite
@article{arxiv.0704.1201,
title = {Evaluation of the Axial Vector Commutator Sum Rule for Pion-Pion Scattering},
author = {Stephen L. Adler and F. J. Yndurain},
journal= {arXiv preprint arXiv:0704.1201},
year = {2008}
}
Comments
Plain TeX file;minor changes; version to be published in Pys. Rev. D; corrected refs.12,13