Pion mass and decay constant
Abstract
Independent of assumptions about the form of the quark-antiquark scattering kernel we derive the explicit relation between the pion Bethe-Salpeter amplitude, Gamma_pi, and the quark propagator in the chiral limit; Gamma_pi necessarily involves a non-negligible gamma_5 gamma.P term (P is the pion four-momentum). We also obtain exact expressions for the pion decay constant, f_pi, and mass, both of which depend on Gamma_pi; and demonstrate the equivalence between f_pi and the pion Bethe-Salpeter normalisation constant in the chiral limit. We stress the importance of preserving the axial-vector Ward-Takahashi identity in any study of the pion itself, and in any study whose goal is a unified understanding of the properties of the pion and other hadronic bound states.
Cite
@article{arxiv.nucl-th/9707003,
title = {Pion mass and decay constant},
author = {P. Maris and C. D. Roberts and P. C. Tandy},
journal= {arXiv preprint arXiv:nucl-th/9707003},
year = {2010}
}
Comments
11 pages, LaTeX, elsart.sty