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, Γπ, and the quark propagator in the chiral limit; Γπ necessarily involves a non-negligible γ5γ.P term (P is the pion four-momentum). We also obtain exact expressions for the pion decay constant, fπ, and mass, both of which depend on Γπ and demonstrate the equivalence between fπ 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.
- Publication:
-
Physics Letters B
- Pub Date:
- February 1998
- DOI:
- 10.1016/S0370-2693(97)01535-9
- arXiv:
- arXiv:nucl-th/9707003
- Bibcode:
- 1998PhLB..420..267M
- Keywords:
-
- GOLDSTONE BOSONS;
- DYNAMICAL CHIRAL SYMMETRY BREAKING;
- DYSON-SCHWINGER EQUATIONS;
- NONPERTURBATIVE QCD;
- Nuclear Theory;
- High Energy Physics - Phenomenology
- E-Print:
- 11 pages, LaTeX, elsart.sty