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Pion mass and decay constant
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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.
Forward citations
Cited by 3 Pith papers
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Spectra of light and heavy mesons with $J \le 5$ in a relativistic Bethe-Salpeter approach
First J=4,5 meson Bethe-Salpeter tensor bases plus exploratory rainbow-ladder spectra and Regge trajectories from light through bottom quarkonia.
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Distribution amplitudes of heavy-light pseudo-scalar and vector mesons from Dyson-Schwinger equations framework
First DSE predictions for B*, B*_s, and B*_c distribution amplitudes show peaks near the Euclidean constituent quark mass ratio and a universal spin ordering.
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$D^* D \pi$ and $B^* B \pi$ couplings from Dyson-Schwinger equations framework
A Dyson-Schwinger/Bethe-Salpeter calculation predicts g_D*Dpi = 16.22 and g_B*Bpi = 40.09, with static couplings consistent with lattice results.
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