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pi^+ - pi^0 mass difference from the Bethe-Salpeter equation

Masayasu Harada·Masafumi Kurachi·Koichi Yamawaki
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Abstract

In the framework of the Schwinger-Dyson equation and the Bethe-Salpeter equation in the improved ladder approximation, we calculate the pi^+ - pi^0 mass difference on the same footing as the pion decay constant and the QCD S parameter (or L_{10}) through the difference between the vector current correlator Π_{VV} and the axial-vector current correlator Π_{AA}. We find that all the results can be fit to the experimental values for rather large Lambda_{QCD} \sim 700 MeV which reflects the ``scale ambiguity''. By fitting to the calculated data using the pole saturated form of Π_{VV} - Π_{AA}, we also derive masses and decay constants of rho meson and a_1 meson, which we found are consistent with the experiments rather insensitively to the ``scale ambiguity''.

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Masayasu Harada, Masafumi Kurachi, Koichi Yamawaki. 2004-03-11. pi^+ - pi^0 mass difference from the Bethe-Salpeter equation. https://doi.org/10.1103/physrevd.70.033009

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