Arranging Dirac covariants in hadronic Bethe-Salpeter wave functions for pseudoscalar meson decays

TL;DR

This paper employs the Bethe-Salpeter framework with a covariant ansatz to calculate decay constants of pseudoscalar mesons, validating a power counting rule for Dirac covariants that improves accuracy.

Contribution

It introduces a systematic way to incorporate Dirac covariants order-by-order in meson mass inverse, enhancing decay constant calculations.

Findings

Inclusion of LO and NLO covariants improves decay constant predictions.

The power counting rule effectively guides covariant inclusion.

Results validate the systematic incorporation of covariants in Bethe-Salpeter calculations.

Abstract

We have employed the framework of Bethe-Salpeter equation under covariant instantaneous ansatz to calculate leptonic decay constants of unequal mass pseudoscalar mesons like pi, K, D, Ds and B and radiative decay constants of neutral pseudoscalar mesons like pi and etac in two photon decays of these mesons. In the Dirac structure of hadronic BS wave function, the covariants are incorporated from their complete set in accordance with a recently proposed power counting rule, order-by-order in powers of inverse of meson mass. The decay constants are calculated with the incorporation of both Leading order (LO) and the Next-to-leading order (NLO) Dirac covariants. The contribution of both LO as well as NLO Dirac covariants are studied in detail in this paper. The results are found to improve dramatically and hence validating the power counting rule which also provides a practical means of incorporating Dirac covariants in the BS wave function for a hadron.