Relevance of various Dirac covariants in hadronic Bethe-Salpeter wave functions in electromagnetic decays of ground state vector mesons

TL;DR

This paper investigates how different Dirac covariants in the Bethe-Salpeter wave functions influence the electromagnetic decay constants of ground state vector mesons using a covariant framework.

Contribution

It introduces a comprehensive analysis of Dirac structures in the Bethe-Salpeter formalism for meson decays, including LO and NLO contributions, to understand their relevance.

Findings

Relevance of various Dirac structures in decay calculations.

Quantitative decay constants for multiple mesons.

Comparison of LO and NLO contributions.

Abstract

In this work we have employed Bethe-Salpeter equation (BSE) under covariant instantaneous ansatz (CIA) to study electromagnetic decays of ground state equal mass vector mesons: $\rho$, $\omega$, $\phi$, $\psi$ and $Y$ through the process $V\rightarrow\gamma*\rightarrow e^+ + e^-$. We employ the generalized structure of hadron-quark vertex function $\Gamma$ which incorporates various Dirac structures from their complete set order-by-order in powers of inverse of meson mass. The electromagnetic decay constants for the above mesons are calculated using the leading order (LO) and the next-to-leading order (NLO) Dirac structures. The relevance of various Dirac structures in this calculation is studied.