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

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: ρ, ω, φ, ψ and Y through the process V → γ * → e + +e − . We employ the generalized structure of hadron-quark vertex function Γ 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.

Approach to calculation of mass spectra and two-photon decays of cc¯ mesons in the framework of Bethe-Salpeter equation

“…This is in contrast to the BSE approach [27] [involving the 16 × 1 structure of the two-body BS amplitude ΨðP; qÞ], which leads to an exact connection [27] between the 3D and 4D forms of the BSE. After the 3D reduction, we get a single 3D Salpeter equation [as in Eq.…”

“…(30) of Ref. [27]], and the 3D BS amplitudes (f i s) remain independent, and thus they remain classified in terms of leading and subleading amplitudes.…”

“…We start with the most general decomposition of a 4D BS wave function for a scalar meson [17,19] Until now these amplitudes have all been independent, and per the power-counting rule [25][26][27] proposed by us earlier, f 1 and f 2 are the amplitudes associated with the leading Dirac structures, namely, M and = P, while f 3 and f 4 will be the amplitudes associated with the subleading Dirac structures, namely, = q, and…”

“…The solution of these equations needs information about the BS kernel Kðq;q 0 Þ [27,48], which is taken to be one-gluonexchange-like as regards the color (…”

Radiative Decay Widths of Ground and Excited States of Vector Charmonium and Bottomonium

“…Bethe-Salpeter equation (BSE) [11,15,[17][18][19]] is a conventional approach in dealing with relativistic bound state problems. From the solutions, we can obtain useful information about the inner structure of hadrons, which is also crucial in treating hadronic decays.…”