$\chi_{cJ}\rightarrow e^{+}e^{-}$ decays revisited

TL;DR

This paper recalculates the decay widths of $ ext{chi}_{cJ} ightarrow e^{+}e^{-}$ using NRQCD, highlighting the dominance of ultrasoft photon contributions and providing updated estimates for specific states.

Contribution

It introduces a novel calculation of $ ext{chi}_{cJ} ightarrow e^{+}e^{-}$ decay widths within the NRQCD framework, emphasizing the role of ultrasoft photons and higher Fock states.

Findings

Decay widths for $ ext{chi}_{c1}$ and $ ext{chi}_{c2}$ are 0.09 eV and 0.06 eV.

Ultrasoft photon contributions are numerically dominant.

The approach combines NRQCD with heavy hadron chiral perturbation theory.

Abstract

We present a calculation of the width for $\chi_{cJ}\rightarrow e^{+}e^{-}$ decay. The amplitude of the process is computed within the NRQCD framework. The leading-order contribution is described by two terms associated with the two different integration domains in the electromagnetic loop describing two-photon annihilation of the heavy quark-antiquark pair. The corresponding operators are defined in the framework of NRQCD. The matrix element of one of these operators describes a configuration with an ultrasoft photon and can be associated with the higher Fock state of the heavy meson. In order to compute this contribution we use the heavy hadron chiral perturbation theory. We obtain that this contribution is numerically dominant. The obtained estimates for the decay widths of the $\chi_{c1}$ and $\chi_{c2}$ states are $0.09$ eV and $0.06$ eV, respectively.