Two-Photon and Two-gluon Decays of $0^{++}$ and $2^{++}$ P-wave Heavy Quarkonium States

TL;DR

This paper presents a theoretical calculation of two-photon and two-gluon decay rates of P-wave heavy quarkonium states using an effective Lagrangian approach based on the heavy quark energy-momentum tensor, providing estimates consistent with QCD sum rules.

Contribution

It introduces a novel effective Lagrangian framework for P-wave heavy quarkonium decays, relating decay rates to decay constants and using QCD sum rules for numerical estimates.

Findings

Calculated $ ext{chi}_{c0}$ two-photon width as 5 keV, slightly larger than experimental data.

Derived simple decay rate expressions in terms of decay constants.

Connected decay amplitudes to local heavy quark operators.

Abstract

By neglecting the relative quark momenta in the propagator term, the two-photon and two-gluon decay amplitude of heavy quarkonia states can be written as a local heavy quark field operator matrix element which could be obtained from other processes or computed with QCD sum rules technique or lattice simulation, as shown in a recent work on $\eta_{c,b}$ two-photon decays. In this talk, I would like to discuss a similar calculation on $P$-wave $\chi_{c0,2}$ and $\chi_{b0,2}$ two-photon decays. We show that the effective Lagrangian for the two-photon decays of the $P$-wave $\chi_{c0,2}$ and $\chi_{b0,2}$ is given by the heavy quark energy-momentum tensor local operator and its trace, the $\bar{Q}Q$ scalar density. A simple expression for $\chi_{c0}$ two-photon and two-gluon decay rate in terms of the $f_{\chi_{c0}}$ decay constant, similar to that of $\eta_{c}$ is obtained. From the existing QCD sum rules value for $f_{\chi_{c0}}$, we get $5\rm\,keV$ for the $\chi_{c0}$ two-photon width, somewhat larger than measurement.