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

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 $5\mathrm{keV}$ for the ${\chi }_{c0}$ two-photon width, somewhat larger than measurement.

Comments: LaTeX, 9 pages, Talk given at the QCD@Work 2010 International Workshop on QCD: Theory and Experiment, Martina Franca, Valle d'Istria, Italy, 20-23 June 2010