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

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}{sub c,b} two-photon decays. In this talk, I would like to discuss a similar calculation on P-wave {chi}{sub c0,2} and {chi}{sub b0,2} two-photon decays. We show that the effective Lagrangian for the two-photon decays of the P-wave {eta}{sub c0,2} and {chi}{sub b0,2} is given by the heavy quark energy-momentum tensor local operator and its trace, the QQ scalar density. A simple expression for {chi}c0 two-photon and two-gluon decay rate in terms of the f{sub {chi}c0} decay constant, similar to that of {eta}{sub c} is obtained. From the existing QCD sum rules value for f{sub {chi}c0,} we get 5 keV for the {chi}{sub c0} two-photon width, somewhat larger than measurement.