Electromagnetic Annihilation Rates of $χ_{c0}$ and $χ_{c2}$ with Both Relativistic and QCD Radiative Corrections

Details Electromagnetic Annihilation Rates of $χ_{c0}$ and $χ_{c2}$ with Both Relativistic and QCD Radiative Corrections Electromagnetic Annihilation Rates of $χ_{c0}$ and $χ_{c2}$ with Both Relativistic and QCD Radiative Corrections

1996-01-31

arxiv.org/abs/hep-ph/9601380v1

Phys.Rev. D54 (1996) 2123-2131

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages LaTex (2 figures included)

Scientific paper

10.1103/PhysRevD.54.2123

We estimate the electromagnetic decay rates of $\chi_{c0}\rightarrow \gamma\gamma$ and $\chi_{c2}\rightarrow\gamma\gamma$ by taking into account both relativistic and QCD radiative corrections. The decay rates are derived in the Bethe-Salpeter formalism and the QCD radiative corrections are included in accordance with factorization assumption. Using a QCD-inspired interquark potential, we obtain relativistic BS wavefunctions of $\chi_{c0}$ and $\chi_{c2}$ by solving BS equations for the corresponding $^{2S+1}L_J$ states. Our numerical result for the ratio $R=\frac{\Gamma(\chi_{c0}\rightarrow\gamma\gamma)}{\Gamma(\chi_{c2} \rightarrow\gamma\gamma)}$ is about $11-13$ which agrees with the update E760 experimental data. Explicit calculations show that the relativistic corrections due to spin-dependent interquark forces induced by gluon exchange enhance the ratio $R$ substantially and its value is insensitive to the choice of parameters that characterize the interquark potential. Our expressions for the decay widths are identical with that obtained in the NRQCD theory to the next-to-leading order in $v^2$ and $\alpha_s$. Moreover, we have determined two new coefficents in the nonperturbative matrix elements for these decay widths.

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