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arXiv · 1811.07634

Correction to the energy spectrum of $^1S_0$ heavy quarkonia due to two-gluon annihilation effect

Hui-Yun Cao·Hai-Qing Zhou
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Abstract

In this work, the non-relativistic asymptotic behavior of the transition $q\overline{q}\rightarrow2g\rightarrow q\overline{q}$ in the $^1S_0$ channel is discussed. Different with the usual calculation which expands the physical amplitude around the quark anti-quark threshold, we take the quark anti-quark pairs as off shell and only expand the expression on the three-dimensional momenta of the quarks and anti-quarks. We calculate the results to order 6. The imagine part of the results after applying the on shell conditions can reproduce the non-relativistic QCD (NRQCD) results in leading order of $\alpha_s$. The real part of the results can be used to estimate the mass shift of the $^1S_0$ heavy quark anti-quark system due to the $2g$ annihilation effect. The results can also be used to estimate the energy shifts of the positronium system due to the two-photon annihilation.

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Hui-Yun Cao, Hai-Qing Zhou. 2018-11-19. Correction to the energy spectrum of $^1S_0$ heavy quarkonia due to two-gluon annihilation effect. https://doi.org/10.1103/physrevd.99.074007

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