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arXiv 0910.0394hep-ph
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e^+e^-湮灭中S波和P波粲偶素双产生的相对论效应

Relativistic effects in the double S- and P-wave charmonium production in e^+e^- annihilation

E. N. Elekina, A. P. Martynenko

摘要:

在微扰QCD和相对论夸克模型的基础上,计算了一对S波和P波粲偶素态产生过程中的相对论修正和束缚态修正。考虑了产生振幅中与重夸克相对运动有关的相对论因素以及束缚态波函数到运动S、P波介子参考系的变换规律。对于胶子和夸克传播子进入生产顶点函数,我们使用截断展开的相对夸克动量的质量中心能量$\sqrt{s}$的比率高达二阶。精确的相对论处理的波函数使所有这些二阶项收敛,从而允许可靠的计算它们的贡献的生产截面。利用类Breit势研究了静止坐标系下夸克束缚态波函数的相对论修正。结果表明,所研究的效应本质上改变了反应$e^++e^-\to J/Ψ(η_c)+χ_{cJ}(h_c)$在质心能量为$\sqrt{s}=10.6$ GeV的截面的非相对论结果。

英文摘要:

On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of S-wave and P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving S- and P-wave mesons are taken into account. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy $\sqrt{s}$ up to the second order. The exact relativistic treatment of the wave functions makes all such second order terms convergent, thus allowing the reliable calculation of their contributions to the production cross section. Relativistic corrections to the quark bound state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that the examined effects change essentially the nonrelativistic results of the cross section for the reaction $e^++e^-\to J/Ψ(η_c)+χ_{cJ}(h_c)$ at the center-of-mass energy $\sqrt{s}=10.6$ GeV.

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