Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2009-10-02
Phys.Rev.D81:054006,2010
Physics
High Energy Physics
High Energy Physics - Phenomenology
13 pages, 1 figure
Scientific paper
10.1103/PhysRevD.81.054006
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 $e^++e^-\to J/\Psi(\eta_c)+\chi_{cJ}(h_c)$ at the center-of-mass energy $\sqrt{s}=10.6$ GeV.
Elekina E. N.
Martynenko A. P.
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