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

Abstract

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.

13 pages, 1 figure

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Cited by in corpus (13)

• Relativistic corrections to double charmonium production in high energy proton-proton interaction
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• Pair double heavy diquark production in high energy proton-proton collisions
• Relativistic corrections to the pair double heavy diquark production in e^+e^- annihilation
• Relativistic corrections to the pair $B_c$-meson production in $e^{+}{e}^{-}$ annihilation
• Higgs boson decay to paired $B_c$: relativistic and one-loop corrections
• ${\alpha }_s{v}^2$ corrections to ${\eta }_c$ and ${\chi }_{cJ}$ production recoiled with a photon at $e^{+}{e}^{-}$ colliders
• Relativistic corrections to paired production of charmonium and bottomonium in decays of the Higgs boson
• Exclusive double $B_c$ meson production from $e^{+}{e}^{-}$ annihilation into two virtual photons
• Higgs boson decay to the pair of S- and P-wave $B_c$ mesons
• Photonic production of the pair of $B_c$ mesons
• Search for $C=+$ charmonium and XYZ states in $e^{+}{e}^{-}\to \gamma +H$ at BESIII
• Relativistic corrections to η_c-pair production in high energy proton-proton collisions