The $\gamma \gamma \to J/\psi J/\psi$ reaction and the $J/\psi J/\psi$ pair production in exclusive ultraperipheral ultrarelativistic heavy ion collisions

Abstract

We calculate the cross section for the $\gamma \gamma \to J/\psi J/\psi$ process. Two mechanisms are considered: box (two-loop) diagrams of the order of $O({\alpha }_{em}^2{\alpha }_s^2)$ and two-gluon exchange of the order of $O({\alpha }_{em}^2{\alpha }_s^4)$. The first mechanism is calculated in the heavy-quark non-relativistic approximation while the second case we also include the effects of quantum motion of quarks in the bound state. The box contribution dominates at energies close to the threshold ($W<$ 15 GeV) while the two-gluon mechanism takes over at $W>$ 15 GeV. Including the bound-state wave function effects for the two-gluon exchange mechanism gives a cross section 0.1 - 0.4 pb, substantially smaller than that in the non-relativistic limit (0.4 - 1.6 pb). We also find a strong infrared sensitivity which manifests itself in a rather strong dependence on the mass for the $t$-channel gluons. The elementary cross section is then used in the Equivalent Photon Approximation (EPA) in the impact parameter space to calculate the cross section for ${}^{208}Pb{+}^{208}Pb{\to }^{208}Pb+J/\psi J/\psi {+}^{208}Pb$ reaction. Distributions in rapidity of the $J/\psi J/\psi$ pair and invariant mass of the pair are shown.

Comments: 15 pages, 11 figures