The γγ → J/ψ J/ψ reaction and the J/ψ J/ψ pair production in exclusive ultraperipheral ultrarelativistic heavy ion collisions

We calculate the cross section for the gamma gamma -> J/psi J/psi process. Two mechanisms are considered: box (two-loop) diagrams of the order of O(alpha(2)(em) alpha(2)(s)) and two-gluon exchange of the order of O(alpha(2)(em) alpha(4)(s)). The first mechanism is calculated in the heavy-quark non-relativistic approximation while in 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 Pb-208 + Pb-208 -> Pb-208 + J/psi J/psi + Pb-208 reaction. Distributions in rapidity of the J/psi J/psi pair and invariant mass of the pair are shown. It is shown that in heavy ion collisions the box mechanism significantly dominates over the two-gluon exchange mechanism.