The $\gamma \gamma \to J/\psi J/\psi$ reaction and the $J/\psi J/\psi$   pair production in exclusive ultraperipheral ultrarelativistic heavy ion   collisions
  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. 
Sergey Baranov, Anna Cisek, Mariola K{\l}usek-Gawenda, Wolfgang   Sch\"afer and Antoni Szczurek
hep-ph