Di-muon and di-electron $\pt$ distribution for ultra-peripheral Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}} } = 2.76$ TeV and $-0.9< y< 0.9$ for events satisfying the event selection in the invariant mass interval $3.0< M_{\rm inv}< 3.2$ GeV/$c^{2}$ and $2.2< M_{\rm inv}< 3.2$ GeV/$c^{2}$ respectively, with the $\pt$-range extended to $p_{\rm T}< 1$ GeV/$c$ and to $p_{\rm T}< 5$ GeV/$c$. The data points are fitted summing six different Monte Carlo templates: coherent J/$\psi$ production (black), incoherent J/$\psi$ production (red), J/$\psi$s from coherent $\psi^{'}$ decay (light blue), J/$\psi$s from incoherent $\psi^{'}$ decay (violet), $\gamma \gamma$ (green), and J/$\psi$ produced in peripheral hadronic collisions (grey). The solid histogram (blue) is the sum.