  The cross section for exclusive production of $\pi^+ \pi^-$ and $\pi^0 \pi^0$
meson pairs in ultrarelativistic heavy ion collisions is calculated for LHC
energy $\sqrt{s_{NN}} =$ 3.5 TeV taking into account photon-photon mechanism.
We concentrate on the production of large two-pion invariant masses where the
mechanism of the elementary $\gamma \gamma \to \pi \pi$ process is not fully
understood. In order to include a size of nuclei we perform calculation in the
impact-parameter equivalent photon approximation (EPA). Realistic charge
densities are used to calculate charged form factor of $^{208}$Pb nucleus and
to generate photon fluxes associated with ultrarelativistic heavy ions.
Sizeable cross sections are obtained that can be measured at LHC. The cross
section for elementary $\gamma \gamma \to \pi \pi$ is calculated in the
framework of pQCD Brodsky-Lepage (BL) mechanism with the distribution amplitude
used to descibe recent data of the BABAR collaboration on pion transition form
factor, using hand-bag mechanism advocated to describe recent Belle data as
well as $t$ and $u$-channel meson/reggeon exchanges. We present distributions
in two-pion invariant mass as well as the pion pair rapidity for the nuclear
process.
