Joint ECFA-NuPECC-APPEC Workshop “Synergies between the EIC and the LHC”

We discuss the central exclusive photoproduction of $\pi^{+}\pi^{-}$ pairs in diffractive photon-proton and in proton-proton collisions at high energies. We consider the resonant ($\rho^{0}$, $\omega$, $f_{2}(1270)$) and non-resonant (Drell-S\"oding) contributions. Our calculation is based on the tensor-pomeron approach. For the $pp\to pp\pi^{+}\pi^{-}$ reaction, we calculate differential cross sections as a function of the two-pion invariant mass. We discuss the important role of the Drell-S\"oding mechanism in shaping the $\rho(770)$ resonance line. Our research is relevant in the context of ALICE, ATLAS, CMS, and LHCb measurements in $pp$ collisions at the LHC, even when the leading protons are not detected and instead only rapidity-gap conditions are checked experimentally. Our results can also serve as basis for the description of coherent $\pi^{+}\pi^{-}$ production in ultra-peripheral $p$A and AA collisions. This approach can be directly applied to the analysis of photoproduction and small-$Q^{2}$ electroproduction in $ep$ collisions at high energies. Such data exist from the HERA experiments and will be obtained in the future at the EIC.

The presentation is based on arXiv:2508.06334 [hep-ph].