Light-by-Light scattering in ultraperipheral heavy ion collisions: Estimating inelastic contributions

The current state-of-the-art theoretical estimations lead to cross-sections for $AA \to \gamma \gamma AA$ which are somewhat smaller than the measured ones by the ATLAS and CMS Collaborations, which motivates the searching and calculation of subleading corrections disregarded in these previous studies. In this paper, we estimate for the first time the contribution of inelastic channels to the Light-by-Light (LbL) scattering in ultraperipheral collisions of heavy ions (UPHICs), in which one or both of the incident nuclei dissociate ($A A \to \gamma \gamma X Y$ where $X, Y = A, A'$) due to the photon emission. These new mechanisms are related to extra emissions that are rather difficult to identify at the LHC and may be misinterpreted as enhanced $\gamma \gamma \to \gamma \gamma$ scattering compared to the Standard Model result. We include processes of coupling of photons to individual nucleons (protons and neutrons) in addition to coherent coupling to the whole nuclei (called standard approach here). Both elastic (nucleon in the ground state) and inelastic (nucleon in an excited state) in the couplings of photons to nucleons are taken into account. The inelastic nucleon fluxes are calculated using CT18qed photon in nucleon PDFs. The inelastic photon fluxes are shown and compared to standard photon fluxes in the nucleus. In addition, we show the ratio of the inelastic corrections to the standard contribution as a function of diphoton invariant mass and photon rapidity difference. We find that for the ATLAS acceptance region the inelastic corrections grow with $M_{\gamma \gamma}$ and rapidity difference. Our results indicate that the inelastic contributions can be of the order of 20-40 \% of the traditional (no nuclear excitation) predictions. Uncertainties due to factorization scale choice are quantified.