Probing the $\tau$ anomalous magnetic and electric dipole moments in photon-induced $\gamma \gamma \to {\tau }^{+}{\tau }^{-}$ production at the FCC-hh

The sensitivity of the FCC-hh to the anomalous magnetic moment $a_{\tau }$ and the electric dipole moment $d_{\tau }$ of the $\tau$ lepton is studied in photon-induced $\gamma \gamma \to {\tau }^{+}{\tau }^{-}$ production with both $\tau$ leptons decaying hadronically. Central exclusive (elastic) signal events, in which both protons remain intact, are generated with MadGraph5_aMC@NLO using a FeynRules UFO model of the anomalous $\gamma \tau \tau$ vertex merged with the TauDecay model, so that the $\tau$ decays and their spin correlations are included in the matrix element. Single- and double-dissociative production is estimated with SuperChic and added to the elastic signal with its own coupling dependence and with normalisation and shape uncertainties of 25%. Pythia 8 decays the unstable hadrons in the signal, decays the $\tau$ leptons and simulates the parton shower and hadronisation in the backgrounds, and hadronises the dissociated protons. Signal and backgrounds are passed through the Delphes simulation of the FCC-hh detector. Hadronic $\tau$ decays are reconstructed from particle-flow tracks and photons with an algorithm based on the hadrons-plus-strips approach, with an efficiency of 73.4% within the acceptance. Requiring no additional tracks from the $\tau$ vertices retains part of the dissociative contribution and reduces the Drell-Yan and $\gamma \gamma \to WW$ backgrounds to 0.9% of the SM yield. The couplings are constrained from the shape of the total transverse mass distribution. For a centre-of-mass energy of 84 TeV and 30 ab${}^{-1}$, the expected 95% CL limits are $-3.38\times {10}^{-4}<a_{\tau }<3.36\times {10}^{-4}$ and $\mathrm{\mid }{d}_{\tau }\mathrm{\mid }<1.88\times {10}^{-18}e$cm, about an order of magnitude beyond the current bounds. Results are also given for FCC-hh scenarios between 72 and 120 TeV and for an optimistic detector parametrisation.