Detecting a {\mu}{\tau}-philic Z' boson via photon initiated processes at the LHC

Discrepancy between the measured value and the Standard Model prediction of the muon anomalous magnetic moment is a possible hint for new physics. A $Z^{\mathrm{\prime }}$ particle with $\mu \tau$ flavor violating couplings can give a large contribution to the muon anomalous magnetic moment due to the $\tau$ mass enhancement at the one-loop level, and is known to explain the above discrepancy. In this paper, we study the potential of the Large Hadron Collider (LHC) for detecting such a $Z^{\mathrm{\prime }}$ boson via the $p p \to\mu^-\mu^-\tau^+\tau^+ $ process. Earlier studies in the literature only considered the production channel with quark initial states ($p p \to q \bar q \to\mu^-\mu^-\tau^+\tau^+ $)\mathrm{.}Here,weshowthatthephotoninitiatedprocess,$p p \to \gamma \gamma \to \mu^-\mu^-\tau^+\tau^+ $, is in fact the dominant production mode, for a heavy $Z^{\mathrm{\prime }}$ boson of mass greater than a few hundred GeV. The potential of the high luminosity (HL) LHC is also considered.