Search for the electromagnetic moments of the $τ$ lepton in photon-photon collisions at the LHeC and the FCC-he

Abstract

We examine the potential of the process $ep \rightarrow eγ^{*} γ^{*} p\rightarrow eτ\barτp$ at the Large Hadron Electron Collider (LHeC) and the Future Circular Hadron Electron Collider (FCC-he) to examine non-standard $τ\barτγ$ coupling in a model independent way by means of the effective Lagrangian approach. We perform pure leptonic and semileptonic decays for $τ^{-}τ^{+}$ production in the final state. Furthermore, we use $L = 10, 50, 100, 300, 500, 1000$ fb$^{-1}$ with at $\sqrt{s}=1.30, 1.98, 7.07, 10$ TeV and we consider systematic uncertainties of $δ_{sys}=0,5,10 \%$. The best sensitivity bounds obtained from the process $ep \rightarrow eγ^{*} γ^{*} p\rightarrow eτ\barτp$ on the anomalous couplings are $-0.0025<\tilde{a}_τ<0.0009$ and $|\tilde{{d}_τ}|<8.85 \times 10^{-18}\, e\,cm$, respectively. Therefore, our results show that the process $ep \rightarrow eγ^{*} γ^{*} p\rightarrow eτ\barτp$ at the LHeC and FCC-he are a very good prospect for probing the anomalous magnetic and electric dipole moments of the $τ$ lepton at $γ^{*} γ^{*}$ mode of the future $ep$ collider.