Constraints on τ electromagnetic moments via tau pair production at the Muon colliders

The anomalous magnetic (${\tilde{a}}_{\tau }$) and electric dipole (${\tilde{d}}_{\tau }$) moment of tau lepton described in $\tau \bar{\tau }\gamma$ vertices are studied via ${\mu }^{+}{\mu }^{-}\to {\tau }^{+}{\tau }^{-}$ process at the Muon colliders designed with the proposed center-of-mass-energy/integrated luminosity configurations of 3 TeV/ 1 ab⁻¹ and 10 TeV/ 10 ab⁻¹. We obtained the 95% confidence level limits on the ${\tilde{a}}_{\tau }$ and ${\tilde{d}}_{\tau }$ parameters without and with systematic uncertainty of 10% and compared with the experimental results. The most stringent limits on the anomalous couplings without systematic uncertainty are $-2.63\times 10^{-4}<{\tilde{a}}_{\tau }<2.65\times 10^{-4}$ and $\mid {\tilde{d}}_{\tau }\mid \le 1.47\times 10^{-18}ecm$ at $\sqrt{s}=10\mathrm{TeV}$ and $L_{int}=$ 10 ab⁻¹ option of the Muon collider. Our results show that the Muon colliders lead to a remarkable improvement on the current experimental limits of the anomalous magnetic and electric dipole moments of the tau lepton.