Constraints on $\tau$ 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 ${\mu }^{+}{\mu }^{-}\to {\tau }^{+}{\bar{\tau }}^{-}$ 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 $95\mathrm{\%}$ confidence level limits on the ${\tilde{a}}_{\tau }$ and ${\tilde{d}}_{\tau }$ parameters without and with systematic uncertainty of $10\mathrm{\%}$ 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 $\sqrt{s}=10$ 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.