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

The anomalous magnetic (ã_τ) and electric dipole (d̃_τ) moment of tau lepton described in ττ̄γ vertices are studied via μ⁺μ⁻ → τ⁺τ̄⁻ 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 ã_τ and d̃_τ 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 -2.63×10⁻⁴< ã_τ <2. 65×10⁻⁴ and d̃_τ ≤ 1.47×10⁻¹⁸ e cm at √ s =10 TeV and Lᵢₙₜ=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.