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

The anomalous magnetic (a_) and electric dipole (d_) moment of tau lepton described in vertices are studied via ^+^- ^+^- 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 a_ and d_ 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. 6310^-4< a_ <2. 6510^-4 and d_ 1. 4710^-18 e cm at s =10 TeV and L₈₍ₓ=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.