The $\mu^+\mu^-$ collider to sensitivity estimates on the magnetic and electric dipole moments of the tau-lepton

Using the effective Lagrangian formalism, the anomalous magnetic and electric dipole moments of the tau-lepton in the $\mu^{+}\mu^{-} \rightarrow \mu^{+}\gamma^{*} \gamma^{*} \mu^{-}\rightarrow \mu^{+}\tau \bar{\tau}\mu^{-}$ process at the future muon colliders at the $\sqrt{s}=1.5, 3$ and $6$ TeV are investigated. In addition, the bounds at the $95\%$ confidence level on the dipole moments of the tau-lepton using different integrated luminosities are estimated. It is shown that the $\mu^{+}\mu^{-} \rightarrow \mu^{+}\gamma^{*} \gamma^{*} \mu^{-}\rightarrow \mu^{+}\tau \bar{\tau}\mu^{-}$ process leads to a remarkable improvement in the existing experimental bounds on the anomalous magnetic and electric dipole moments of the tau-lepton.