Gauged L μ − L τ at a muon collider

We investigate the sensitivity of the projected TeV muon collider to the gauged ${L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ model. Two processes are considered: ${Z}^{\ensuremath{'}}$-mediated two-body scatterings ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ with $\ensuremath{\ell}=\ensuremath{\mu}$ or $\ensuremath{\tau}$ and scattering with initial state photon emission, ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\gamma}{Z}^{\ensuremath{'}},{Z}^{\ensuremath{'}}\ensuremath{\rightarrow}\ensuremath{\ell}\overline{\ensuremath{\ell}}$, where $\ensuremath{\ell}$ can be $\ensuremath{\mu}$, $\ensuremath{\tau}$, or ${\ensuremath{\nu}}_{\ensuremath{\mu}/\ensuremath{\tau}}$. We quantitatively study the sensitivities of these two processes by taking into account possible signals and relevant backgrounds in a muon collider experiment with a center-of-mass energy $\sqrt{s}=3\text{ }\text{ }\mathrm{TeV}$ and a luminosity $L=1\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$. For two-body scattering, one can exclude ${Z}^{\ensuremath{'}}$ masses ${M}_{{Z}^{\ensuremath{'}}}\ensuremath{\lesssim}100\text{ }\text{ }\mathrm{TeV}$ with $\mathcal{O}(1)$ gauge couplings. When ${M}_{{Z}^{\ensuremath{'}}}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{TeV}l\sqrt{s}$, one can exclude ${g}^{\ensuremath{'}}\ensuremath{\gtrsim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$. The process with photon emission is more powerful than the two-body scattering if ${M}_{{Z}^{\ensuremath{'}}}l\sqrt{s}$. For instance, a sensitivity of ${g}^{\ensuremath{'}}\ensuremath{\simeq}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ can be achieved at ${M}_{{Z}^{\ensuremath{'}}}=1\text{ }\text{ }\mathrm{TeV}$. The parameter spaces favored by the $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ and $B$ anomalies with ${M}_{{Z}^{\ensuremath{'}}}g100\text{ }\text{ }\mathrm{GeV}$ are entirely covered by a muon collider.