Gauged $L^{}_{\mu}{-}L^{}_{\tau}$ at a muon collider

TL;DR

This paper assesses the potential of a 3 TeV muon collider to detect or constrain a $L_\mu - L_ au$ gauge boson, exploring processes sensitive to different mass ranges and comparing their effectiveness.

Contribution

It provides a detailed sensitivity analysis of a muon collider for the $L_\mu - L_ au$ model, highlighting the collider's ability to probe parameter spaces relevant to current anomalies.

Findings

Can exclude $Z'$ masses up to 100 TeV with order-one couplings.

Photon emission processes are more sensitive for $Z'$ masses below 3 TeV.

Muon collider can cover parameter space relevant to $(g-2)_\mu$ and B anomalies.

Abstract

We investigate the sensitivity of the projected TeV muon collider to the gauged $L^{}_{\mu}$-$L^{}_{\tau}$ model. Two processes are considered: $Z'$-mediated two-body scatterings $\mu^+ \mu^- \to \ell^+ \ell^-$ with $\ell = \mu$ or $\tau$, and scattering with initial state photon emission, $\mu^+ \mu^- \to \gamma Z',~Z' \to \ell \overline{\ell}$, where $\ell$ can be $\mu$, $\tau$ or $\nu_{\mu/\tau}$. 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 $\sqrt{s} = 3~{\rm TeV}$ and a luminosity $L=1~{\rm ab^{-1}}$. For two-body scattering one can exclude $Z'$ masses $M^{}_{Z'} \lesssim 100~{\rm TeV}$ with $\mathcal{O}(1)$ gauge couplings. When $M^{}_{Z'} \lesssim 1~{\rm TeV} <\sqrt{s}$, one can exclude $g' \gtrsim 2\times 10^{-2}$. The process with photon emission is more powerful than the two-body scattering if $M^{}_{Z'} < \sqrt{s}$. For instance, a sensitivity of $g' \simeq 4 \times 10^{-3}$ can be achieved at $M^{}_{Z'} = 1~{\rm TeV}$. The parameter spaces favored by the $(g-2)^{}_{\mu}$ and $B$ anomalies with $M^{}_{Z'} > 100~{\rm GeV}$ are entirely covered by a muon collider.