Constraints on $L_{\mu }-L_{\tau }$ interactions at the LHC and beyond

Abstract

In this paper we examine the constraints dedicated LHC multi lepton searches can place on $Z^{\prime }$ bosons coming from gauged muon number minus tau number, $L_{\mu }-L_{\tau }$. As the $L_{\mu }-L_{\tau }$ gauge boson does not couple to proton constituents or electrons at tree level, the current bounds are fairly loose, especially for $M_{Z^{\prime }}\gtrsim 1\mathrm{GeV}$. For $2m_{\mu }<M_{Z^{\prime }}<M_Z/2$ we develop search strategies using the $pp\to Z\to 4\mu$ channel. The cleanliness of the final state, combined with the fact that $pp\to Z\to 4e$, $Z\to 2e2\mu$ can be used as background control samples, allow us to spot $L_{\mu }-L_{\tau }$ $Z^{\prime }$ with couplings $\mathcal{O}(10^{-3})$ times the Standard Model couplings. For lighter $Z^{\prime }$, we propose the mode $pp\to 2\mu +/E_T$. The presence of missing energy means there is a wider set of backgrounds to consider in this final state, such as Drell-Yan production of leptonically decaying $\tau$ pairs, however we find these can be controlled with careful cuts. Combining the $4\mu$ and $2\mu +/E_T$ modes, we find that with $\sim 3{\text{ab}}^{-1}$ of integrated luminosity we are sensitive to couplings $g_{Z^{\prime }}\gtrsim 0.005g_1$ and $0.5\mathrm{GeV}\le {\mathrm{M}}_{{\mathrm{Z}}^{\prime }}\le 40\mathrm{GeV}$ and $g_{Z^{\prime }}\gtrsim 0.001g_1$ for $M_{Z^{\prime }}<2m_{\mu }$. This region includes the parameter space where $L_{\mu }-L_{\tau }$ models can ameliorate the muon $g-2$ anomaly. We repeat these analyses at a future $e^{+}{e}^{-}$ Z-factory, where we find improved sensitivity. Specifically, given $2.6\mathrm{a}{\mathrm{b}}^{-1}$ of luminosity, we can exclude $g_{Z^{\prime }}\gtrsim 0.001g_1$ for $2m_{\mu }\le M_{Z^{\prime }}\le M_Z/2$.

version accepted for publication in PRD

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