Heavy Neutral Leptons in Gauged $U(1{)}_{L_{\mu }-L_{\tau }}$ at Muon Collider

Abstract

Heavy neutral leptons $N$ are the most appealing candidates to generate the tiny neutrino masses. In this paper, we study the signature of heavy neutral leptons in gauged $U(1{)}_{L_{\mu }-L_{\tau }}$ at a muon collider. Charged under the $U(1{)}_{L_{\mu }-L_{\tau }}$ symmetry, the heavy neutral leptons can be pair produced via the new gauge boson $Z^{\prime }$ at muon collider as ${\mu }^{+}{\mu }^{-}\to Z^{\prime \ast }\to NN$ and ${\mu }^{+}{\mu }^{-}\to Z^{\prime (\ast )}\gamma \to NN\gamma$. We then perform a detailed analysis on the lepton number violation signature ${\mu }^{+}{\mu }^{-}\to NN\to {\mu }^{\pm }{\mu }^{\pm }{W}^{\mp }{W}^{\mp }$ and ${\mu }^{+}{\mu }^{-}\to NN\gamma \to {\mu }^{\pm }{\mu }^{\pm }{W}^{\mp }{W}^{\mp }\gamma$ at the 3 TeV muon collider, where the hadronic decays of $W$ boson are treated as fat-jets $J$. These lepton number violation signatures have quite clean backgrounds at the muon collider. Our simulation shows that a wide range of viable parameter space is within the reach of the 3 TeV muon collider. For instance, with new gauge coupling $g^{\prime }=0.6$ and an integrated luminosity of 1000 fb${}^{-1}$, the ${\mu }^{\pm }{\mu }^{\pm }JJ$ signal could probe $m_{Z^{\prime }}\lesssim 12.5$ TeV. Meanwhile, if the gauge boson mass satisfies $2m_N<m_{Z^{\prime }}<\sqrt{s}$, the ${\mu }^{\pm }{\mu }^{\pm }JJ\gamma$ signature would be more promising than the ${\mu }^{\pm }{\mu }^{\pm }JJ$ signature.

Comments: 20 pages, 8 figures, 2 tables