$Z^{\prime }$ induced forward dominant processes in $\mu$TRISTAN experiment

Abstract

General $U(1)$ extension of the Standard Model (SM) is a well motivated beyond the Standard Model(BSM) scenario where three generations of right handed neutrinos (RHNs) are introduced to cancel gauge and mixed gauge-gravity anomalies. After the $U(1{)}_X$ is broken, RHNs participate in the seesaw mechanism to generate light neutrino masses satisfying neutrino oscillation data. In addition to that, a neutral gauge boson $Z^{\prime }$ is evolved which interacts with the left and right handed fermions differently manifesting chiral nature of the model which could be probed in future collider experiments. As a result, if we consider ${\mu }^{+}{e}^{-}$ and ${\mu }^{+}{\mu }^{+}$ collisions in $\mu$TRISTAN experiment $Z^{\prime }$ mediated $2\to 2$ scattering will appear in $t-$ and $u-$channels depending on the initial and final states being accompanied by the photon and $Z$ mediated interactions. This will result well motivated resulting forward dominant scenarios giving rise to sizable left-right asymmetry. Estimating constrains on general $U(1)$ coupling from LEP-II and LHC for different $U(1{)}_X$ charges, we calculate differential and integrated scattering cross section and left-right asymmetry for ${\mu }^{+}{e}^{-}\to {\mu }^{+}{e}^{-}$ and ${\mu }^{+}{\mu }^{+}\to {\mu }^{+}{\mu }^{+}$ processes which could be probed at $\mu$TRISTAN experiment further enlightening the interaction between $Z^{\prime }$ and charged leptons and the $U(1{)}_X$ breaking scale.

arXiv comment18 pages

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