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′ 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 μ+e− and μ+μ+ collisions in μTRISTAN experiment Z′ mediated 2→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 constraints 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 μ+e−→μ+e− and μ+μ+→μ+μ+ processes which could be probed at μTRISTAN experiment further enlightening the interaction between Z′ and charged leptons and the U(1)X breaking scale.
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