Probing $\Delta L=2$ lepton number violating SMEFT operators at the same-sign muon collider

We investigate lepton number violation (LNV) induced by $\Delta L = 2$ dimension-seven Standard Model Effective Field Theory (SMEFT) operators in the context of same-sign muon colliders. Specifically, we study $\mu^+ \mu^+ \rightarrow W^+W^+/\;W^+qq'$ production at the $\mu$TRISTAN at $\sqrt{s} =$ 2 TeV with an integrated luminosity of 1 ab$^{-1}$, using the final-state signature comprising two fat jets. This process is sensitive to eight distinct SMEFT operators, providing a unique avenue for testing LNV beyond the Standard Model. We determine the maximal sensitivity to these operators and compare our results with existing LHC constraints and future projections from the FCC. Our findings highlight the potential of same-sign muon colliders to serve as powerful probes of LNV and New Physics (NP) at the TeV scale.