Probing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi>L</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> lepton number violating SMEFT operators at the same-sign m

We investigate lepton number violation (LNV) induced by <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Δ</a:mi> <a:mi>L</a:mi> <a:mo>=</a:mo> <a:mn>2</a:mn> </a:math> dimension-seven Standard Model effective field theory (SMEFT) operators in the context of same-sign muon colliders. Specifically, we study <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msup> <d:mi>μ</d:mi> <d:mo>+</d:mo> </d:msup> <d:msup> <d:mi>μ</d:mi> <d:mo>+</d:mo> </d:msup> <d:mo stretchy="false">→</d:mo> <d:msup> <d:mi>W</d:mi> <d:mo>+</d:mo> </d:msup> <d:msup> <d:mi>W</d:mi> <d:mo>+</d:mo> </d:msup> <d:mo>/</d:mo> <d:msup> <d:mi>W</d:mi> <d:mo>+</d:mo> </d:msup> <d:mi>q</d:mi> <d:msup> <d:mi>q</d:mi> <d:mo>′</d:mo> </d:msup> </d:math> production at the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>μ</g:mi> <g:mi>TRISTAN</g:mi> </g:math> at <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msqrt> <i:mi>s</i:mi> </i:msqrt> <i:mo>=</i:mo> <i:mn>2</i:mn> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>TeV</i:mi> </i:math> with an integrated luminosity of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mn>1</k:mn> <k:mtext> </k:mtext> <k:mtext> </k:mtext> <k:msup> <k:mrow> <k:mi>ab</k:mi> </k:mrow> <k:mrow> <k:mo>−</k:mo> <k:mn>1</k:mn> </k:mrow> </k:msup> </k:mrow> </k:math> , 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 future circular collider. 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.