Probing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>C</mml:mi> <mml:mi>P</mml:mi> </mml:math> violation through vector boson fusion at high-energy muon colliders

We investigate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>C</a:mi> <a:mi>P</a:mi> </a:math> -violating effects in electroweak interactions at future high-energy muon colliders within the Standard Model effective field theory framework. Focusing on four dimension-six <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>C</c:mi> <c:mi>P</c:mi> </c:math> -odd operators— <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:msub> <e:mrow> <e:mi mathvariant="script">O</e:mi> </e:mrow> <e:mrow> <e:mover accent="true"> <e:mrow> <e:mi>W</e:mi> </e:mrow> <e:mrow> <e:mo stretchy="false">˜</e:mo> </e:mrow> </e:mover> </e:mrow> </e:msub> <e:mo>,</e:mo> <e:msub> <e:mrow> <e:mi mathvariant="script">O</e:mi> </e:mrow> <e:mrow> <e:mi>H</e:mi> <e:mover accent="true"> <e:mrow> <e:mi>W</e:mi> </e:mrow> <e:mrow> <e:mo stretchy="false">˜</e:mo> </e:mrow> </e:mover> </e:mrow> </e:msub> <e:mo>,</e:mo> <e:msub> <e:mrow> <e:mi mathvariant="script">O</e:mi> </e:mrow> <e:mrow> <e:mi>H</e:mi> <e:mover accent="true"> <e:mrow> <e:mi>W</e:mi> </e:mrow> <e:mrow> <e:mo stretchy="false">˜</e:mo> </e:mrow> </e:mover> <e:mi>B</e:mi> </e:mrow> </e:msub> <e:mo>,</e:mo> <e:msub> <e:mrow> <e:mi mathvariant="script">O</e:mi> </e:mrow> <e:mrow> <e:mi>H</e:mi> <e:mover accent="true"> <e:mrow> <e:mi>B</e:mi> </e:mrow> <e:mrow> <e:mo stretchy="false">˜</e:mo> </e:mrow> </e:mover> </e:mrow> </e:msub> </e:mrow> </e:math> —we analyze vector boson fusion production of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>W</s:mi> </s:math> and Higgs bosons using <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>C</u:mi> <u:mi>P</u:mi> </u:math> -odd observables and their asymmetries. With detailed simulations including parton showering, hadronization, and detector effects, we derive exclusion sensitivities through a binned likelihood analysis. For example, at <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msqrt> <w:mi>s</w:mi> </w:msqrt> <w:mo>=</w:mo> <w:mn>3</w:mn> <w:mtext> </w:mtext> <w:mtext> </w:mtext> <w:mi>TeV</w:mi> </w:math> with <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mrow> <y:mn>2</y:mn> <y:mtext> </y:mtext> <y:mtext> </y:mtext> <y:msup> <y:mrow> <y:mi>ab</y:mi> </y:mrow> <y:mrow> <y:mo>−</y:mo> <y:mn>1</y:mn> </y:mrow> </y:msup> </y:mrow> </y:math> , the coefficient <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>C</ab:mi> <ab:mover accent="true"> <ab:mi>W</ab:mi> <ab:mo stretchy="false">˜</ab:mo> </ab:mover> </ab:msub> </ab:math> can be constrained at the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi mathvariant="script">O</eb:mi> <eb:mo stretchy="false">(</eb:mo> <eb:mn>0.02</eb:mn> <eb:mo stretchy="false">)</eb:mo> </eb:math> level, improving to <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mi mathvariant="script">O</jb:mi> <jb:mo stretchy="false">(</jb:mo> <jb:mn>0.008</jb:mn> <jb:mo stretchy="false">)</jb:mo> </jb:math> at 10 TeV with <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:mrow> <ob:mn>2</ob:mn> <ob:mtext> </ob:mtext> <ob:mtext> </ob:mtext> <ob:msup> <ob:mrow> <ob:mi>ab</ob:mi> </ob:mrow> <ob:mrow> <ob:mo>−</ob:mo> <ob:mn>1</ob:mn> </ob:mrow> </ob:msup> </ob:mrow> </ob:math> , and <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:mi mathvariant="script">O</qb:mi> <qb:mo stretchy="false">(</qb:mo> <qb:mn>0.003</qb:mn> <qb:mo stretchy="false">)</qb:mo> </qb:math> with <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:mrow> <vb:mn>10</vb:mn> <vb:mtext> </vb:mtext> <vb:mtext> </vb:mtext> <vb:msup> <vb:mrow> <vb:mi>ab</vb:mi> </vb:mrow> <vb:mrow> <vb:mo>−</vb:mo> <vb:mn>1</vb:mn> </vb:mrow> </vb:msup> </vb:mrow> </vb:math> . These results significantly surpass current LHC and projected International linear collider sensitivities, demonstrating the unique potential of high-energy muon colliders to provide direct and model-independent probes of <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"> <xb:mi>C</xb:mi> <xb:mi>P</xb:mi> </xb:math> violation in the electroweak sector.