Probing a heavy dark Z boson at multi-TeV muon colliders: Leveraging the optimized recoil mass technique Article Swipe

We investigate the discovery potential of multi-TeV muon colliders for a heavy dark <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Z</a:mi> </a:math> boson ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>Z</c:mi> <c:mi mathvariant="normal">D</c:mi> </c:msub> </c:math> ) with a mass above 1 TeV, via the associated production process <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msup> <f:mi>μ</f:mi> <f:mo>+</f:mo> </f:msup> <f:msup> <f:mi>μ</f:mi> <f:mo>−</f:mo> </f:msup> <f:mo stretchy="false">→</f:mo> <f:msub> <f:mi>Z</f:mi> <f:mi mathvariant="normal">D</f:mi> </f:msub> <f:mi>γ</f:mi> </f:math> . This process enables precise reconstruction of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msub> <j:mi>M</j:mi> <j:msub> <j:mi>Z</j:mi> <j:mi mathvariant="normal">D</j:mi> </j:msub> </j:msub> </j:math> through the photon recoil mass ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>m</m:mi> <m:mi>recoil</m:mi> </m:msub> </m:math> ). Focusing on the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>Z</o:mi> <o:mi mathvariant="normal">D</o:mi> </o:msub> <o:mo stretchy="false">→</o:mo> <o:mi>j</o:mi> <o:mi>j</o:mi> <o:mi>X</o:mi> </o:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>Z</s:mi> <s:mi mathvariant="normal">D</s:mi> </s:msub> <s:mo stretchy="false">→</s:mo> <s:msup> <s:mi>e</s:mi> <s:mo>+</s:mo> </s:msup> <s:msup> <s:mi>e</s:mi> <s:mo>−</s:mo> </s:msup> </s:math> decay modes, we present strategies to achieve high sensitivity to the kinetic mixing parameter <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>ϵ</w:mi> </w:math> at 3, 6, and 10 TeV muon colliders with integrated luminosities of 1, 4, and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mrow> <y:mn>10</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> , respectively, assuming that <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>Z</ab:mi> <ab:mi mathvariant="normal">D</ab:mi> </ab:msub> </ab:math> decays exclusively into Standard Model particles. We apply mass-dependent cuts on <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:msub> <db:mi>m</db:mi> <db:mi>recoil</db:mi> </db:msub> </db:math> and <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msub> <fb:mi>m</fb:mi> <fb:mrow> <fb:mi>e</fb:mi> <fb:mi>e</fb:mi> </fb:mrow> </fb:msub> </fb:math> to account for the energy-dependent detector response. For heavier <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:msub> <hb:mi>M</hb:mi> <hb:msub> <hb:mi>Z</hb:mi> <hb:mi mathvariant="normal">D</hb:mi> </hb:msub> </hb:msub> </hb:math> , the associated photon becomes less energetic, leading to better photon energy resolution and enabling more stringent <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:msub> <kb:mi>m</kb:mi> <kb:mi>recoil</kb:mi> </kb:msub> </kb:math> cuts. Conversely, for lighter <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:msub> <mb:mi>M</mb:mi> <mb:msub> <mb:mi>Z</mb:mi> <mb:mi mathvariant="normal">D</mb:mi> </mb:msub> </mb:msub> </mb:math> , the lower-energy electron pair from <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"> <pb:msub> <pb:mi>Z</pb:mi> <pb:mi mathvariant="normal">D</pb:mi> </pb:msub> <pb:mo stretchy="false">→</pb:mo> <pb:msup> <pb:mi>e</pb:mi> <pb:mo>+</pb:mo> </pb:msup> <pb:msup> <pb:mi>e</pb:mi> <pb:mo>−</pb:mo> </pb:msup> </pb:math> allows tighter invariant mass ( <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"> <tb:msub> <tb:mi>m</tb:mi> <tb:mrow> <tb:mi>e</tb:mi> <tb:mi>e</tb:mi> </tb:mrow> </tb:msub> </tb:math> ) cuts. By combining these complementary <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:msub> <vb:mi>m</vb:mi> <vb:mi>recoil</vb:mi> </vb:msub> </vb:math> - and <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"> <xb:msub> <xb:mi>m</xb:mi> <xb:mrow> <xb:mi>e</xb:mi> <xb:mi>e</xb:mi> </xb:mrow> </xb:msub> </xb:math> -based selections across both the <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"> <zb:mi>j</zb:mi> <zb:mi>j</zb:mi> <zb:mi>X</zb:mi> </zb:math> and <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"> <bc:msup> <bc:mi>e</bc:mi> <bc:mo>+</bc:mo> </bc:msup> <bc:msup> <bc:mi>e</bc:mi> <bc:mo>−</bc:mo> </bc:msup> </bc:math> channels, we achieve sensitivity to <dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"> <dc:mi>ϵ</dc:mi> </dc:math> down to <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"> <fc:mi mathvariant="script">O</fc:mi> <fc:mo stretchy="false">(</fc:mo> <fc:msup> <fc:mn>10</fc:mn> <fc:mrow> <fc:mo>−</fc:mo>