Higgs boson production at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>μ</mml:mi></m

We study Higgs boson production at <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>μ</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>μ</a:mi><a:mo>+</a:mo></a:msup></a:math> colliders at high energy. Since both initial-state particles are positively charged, there is no <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>W</c:mi></c:math> boson fusion at the leading order, as it requires a <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>W</e:mi><e:mo>+</e:mo></e:msup><e:msup><e:mi>W</e:mi><e:mo>−</e:mo></e:msup></e:math> pair. However, we find that the cross section of the higher-order, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>γ</g:mi></g:math>-and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>Z</i:mi></i:math>-mediated <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>W</k:mi></k:math> boson fusion process is large at high center-of-mass energies <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msqrt><m:mi>s</m:mi></m:msqrt></m:math>, growing as <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo stretchy="false">(</o:mo><o:mi>log</o:mi><o:mi>s</o:mi><o:msup><o:mo stretchy="false">)</o:mo><o:mn>3</o:mn></o:msup></o:math>. This is in contrast to the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>log</s:mi><s:mi>s</s:mi></s:math> behavior of the leading-order <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>W</u:mi></u:math> boson fusion. Thus, even though it is a higher-order process, the rate of Higgs boson production for 10 TeV energies at <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msup><w:mi>μ</w:mi><w:mo>+</w:mo></w:msup><w:msup><w:mi>μ</w:mi><w:mo>+</w:mo></w:msup></w:math> colliders with polarized beams can be as high as about half of the one at <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msup><y:mi>μ</y:mi><y:mo>+</y:mo></y:msup><y:msup><y:mi>μ</y:mi><y:mo>−</y:mo></y:msup></y:math> colliders, assuming the same integrated luminosity. To calculate the cross section of this process accurately, we carefully treat the collinear emission of the photon in the intermediate state. The thereby obtained large cross section furthermore shows the significance of Higgs production with an extra <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>W</ab:mi></ab:math> boson in the final state also at <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msup><cb:mi>μ</cb:mi><cb:mo>+</cb:mo></cb:msup><cb:msup><cb:mi>μ</cb:mi><cb:mo>−</cb:mo></cb:msup></cb:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msup><eb:mi>e</eb:mi><eb:mo>+</eb:mo></eb:msup><eb:msup><eb:mi>e</eb:mi><eb:mo>−</eb:mo></eb:msup></eb:math> colliders. Published by the American Physical Society 2024