Probing charm Yukawa coupling through <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>c</mml:mi><mml:mi>h</mml:mi></mml:math> associated production at the hadron colliders

At present, the study of the charm-quark Yukawa coupling at the Large Hadron Collider mainly focuses on the Higgs decay processes. Such signal suffers from overwhelming QCD background and derives its sensitivity primarily from the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>V</a:mi><a:mi>h</a:mi></a:math> associated production channel. In addition, sensitivity to a possible <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> phase in charm-quark Yukawa at the hadron collider is not discussed. We investigate the charm-Higgs associated production signal that contains a potentially detectable interference term between <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>c</e:mi><e:mi>c</e:mi><e:mi>h</e:mi></e:math> Yukawa coupling mediated diagrams and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>g</g:mi><g:mi>g</g:mi><g:mi>h</g:mi></g:math> coupling mediated diagram. Such an interference term is sensitive to the relative <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>C</i:mi><i:mi>P</i:mi></i:math> phase between contributing diagrams. High dimensional kinematic information is exploited by machine learning techniques to separate the different contribution, and sensitivity on the coupling is derived. Assuming a real <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>κ</k:mi><k:mi>c</k:mi></k:msub></k:math> modification framework, the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mn>1</m:mn><m:mi>σ</m:mi></m:mrow></m:math> bound of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo>−</o:mo><o:mn>5.6</o:mn><o:mo>&lt;</o:mo><o:msub><o:mi>κ</o:mi><o:mi>c</o:mi></o:msub><o:mo>&lt;</o:mo><o:mn>5.6</o:mn></o:math> (HL-LHC) and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mo>−</q:mo><q:mn>1.51</q:mn><q:mo>&lt;</q:mo><q:msub><q:mi>κ</q:mi><q:mi>c</q:mi></q:msub><q:mo>&lt;</q:mo><q:mn>1.62</q:mn></q:math> (FCC) are achieved. When allowing for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>C</s:mi><s:mi>P</s:mi></s:math> phase in the charm Yukawa, a combined <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:mn>1</u:mn><u:mi>σ</u:mi></u:mrow></u:math> bound of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mn>0.32</w:mn><w:mo>&lt;</w:mo><w:mo stretchy="false">|</w:mo><w:msub><w:mi>κ</w:mi><w:mi>c</w:mi></w:msub><w:mo stretchy="false">|</w:mo><w:mo>&lt;</w:mo><w:mn>1.69</w:mn></w:math>, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mo>−</ab:mo><ab:mn>7</ab:mn><ab:mn>7</ab:mn><ab:mi>°</ab:mi><ab:mo>&lt;</ab:mo><ab:mi>α</ab:mi><ab:mo>&lt;</ab:mo><ab:mn>7</ab:mn><ab:mn>7</ab:mn><ab:mi>°</ab:mi></ab:math> (HL-LHC) and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mn>0.70</cb:mn><cb:mo>&lt;</cb:mo><cb:mo stretchy="false">|</cb:mo><cb:msub><cb:mi>κ</cb:mi><cb:mi>c</cb:mi></cb:msub><cb:mo stretchy="false">|</cb:mo><cb:mo>&lt;</cb:mo><cb:mn>1.29</cb:mn></cb:math>, <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mo>−</gb:mo><gb:mn>5</gb:mn><gb:mn>5</gb:mn><gb:mi>°</gb:mi><gb:mo>&lt;</gb:mo><gb:mi>α</gb:mi><gb:mo>&lt;</gb:mo><gb:mn>5</gb:mn><gb:mn>5</gb:mn><gb:mi>°</gb:mi></gb:math> (FCC) can be achieved on the magnitude and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>C</ib:mi><ib:mi>P</ib:mi></ib:math> phase of the coupling, respectively.