CP violation in the HZZ vertex and left-right asymmetries

We investigate new contributions to the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>H</a:mi><a:mi>Z</a:mi><a:mi>Z</a:mi></a:math> vertex from the flavor changing neutral current (FCNC) involving the Higgs and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>Z</c:mi></c:math> bosons. Our calculations reveal that the form factors <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msubsup><e:mi>h</e:mi><e:mn>2</e:mn><e:mi>V</e:mi></e:msubsup></e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msubsup><g:mi>h</g:mi><g:mn>3</g:mn><g:mi>V</g:mi></g:msubsup></g:math> (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>V</i:mi><i:mo>=</i:mo><i:mi>H</i:mi></i:math>, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>Z</k:mi></k:math>) can be induced through these couplings, and we present our results in terms of the Passarino-Veltman scalar functions. Using the current limits on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>H</m:mi><m:mover accent="true"><m:mi>t</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mi>c</m:mi></m:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>Z</q:mi><q:mover accent="true"><q:mi>t</q:mi><q:mo stretchy="false">¯</q:mo></q:mover><q:mi>c</q:mi></q:math> couplings, we determine that the new contributions to the <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>-conserving form factor <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msubsup><w:mi>h</w:mi><w:mn>2</w:mn><w:mi>V</w:mi></w:msubsup></w:math> are small compared to the Standard Model (SM) predictions. However, for the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>C</y:mi><y:mi>P</y:mi></y:math>-violating form factor <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msubsup><ab:mi>h</ab:mi><ab:mn>3</ab:mn><ab:mi>V</ab:mi></ab:msubsup></ab:math>, the contributions can reach values as high as <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msup><cb:mn>10</cb:mn><cb:mrow><cb:mo>−</cb:mo><cb:mn>6</cb:mn></cb:mrow></cb:msup></cb:math>, 5 orders of magnitude larger than in the SM. Furthermore, we examine how these results influence the left-right asymmetries in the processes <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msup><eb:mi>H</eb:mi><eb:mo>*</eb:mo></eb:msup><eb:mo stretchy="false">→</eb:mo><eb:mi>Z</eb:mi><eb:mi>Z</eb:mi></eb:math> and <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msup><hb:mi>Z</hb:mi><hb:mo>*</hb:mo></hb:msup><hb:mo stretchy="false">→</hb:mo><hb:mi>Z</hb:mi><hb:mi>H</hb:mi></hb:math>. Our findings suggest that significant deviations from SM predictions may occur when considering FCNC contributions.