Scalar leptoquark contributions to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>g</mml:mi> <mml:mi>g</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mi>Z</mml:mi> <mml:mi>h</mml:mi> </mml:math> process

In this manuscript, we study the general scalar leptoquark contributions to the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>g</a:mi> <a:mi>g</a:mi> <a:mo stretchy="false">→</a:mo> <a:mi>Z</a:mi> <a:mi>h</a:mi> </a:math> process at a one-loop level. We find that the contributions only show up for the off diagonal Higgs and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>Z</d:mi> </d:math> boson interactions with scalar leptoquarks, which can lead to new tensor structures different from the standard model. In the one-field and two-field models, the contributions vanish exactly; thus, the contributions are possible at least in the three-field models. We exemplify the contributions in the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mi>S</f:mi> <f:mn>1</f:mn> </f:msub> <f:mo>+</f:mo> <f:msub> <f:mover accent="true"> <f:mi>R</f:mi> <f:mo stretchy="false">˜</f:mo> </f:mover> <f:mn>2</f:mn> </f:msub> <f:mo>+</f:mo> <f:msub> <f:mi>S</f:mi> <f:mn>3</f:mn> </f:msub> </f:math> model, which can appear in the presence of scalar leptoquark mass splittings and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>C</j:mi> <j:mi>P</j:mi> </j:math> violation. In view of the heavy scalar leptoquark mass suppression, the leading contributions are typically small and difficult to observe at hadron colliders. However, this work offers a quantitative and systematic investigation of scalar leptoquark contributions, also making it valuable for the new physics studies in other models.