Next-to-leading-order electroweak correction to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>H</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mn>0</mml:m

Inspired by the recent observation of the Higgs boson radiative decay into <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>Z</a:mi><a:mn>0</a:mn></a:msup></a:math> by and Collaborations, we investigate the next-to-leading-order (NLO) electroweak correction to this rare decay process in Standard Model (SM). Implementing the on shell renormalization scheme, we find that the magnitude of the NLO electroweak correction may reach 7% of the leading-order (LO) prediction, much more significant than that of the NLO QCD correction, which is merely about 0.3%. After incorporating the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi mathvariant="script">O</c:mi><c:mo stretchy="false">(</c:mo><c:mi>α</c:mi><c:mo stretchy="false">)</c:mo></c:math> correction, the predicted partial width from various <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>α</h:mi></h:math> schemes tend to converge to each other. Including both NLO electroweak and QCD corrections, the SM prediction for the branching fraction shifts from the LO value of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:mo stretchy="false">(</j:mo><j:mn>1.40</j:mn><j:mi>–</j:mi><j:mn>1.71</j:mn><j:mo stretchy="false">)</j:mo><j:mo>×</j:mo><j:msup><j:mrow><j:mn>10</j:mn></j:mrow><j:mrow><j:mo>−</j:mo><j:mn>3</j:mn></j:mrow></j:msup></j:mrow></j:math> to <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mo stretchy="false">(</n:mo><n:mn>1.55</n:mn><n:mo>±</n:mo><n:mn>0.06</n:mn><n:mo stretchy="false">)</n:mo><n:mo>×</n:mo><n:msup><n:mn>10</n:mn><n:mrow><n:mo>−</n:mo><n:mn>3</n:mn></n:mrow></n:msup></n:math>, considerably lower than the measured value <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msub><r:mi mathvariant="script">B</r:mi><r:mi>exp</r:mi></r:msub><r:mo stretchy="false">[</r:mo><r:mi>H</r:mi><r:mo stretchy="false">→</r:mo><r:msup><r:mi>Z</r:mi><r:mn>0</r:mn></r:msup><r:mi>γ</r:mi><r:mo stretchy="false">]</r:mo><r:mo>=</r:mo><r:mo stretchy="false">(</r:mo><r:mn>3.4</r:mn><r:mo>±</r:mo><r:mn>1.1</r:mn><r:mo stretchy="false">)</r:mo><r:mo>×</r:mo><r:msup><r:mn>10</r:mn><r:mrow><r:mo>−</r:mo><r:mn>3</r:mn></r:mrow></r:msup></r:math>. Resolving this discrepancy clearly calls for further theoretical investigations, and, more importantly, experimental efforts from and the prospective Higgs factories such as and . Published by the American Physical Society 2024