Two-loop electroweak corrections to the Higgs boson rare decay process <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>H</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>Z</mml:mi><mml:mi>γ</mml:mi></mml:math>

Recently, the ATLAS and CMS collaborations jointly announced the first evidence of the rare Higgs boson decay channel <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>H</a:mi><a:mo stretchy="false">→</a:mo><a:mi>Z</a:mi><a:mi>γ</a:mi></a:math>, with a ratio of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mn>2.2</d:mn><d:mo>±</d:mo><d:mn>0.7</d:mn></d:math> times the leading order standard model (SM) prediction. In order to face this challenge, it is urgent to produce an even more accurate calculation within the SM. To this end, we calculate in this paper the next-to-leading order (NLO) electroweak (EW) corrections to the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>H</f:mi><f:mo stretchy="false">→</f:mo><f:mi>Z</f:mi><f:mi>γ</f:mi></f:math> process, in which the NLO quantum chromodynamics (QCD) corrections were found tiny. Our calculation finds that the inclusion of NLO EW corrections greatly enhances the prediction reliability. To tame the theoretical uncertainty, we adopt five different renormalization schemes. Combining our result with previous NLO QCD corrections and the signal-background interference, we conclude that the excess in <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>H</i:mi><i:mo stretchy="false">→</i:mo><i:mi>Z</i:mi><i:mi>γ</i:mi></i:math> cannot be explained within the SM. In fact, the incompatibility between the SM prediction and the LHC measurement of the concerned process is exacerbated upon considering the higher order EW corrections, which implies that something beyond the SM could be involved. Published by the American Physical Society 2024