<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>g</mml:mi><mml:mi>g</mml:mi></mml:math> and <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>γ</mml:mi><mml:mi>γ</mml:mi></mml:math> with anomalous couplings at next-to-leading order in QCD

We generalize the next-to-leading order (NLO) QCD calculations for decay rates of $h\ensuremath{\rightarrow}gg$ and $h\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ to case anomalous couplings Higgs boson. demonstrate how this computation can be done in a consistent way within framework an electroweak chiral Lagrangian, based on systematic power counting. It turns out that no additional coupling parameters arise at NLO beyond those already present leading order. The impact is large uncertainties from are significantly reduced NLO. only mildly affected by QCD; here treatment practically eliminates uncertainties. Consequently, our results will allow improved determination these processes. relation Standard Model effective field theory also discussed.