Pseudoscalar Higgs boson decay to three parton amplitudes at NNLO to higher orders in the dimensional regulator

We present for the first time the second-order corrections of pseudoscalar(<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>A</a:mi></a:mrow></a:math>) Higgs decay to three parton to higher orders in the dimensional regulator. We compute the one- and two-loop amplitudes for processes, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>A</c:mi><c:mo stretchy="false">→</c:mo><c:mi>g</c:mi><c:mi>g</c:mi><c:mi>g</c:mi></c:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>A</f:mi><f:mo stretchy="false">→</f:mo><f:mi>q</f:mi><f:mover accent="true"><f:mi>q</f:mi><f:mo stretchy="false">¯</f:mo></f:mover><f:mi>g</f:mi></f:math>, in the effective theory framework. With suitable crossing of the external momenta, these calculations are well-suited for predicting the differential distribution of pseudoscalar Higgs in association with a jet at hadron colliders, up to next-to-next-to-leading order in the strong coupling constant. These results expanded to higher orders in the dimensional regulator will contribute to the full three-loop cross section. We implement the finite pieces of the amplitudes in a numerical code which can be used with any Monte Carlo phase space generator.