Top-induced contributions to H → $$ b\overline{b} $$ and H → $$ c\overline{c} $$ at $$ \mathcal{O}\left({\alpha}_s^3\right) $$

A bstract In this paper we present a fully-differential calculation for the contributions to the partial widths H → $$ b\overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>b</mml:mi><mml:mover><mml:mi>b</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> and H → $$ c\overline{c} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>c</mml:mi><mml:mover><mml:mi>c</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> that are sensitive to the top quark Yukawa coupling y t to order $$ {\alpha}_s^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>α</mml:mi><mml:mi>s</mml:mi><mml:mn>3</mml:mn></mml:msubsup></mml:math> . These contributions first enter at order $$ {\alpha}_s^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>α</mml:mi><mml:mi>s</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:math> through terms proportional to y t y q ( q = b, c ). At order $$ {\alpha}_s^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>α</mml:mi><mml:mi>s</mml:mi><mml:mn>3</mml:mn></mml:msubsup></mml:math> corrections to the mixed terms are present as well as a new contribution proportional to $$ {y}_t^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>y</mml:mi><mml:mi>t</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:math> . Our results retain the mass of the final-state quarks throughout, while the top quark is integrated out resulting in an effective field theory (EFT). Our results are implemented into a Monte Carlo code allowing for the application of arbitrary final-state selection cuts. As an example we present differential distributions for observables in the Higgs boson rest frame using the Durham jet clustering algorithm. We find that the total impact of the top-induced (i.e. EFT) pieces is sensitive to the nature of the final-state cuts, particularly b -tagging and c -tagging requirements. For bottom quarks, the EFT pieces contribute to the total width (and differential distributions) at around the percent level. The impact is much bigger for the H → $$ c\overline{c} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>c</mml:mi><mml:mover><mml:mi>c</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> channel, with effects as large as 15%. We show however that their impact can be significantly reduced by the application of jet-tagging selection cuts.