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A bstract We present a next-to-next-to-leading order (NNLO) QCD calculation of the bottom-induced contributions to the production of a Higgs boson plus a jet, i.e. the process pp → H + j to $$ \mathcal{O}\left({y}_b^2{\alpha}_s^3\right) $$ O y b 2 α s 3 . We work in the five-flavor scheme (5FS) in which the bottom quark mass is retained only in the coupling to the Higgs boson. Our calculation uses N -jettiness slicing to regulate infrared divergences, allowing for fully-differential predictions for collider observables. After extensively validating the methodology, we present results for the 13 TeV LHC. Our NNLO predictions show a marked improvement in the overall renormalization and factorization scale dependence, the latter of which proves to be particularly troublesome for 5FS calculations at lower orders. In addition, using the same methodology we present a NNLO computation of $$ b\overline{b} $$ b b ¯ → H . Our results are implemented into MCFM. 

A bstract In this paper we present a fully-differential calculation for the contributions to the partial widths H → $$ b\overline{b} $$ b b ¯ and H → $$ c\overline{c} $$ c c ¯ that are sensitive to the top quark Yukawa coupling y t to order $$ {\alpha}_s^3 $$ α s 3 . These contributions first enter at order $$ {\alpha}_s^2 $$ α s 2 through terms proportional to y t y q ( q = b, c ). At order $$ {\alpha}_s^3 $$ α s 3 corrections to the mixed terms are present as well as a new contribution proportional to $$ {y}_t^2 $$ y t 2 . 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 → $$ c\overline{c} $$ c c ¯ 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. 

A bstract We showcase the calculation of the master integrals needed for the two loop mixed QCD-QED virtual corrections to the neutral current Drell-Yan process ( $$ q\overline{q} $$ q q ¯ → l + l − ). After establishing a basis of 51 master integrals, we cast the latter into canonical form by using the Magnus algorithm. The dependence on the lepton mass is then expanded such that potentially large logarithmic contributions are kept. After determining all boundary constants, we give the coefficients of the Taylor series around four space-time dimensions in terms of generalized polylogarithms up to weight four.