Two-loop master integrals for the leading QCD corrections to the Higgs coupling to a W pair and to the triple gauge couplings ZW W and γ∗ W W

Abstract

Abstract:We compute the two-loop master integrals required for the leading QCD corrections to the interaction vertex of a massive neutral boson X 0 , e.g. H, Z or γ * , with a pair of W bosons, mediated by a SU(2) L quark doublet composed of one massive and one massless flavor. All the external legs are allowed to have arbitrary invariant masses. The Magnus exponential is employed to identify a set of master integrals that, around d = 4 space-time dimensions, obey a canonical system of differential equations. The canonical master integrals are given as a Taylor series in = (4 − d)/2, up to order four, with coefficients written as combination of Goncharov polylogarithms, respectively up to weight four. In the context of the Standard Model, our results are relevant for the mixed EW-QCD corrections to the Higgs decay to a W pair, as well as to the production channels obtained by crossing, and to the triple gauge boson vertices ZW W and γ * W W .

Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs

“…where the matrices A x ( , x, y) and A y ( , x, y) are linear in the dimensional regularization parameter = (4 − d)/2, being d the number of space-time dimensions. According to the algorithm described in [41][42][43][44], by means of Magnus exponential matrix, we identify a set of MIs I obeying canonical systems of DEQs [40], where the dependence on is factorized from the kinematics,…”

“…The arguments η i of this d log-form, which contain all the dependence of the DEQ on the kinematics, are referred to as the alphabet and they consist in the following 9 letters: Let us observe that, currently, there is neither a proof of existence, nor any systematic algorithm to build a basis of integrals whose system of DEQs is linear in . Nevertheless, by trial and error, we have been always able to find it within the physical contexts we have so far studied [41][42][43][44], as well as for the µe scattering. We believe it is a very important property which could be considered a prerequisite for the existence a canonical basis: in fact, a system of DEQs whose matrix is linear in can be brought into canonical form by a rotation matrix built either by means of Magnus exponential, or equivalently by means of the Wronskian matrix (formed by the solutions of the associated homogenous equations, and their derivatives), as shown for the case of systems of DEQs involving elliptic solutions [59][60][61].…”

Master integrals for the NNLO virtual corrections to $$ q\overline{q}\to t\overline{t} $$ scattering in QCD: the non-planar graphs

“…By following the same the path of the calculation of two-loop integrals for µe → µe and the crossing-related processes considered in [24,25], we adopt a consolidated strategy [26,27], which was proven to be particularly effective in the context of multi-loop integrals that involve multiple kinematic scales [24,25,[27][28][29][30][31]. By means of integration-by-parts identities (IBPs) [32][33][34], we identify a set of 52 master integrals (MIs) that we evaluate analytically, through the differential equations method [35][36][37][38].…”

Exact top Yukawa corrections to Higgs boson decay into bottom quarks

“…and by using the Magnus exponential method [33][34][35][36][37][38] in order to identify a basis of MIs that fulfil a system of canonical DEs [39],…”