The dipole formalism for next-to-leading order QCD calculations with massive partons

Abstract

The dipole subtraction method for calculating next-to-leading order corrections in QCD was originally only formulated for massless partons. In this paper we extend its definition to include massive partons, namely quarks, squarks and gluinos. We pay particular attention to the quasi-collinear region, which gives rise to terms that are enhanced by logarithms of the parton masses, M. By ensuring that our subtraction cross section matches the exact real cross section in all quasi-collinear regions we achieve uniform convergence both for hard scales Q ∼ M and Q ≫ M. Moreover, taking the masses to zero, we exactly reproduce the previously-calculated massless results. We give all the analytical formulae necessary to construct a numerical program to evaluate the next-to-leading order QCD corrections to arbitrary observables in an arbitrary process.

Hadronic top-quark pair-production with one jet and parton showering

“…Perfect agreement with [7,8] has been found typically at the per-mille level. Also note that the computation of [7,8] has employed dipole subtraction with massive partons [35] for the cancellation of the soft and collinear divergences between the real and virtual contributions. As mentioned, the POWHEG BOX relies on FKS subtraction [26] and, of course, the results for physical cross sections at NLO must be independent of the chosen scheme, which constitutes another strong check of the current implementation.…”

Electroweak production of top-quark pairs ine+e−annihilation at NNLO in QCD: The vector current contributions

“…Therefore, in general the power corrections are proportional to the LO cross sections and depend on threshold behaviors of dσ (2) /dτ as shown in Eq. (45). Furthermore, the power corrections contain logarithmic terms of the form ln(s/m 2 t ), which become large as s increased.…”

“…At NLO, this is relatively straightforward to do and both phase-space slicing [33][34][35][36][37][38][39] and subtraction [40][41][42][43][44][45] techniques which solve the problem were worked out long time ago. However, as is clear from the massive amount of literature on the subject [46,47,, analogous techniques at NNLO are considerably more complicated to develop and complete solutions took much longer to emerge.…”

QCD corrections to the hadronic production of a heavy quark pair and a W-boson including decay correlations

“…The tree-level real radiation process has been computed using the diagrams shown in figure 15, adopting the same choice of massive spinors as used in the virtual contribution. Infrared singularities are handled using the subtraction method [33] implemented using the dipole formulation [34] and extended to the case of massive emitters and spectators [35]. The full calculation will be made available as part of the the MCFM code [31,32].…”