Resummation prescriptions and ambiguities in SCET vs. direct QCD: Higgs production as a case study

Abstract

Abstract:We perform a comparison of soft-gluon resummation in SCET vs. direct QCD (dQCD), using Higgs boson production in gluon fusion as a case study, with the goal of tracing the quantitative impact of each source of difference between the two approaches. We show that saddle-point methods enable a direct quantitative comparison despite the fact that the scale which is resummed in the two approaches is not the same. As a byproduct, we put in one-to-one analytic correspondence various features of either approach: specifically, we show how the SCET method for treating the Landau pole can be implemented in dQCD, and how the resummation of the optimal partonic scale of dQCD can be implemented in SCET. We conclude that the main quantitative difference comes from power-suppressed subleading contributions, which could in fact be freely tuned in either approach, and not really characteristic of either. This conclusion holds for Higgs production in gluon fusion, but it is in fact generic for processes with similar kinematics. For Higgs production, everything else being equal, SCET resummation at NNLL in the BecherNeubert implementation leads to essentially no enhancement of the NNLO cross-section, unlike dQCD in the standard implementation of Catani et al.

On the Higgs cross section at N3LO+N3LL and its uncertainty

“…In the present case N saddle 2, so we find that the scale that minimizes the size of the logarithms is close to µ 0 = m H /2. Similar conclusions have been obtained from z-space arguments [53] and within an effective theory framework [54,55]. As the process gets closer to threshold, N saddle grows and the optimal scale gets correspondingly smaller: we have indeed verified that closer to threshold (larger m H or smaller collider energy) the perturbative convergence is much improved at smaller scales.…”

Top quark pair production beyond NNLO

“…The position N 0 of the saddle typically depends very weakly on the partonic cross section, and is mainly determined by the parton luminosity; the saddle-point approximation, with the inclusion of quadratic fluctuations around the saddle, turns out to be generally quite accurate [51]. It is then possible to infer properties of the hadronic cross section from the behaviour of the partonic cross section at the value of N which corresponds to the saddle point for given hadronic kinematics.…”

Three loop soft function forN3LL′gluon fusion Higgs boson production in soft-collinear effective theory

“…Soft gluon resummation is currently known at next-to-next-to-next-to-leading logarithmic accuracy N 3 LL [15], where the prime denotes the inclusion of some formally higher order terms, which however contain the bulk of the next order correction [19]. This result has been computed with the standard formalism of QCD, sometimes referred to as direct QCD (dQCD).…”

“…1 Exploiting the equivalence of SCET and dQCD [16,19,[21][22][23], we extract the three loop expression of the soft function from the N 3 LL dQCD result. We also consider a modification of the form of the soft logarithms that includes important collinear contributions, and discuss the comparison to the dQCD result of Ref.…”