A new prescription for soft gluon resummation

Abbate, Riccardo; Forte, Stefano; Ridolfi, Giovanni

doi:10.1016/j.physletb.2007.09.060

Cited by 15 publications

(32 citation statements)

References 16 publications

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“…[49], and refined and extended in refs. [50][51][52][53]. This prescription, called Borel Prescription (BP), is typically slower but more flexible.…”

Section: Prescriptions For the Landau Polementioning

confidence: 99%

“…[49][50][51][52][53]. This prescription adopts a Borel method for summing the divergent series, and it is therefore called Borel Prescription (BP).…”

Section: A2 Borel Prescriptionmentioning

confidence: 99%

“…This shows that the series is not Borel summable. The Borel Prescription is now formulated as [49][50][51][52][53] where the w integral has been cut off, and W is minimally W = 2 (corresponding to the inclusion of twist 4 terms). This cut-off makes the integral convergent, because the cut extends always on a finite range.…”

Section: A2 Borel Prescriptionmentioning

confidence: 99%

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Resummed Higgs cross section at N3LL

Bonvini

Marzani

2014

J. High Energ. Phys.

158

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We present accurate predictions for the inclusive production of a Higgs boson in proton-proton collisions, via gluon-gluon fusion. Our calculation includes nextto-next-to-leading order (NNLO) corrections in perturbative QCD, as well as the resummation of threshold-enhanced contributions to next-to-next-to-next-to-leading logarithmic (N 3 LL) accuracy, with the inclusion of the recently-determined three-loop constant coefficient (sometimes referred to as N 3 LL accuracy).Our result correctly accounts for finite top, bottom and charm masses at leading order (LO) and next-to-leading order (NLO), and includes top mass dependence at NNLO. At the resummed level the dependence on top, bottom and charm mass is accounted for at NLL, while only the top mass at NNLL. The all-order calculation is improved by a suitable choice of the soft terms, dictated by analyticity conditions and by the inclusion of subleading corrections of collinear origin, which improve the accuracy of the resummation away from the threshold region.We present results for different collider energies and we study perturbative uncertainties by varying renormalization and factorization scales. We find that, at current LHC energies, the resummation corrects the NNLO result by as much as 20% at µ R = µ F = m H , while the correction is much smaller, 5.5%, at µ R = µ F = m H / 2. While the central value of NNLO+N 3 LL result depends very mildly on the scale choice, we argue that a more realiable estimate of the theoretical uncertainty is found if the perturbative scales are canonically varied about m H .

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“…[49], and refined and extended in refs. [50][51][52][53]. This prescription, called Borel Prescription (BP), is typically slower but more flexible.…”

Section: Prescriptions For the Landau Polementioning

confidence: 99%

“…[49][50][51][52][53]. This prescription adopts a Borel method for summing the divergent series, and it is therefore called Borel Prescription (BP).…”

Section: A2 Borel Prescriptionmentioning

confidence: 99%

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Resummed Higgs cross section at N3LL

Bonvini

Marzani

2014

J. High Energ. Phys.

158

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“…All-order resummed results are known to lead to a divergent series when expanded out in powers of the strong coupling: this is physically due to the fact that resummation is obtained by choosing as a scale of the parton-level process the maximum energy of the radiated partons [6,7], which tends to zero in the threshold limit. The divergence can be tamed by introducing suitable subleading contributions, such as exponentially suppressed terms outside the physical kinematic region [8], or power-suppressed terms [9,10]. * Speaker.…”

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confidence: 99%

The scale of soft resummation in SCET vs perturbative QCD

Bonvini

Forte

Ghezzi

et al. 2013

Nuclear Physics B - Proceedings Supplements

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We summarize and extend previous results on the comparison of threshold resummation, performed, using softcollinear effective theory (SCET), in the Becher-Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross sections. We show that the logarithmic accuracy of this SCET result can be extended by half a logarithmic order, thereby bringing it in full agreement with the standard QCD result if a suitable choice is made for the soft scale µ s which characterizes the SCET result. We provide a master formula relating the two approaches for other scale choices. We then show that with the Becher-Neubert scale choice the Landau pole, which in the perturbative QCD approach is usually removed through power-or exponentially suppressed terms, in the SCET approach is removed by logarithmically subleading terms which break factorization. Such terms may become leading for generic choices of parton distributions, and are always leading when resummation is used far enough from the hadronic threshold.Keywords: QCD, soft-gluon, threshold, resummation, soft-collinear effective theory Soft resummation and scale choicesThreshold resummation [1,2] plays an important role in extending and stabilizing the accuracy of perturbative results, and it may be of some relevance even for hadronic processes which are quite far from threshold [3,4], due to the fact that the underlying partonic process can be rather closer to threshold than the hadronic one [5]. All-order resummed results are known to lead to a divergent series when expanded out in powers of the strong coupling: this is physically due to the fact that resummation is obtained by choosing as a scale of the parton-level process the maximum energy of the radiated partons [6,7], which tends to zero in the threshold limit. The divergence can be tamed by introducing suitable subleading contributions, such as exponentially suppressed terms outside the physical kinematic region [8], or power-suppressed terms [9,10]. * Speaker. In Ref.[11] it was suggested, within the context of a SCET approach to threshold resummation, that the divergence can be tamed by making a hadronic choice of scale. In SCET this is possible because resummed results are characterized by a "soft scale" µ s : the BecherNeubert (BN) scale choice consists of expressing µ s in terms of kinematic variables of the hadronic scattering process. The meaning of this choice is not obvious in the conventional QCD approach, where, because of perturbative factorization, the partonic cross section, which is being resummed, is independent of the hadronic kinematic variables.In Ref.[13] we have clarified this issue by explicitly exhibiting a relation between the µ s dependent resummed SCET result, and the standard (µ s independent) QCD expression. Specializing to the BN scale choice (while taking the Drell-Yan process [12] as an example) we were able to show that in the SCET result, with the BN scale choice, the divergence is removed through arXiv:130...

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“…One possibility is to choose it to be around m t /N in the moment space, as was done in [38] and many earlier works on threshold resummation. In this way, the inverse Mellin or Laplace transform has to be performed numerically, and one needs some prescription to deal with the Landau pole problem such as the Minimal Prescription [40] or the Borel Prescription [41]. Another possibility, advocated in [42,43], is to choose the soft scale directly in the momentum space, which then corresponds to an "average" energy of soft emissions.…”

Section: Jhep12(2014)123mentioning

confidence: 99%