Recent higher-order results in perturbative QCD

“…Our results also agree with the prediction of the N −1 ln N coefficient in Ref. [13] and the small-x resummation result for the 1/N 5 contribution [11].…”

Section: Large-n F All-n Parts Of N 3 Lo Splitting Functions and The Cusupporting

confidence: 91%

“…[7] to four-loop accuracy, and then to construct approximate x-space expressions, analogous to those for P (2) ik (x) in Refs. [8], from these results and information about the small-x and large-x limits [9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 92%

First Forcer results on deep-inelastic scattering and related quantities

Ruijl¹,

Ueda²,

Vermaseren³

et al. 2016

Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2016)

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We present results on the fourth-order splitting functions and coefficient functions obtained using FORCER, a four-loop generalization of the MINCER program for the parametric reduction of selfenergy integrals. We have computed the respective lowest three even-N and odd-N moments for the non-singlet splitting functions and the non-singlet coefficient functions in electromagnetic and ν +ν charged-current deep-inelastic scattering, and the N = 2 and N = 4 results for the corresponding flavour-singlet quantities. Enough moments have been obtained for an LLL-based determination of the analytic N-dependence of the n 3 f and n 2 f parts, respectively, of the singlet and non-singlet splitting functions. The large-N limit of the latter provides the complete n 2 f contributions to the four-loop cusp anomalous dimension. Our results also provide additional evidence of a non-vanishing contribution of quartic group invariants to the cusp anomalous dimension.

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“…However, the failure of standard resummation methods appears already at the LL order for the DGLAP splitting functions. Vogt and collaborators [10][11][12] found that the all-order quark-gluon splitting function with LL accuracy is given in moment space by…”

Section: Jhep10(2020)196mentioning

confidence: 99%

Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization

Beneke

Garny

Jaskiewicz

et al. 2020

J. High Energ. Phys.

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The off-diagonal parton-scattering channels g + γ* and q + ϕ* in deep-inelastic scattering are power-suppressed near threshold x → 1. We address the next-to-leading power (NLP) resummation of large double logarithms of 1 − x to all orders in the strong coupling, which are present even in the off-diagonal DGLAP splitting kernels. The appearance of divergent convolutions prevents the application of factorization methods known from leading power resummation. Employing d-dimensional consistency relations from requiring 1/ϵ pole cancellations in dimensional regularization between momentum regions, we show that the resummation of the off-diagonal parton-scattering channels at the leading logarithmic order can be bootstrapped from the recently conjectured exponentiation of NLP soft-quark Sudakov logarithms. In particular, we derive a result for the DGLAP kernel in terms of the series of Bernoulli numbers found previously by Vogt directly from algebraic all-order expressions. We identify the off-diagonal DGLAP splitting functions and soft-quark Sudakov logarithms as inherent two-scale quantities in the large-x limit. We use a refactorization of these scales and renormalization group methods inspired by soft-collinear effective theory to derive the conjectured soft-quark Sudakov exponentiation formula.

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Recent higher-order results in perturbative QCD

Cited by 4 publications

References 32 publications

The Large-$n_f$ Limit of the Four-Loop Splitting Functions in QCD

The Large-$n_f$ Limit of the Four-Loop Splitting Functions in QCD

First Forcer results on deep-inelastic scattering and related quantities

Large-x resummation of off-diagonal deep-inelastic parton scattering from d-dimensional refactorization

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