Low moments of the four-loop splitting functions in QCD

Moch, S.; Ruijl, Ben; Ueda, Takahiro; Vermaseren, J.A.M.; Vogt, A.

doi:10.1016/j.physletb.2021.136853

Cited by 50 publications

(31 citation statements)

References 43 publications

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“…The DGLAP anomalous dimensions are currently known to three loop order [213][214][215][216], which is sufficient for NNLO computations. In order to achieve N 3 LO accuracy for PDFs, the four-loop corrections to the anomalous dimensions will be required and an effort of their computation is on-going [217][218][219]. Their full computation is technically very challenging, and will benefit from the developments discussed in section 3.…”

Section: Dglap-evolution At Four Loopsmentioning

confidence: 99%

The Path forward to N$^3$LO

Caola¹,

Chen²,

Duhr³

et al. 2022

Preprint

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The LHC experiments will achieve percent level precision measurements of processes key to some of the most pressing questions of contemporary particle physics: What is the nature of the Higgs boson? Can we successfully describe the interaction of fundamental particles at high energies? Is there physics beyond the Standard Model at the LHC? The capability to predict and describe such observables at next-to-nextto-next-to-leading order (N 3 LO) in QCD perturbation theory is paramount to fully exploit these experimental measurements. We describe the current status of N 3 LO predictions and highlight their importance in the upcoming precision phase of the LHC. Furthermore, we identify key conceptual and mathematical developments necessary to see wide-spread N 3 LO phenomenology come to fruition.

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Section: Dglap-evolution At Four Loopsmentioning

confidence: 99%

The Path forward to N$^3$LO

Caola¹,

Chen²,

Duhr³

et al. 2022

Preprint

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“…At cross-section level, the basic lowest-order factorisation properties have of course been well-known since the early days of perturbative QCD [238, 248-250, 287, 289, 506, 507], and they are directly relevant for the cancellation of infrared divergences at NLO. Collinear splitting kernels for hadronic cross sections are also necessary ingredients for all applications of collinear factorisation in QCD, and they have by now been determined to three loops [354,356,[508][509][510], with remarkable partial results at four and five loops [395,397,[511][512][513]. Detailed studies at amplitude level are somewhat more recent: the general form of the factorisation of tree-level gauge amplitudes in soft and collinear limits was established in the late eighties, using recursion relations [514,515] or general expression for the amplitudes derived from string theory [516,517]; a combined factorisation including both soft and collinear limits was later proposed in [518,519].…”

Section: Factorisation For Soft and Collinear Real Radiationmentioning

confidence: 99%

The Infrared Structure of Perturbative Gauge Theories

Agarwal¹,

Magnea²,

Signorile-Signorile³

2021

Preprint

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Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are explored, and high-precision phenomenological applications demand an ever more refined understanding. This review aims to provide a pedagogical overview of the subject. We briefly cover some of the early historical results, we provide some simple examples of low-order applications in the context of perturbative QCD, and discuss the necessary tools to extend these results to all perturbative orders. Finally, we describe recent developments concerning the calculation of soft anomalous dimensions in multi-particle scattering amplitudes at high orders, and we provide a brief introduction to the very active field of infrared subtraction for the calculation of differential distributions at colliders.

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“…The NNLO results 𝑃 (2) ff are all known [1,2]. At N 3 LO, i.e., at four loops, the nonsinglet quark-quark splitting functions have been computed in the large-𝑁 𝑐 limit and number of Mellin moments for the remaining color coefficients are known [28,29] for a general 𝑆𝑈 (𝑁 𝑐 ) gauge theory. In the flavor-singlet sector the leading large-𝑛 𝑓 terms and those proportional to quartic color Casimirs are known [30,29].…”

Section: Space-like Kinematicsmentioning

confidence: 99%

“…quark-quark anomalous dimensions 𝛾 (3) ns (𝑁) as a function of 𝑁 by LLL-based techniques [50,51,52,53] and solving systems of Diophantine equations, cf. [28] for details.…”

Section: Computational Work-flowmentioning

confidence: 99%

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Calculating Four-Loop Corrections in QCD

Moch¹,

Magerya²

2021

Preprint

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We review the current status of perturbative corrections in QCD at four loops for scattering processes with space-and time-like kinematics at colliders, with specific focus on deep-inelastic scattering and electron-positron annihilation. The calculations build on the parametric reduction of loop and phase space integrals up to four-loop order using computer algebra programs such as Form, designed for large scale computations.

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Low moments of the four-loop splitting functions in QCD

Cited by 50 publications

References 43 publications

The Path forward to N$^3$LO

The Path forward to N$^3$LO

The Infrared Structure of Perturbative Gauge Theories

Calculating Four-Loop Corrections in QCD

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