Four-loop splitting functions in QCD- the gluon-gluon case-

G. Falcioni; F. Herzog; S. Moch; A. Pelloni; A. Vogt

doi:10.1016/j.physletb.2024.139194

Four-loop splitting functions in QCD- the gluon-gluon case-

G. Falcioni^*
, F. Herzog
, S. Moch
, A. Pelloni
, A. Vogt

^*Corresponding author for this work

School of Physics and Astronomy

Research output: Contribution to journal › Letter › peer-review

Abstract

We have computed the even-𝑁 moments 𝑁 ≤ 20 of the gluon-gluon splitting function 𝑃gg at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically for a general compact simple gauge group, agree with all results obtained for this function so far, in particular with the lowest five moments obtained via structure functions in deep-inelastic scattering. Using our new moments and all available endpoint constraints, we construct improved approximations for the four-loop 𝑃gg(𝑥) that should
be sufficient for a wide range of collider-physics applications. The N3LO contributions to the scale derivative of the gluon distribution, resulting from these and the corresponding quark-to-gluon splitting functions, amount to 1% or less at 𝑥 >
∼ 10−4 at a standard reference scale with 𝛼s = 0.2.

Original language	English
Article number	139194
Pages (from-to)	1-10
Number of pages	10
Journal	Physics Letters B
Volume	860
Early online date	16 Dec 2024
DOIs	https://doi.org/10.1016/j.physletb.2024.139194
Publication status	Published - 1 Jan 2025

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Cite this

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title = "Four-loop splitting functions in QCD- the gluon-gluon case-",

abstract = "We have computed the even-𝑁 moments 𝑁 ≤ 20 of the gluon-gluon splitting function 𝑃gg at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically for a general compact simple gauge group, agree with all results obtained for this function so far, in particular with the lowest five moments obtained via structure functions in deep-inelastic scattering. Using our new moments and all available endpoint constraints, we construct improved approximations for the four-loop 𝑃gg(𝑥) that should be sufficient for a wide range of collider-physics applications. The N3LO contributions to the scale derivative of the gluon distribution, resulting from these and the corresponding quark-to-gluon splitting functions, amount to 1\% or less at 𝑥 > ∼ 10−4 at a standard reference scale with 𝛼s = 0.2.",

author = "G. Falcioni and F. Herzog and S. Moch and A. Pelloni and A. Vogt",

note = "The authors declare that they have no known competing financial interests or personal relationships that could have appeared to ifluence the work reported in this paper.",

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T1 - Four-loop splitting functions in QCD- the gluon-gluon case-

AU - Falcioni, G.

AU - Herzog, F.

AU - Moch, S.

AU - Pelloni, A.

AU - Vogt, A.

N1 - The authors declare that they have no known competing financial interests or personal relationships that could have appeared to ifluence the work reported in this paper.

PY - 2025/1/1

Y1 - 2025/1/1

N2 - We have computed the even-𝑁 moments 𝑁 ≤ 20 of the gluon-gluon splitting function 𝑃gg at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically for a general compact simple gauge group, agree with all results obtained for this function so far, in particular with the lowest five moments obtained via structure functions in deep-inelastic scattering. Using our new moments and all available endpoint constraints, we construct improved approximations for the four-loop 𝑃gg(𝑥) that should be sufficient for a wide range of collider-physics applications. The N3LO contributions to the scale derivative of the gluon distribution, resulting from these and the corresponding quark-to-gluon splitting functions, amount to 1% or less at 𝑥 > ∼ 10−4 at a standard reference scale with 𝛼s = 0.2.

AB - We have computed the even-𝑁 moments 𝑁 ≤ 20 of the gluon-gluon splitting function 𝑃gg at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically for a general compact simple gauge group, agree with all results obtained for this function so far, in particular with the lowest five moments obtained via structure functions in deep-inelastic scattering. Using our new moments and all available endpoint constraints, we construct improved approximations for the four-loop 𝑃gg(𝑥) that should be sufficient for a wide range of collider-physics applications. The N3LO contributions to the scale derivative of the gluon distribution, resulting from these and the corresponding quark-to-gluon splitting functions, amount to 1% or less at 𝑥 > ∼ 10−4 at a standard reference scale with 𝛼s = 0.2.

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JO - Physics Letters B

JF - Physics Letters B

M1 - 139194

ER -

Four-loop splitting functions in QCD- the gluon-gluon case-

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Particle Theory At The Higgs Centre

Forest Formulas for the LHC

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Four-loop splitting functions in QCD- the gluon-gluon case-

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Particle Theory At The Higgs Centre

Forest Formulas for the LHC

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