Soft-gluon and Coulomb corrections to hadronic top-quark pair production beyond NNLO
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Springer
Received: January 19, 2018 Accepted: March 9, 2018 Published: March 27, 2018
Jan Picluma and Christian Schwinnb a
Theoretische Physik 1, Naturwissenschaftlich-Technische Fakult¨ at, Universit¨ at Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany b Institut f¨ ur Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, Sommerfeldstraße 16, D–52056 Aachen, Germany
E-mail: [email protected], [email protected] Abstract: We construct a resummation at partial next-to-next-to-next-to-leading logarithmic accuracy for hadronic top-quark pair production near partonic threshold, including simultaneously soft-gluon and Coulomb corrections, and use this result to obtain approximate next-to-next-to-next-to-leading order predictions for the total top-quark pair-production cross section at the LHC. We generalize a required one-loop potential in non-relativistic QCD to the colour-octet case and estimate the remaining unknown twoloop potentials and three-loop anomalous dimensions. We obtain a moderate correction of 1.5% relative to the next-to-next-to-leading order prediction and observe a reduction of the perturbative uncertainty below ±5%. Keywords: Perturbative QCD, Resummation ArXiv ePrint: 1801.05788
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP03(2018)164
JHEP03(2018)164
Soft-gluon and Coulomb corrections to hadronic top-quark pair production beyond NNLO
Contents 2
2 Factorization and resummation framework 2.1 Setup of the perturbative calculation 2.2 Top-quark production channels near partonic threshold 2.3 Combined soft and Coulomb resummation at NNLL
4 4 6 7
3 Towards N3 LL resummation 3.1 Hard functions 3.2 Soft function 3.3 Potential corrections 3.3.1 Potentials 3.3.2 Expansion of the potential function 3.4 P-wave contributions 3.5 Next-to-eikonal correction
8 10 12 13 14 15 18 20
4 Approximate N3 LO results 4.1 Partonic cross sections 4.2 Phenomenological results
21 21 24
5 Conclusions
29
A Renormalization group functions A.1 Two-loop hard functions A.2 Two-loop soft function
30 30 32
B Potential corrections B.1 Potential for general spin and colour states B.2 Annihilation contribution
34 34 36
C Scaling functions C.1 Quark-antiquark channel C.2 Gluon fusion colour-singlet channel C.3 Gluon fusion colour-octet channel
38 38 39 40
–1–
JHEP03(2018)164
1 Introduction
1
Introduction
We also indicated a modified counting Nn LL’, where the fixed-order corrections in the second line are included at one order higher than in the “unprimed” counting. The combined resummation of soft and Coulomb corrections at NNLL accuracy [15] was implemented in the program topixs [18], whose current version includes the matching to the complete NNLO corrections [9–12]. NNLO+NNLL soft-gluon resummation with the Mellintransform method [16] with a fixed-order treatment of Coulomb corrections was implemented in the program top++ [17], which further includes the O(αs2 ) constant terms in the resummation that are part of the NNLL’ correctio
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