Abstract
I derive an all-order resummation formula for the logarithmically enhanced contributions proportional to \( \frac{\alpha_s^n}{x\pm \xi } \) log \( {\left(\frac{\xi \pm x}{2\xi}\right)}^k \) in the quark coefficient function of deeply-virtual-Compton scattering and the pion-photon transition form factor in momentum space. The resummation is performed at the next-to-next-to-leading logarithmic accuracy. The key observation is that the quark coefficient function itself factorizes in the x → ±ξ limit, which allows for a resummation using renormalization group equations. A preliminary numerical analysis suggests that the corrections due to resummation for the quark contribution might be small.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Abdul Khalek et al., Snowmass 2021 white paper: electron ion collider for high energy physics, Tech. Rep. FERMILAB-PUB-22-125-QIS-SCD (2022) [arXiv:2203.13199] [INSPIRE].
A.V. Radyushkin, Nonforward parton distributions, Phys. Rev. D 56 (1997) 5524 [hep-ph/9704207] [INSPIRE].
J.C. Collins and A. Freund, Proof of factorization for deeply virtual Compton scattering in QCD, Phys. Rev. D 59 (1999) 074009 [hep-ph/9801262] [INSPIRE].
X.-D. Ji and J. Osborne, One loop corrections and all order factorization in deeply virtual Compton scattering, Phys. Rev. D 58 (1998) 094018 [hep-ph/9801260] [INSPIRE].
V.M. Braun, A.N. Manashov, S. Moch and J. Schoenleber, Two-loop coefficient function for DVCS: vector contributions, JHEP 09 (2020) 117 [Erratum ibid. 02 (2022) 115] [arXiv:2007.06348] [INSPIRE].
V.M. Braun, Y. Ji and J. Schoenleber, Deeply virtual Compton scattering at next-to-next-to-leading order, Phys. Rev. Lett. 129 (2022) 172001 [arXiv:2207.06818] [INSPIRE].
T. Altinoluk, B. Pire, L. Szymanowski and S. Wallon, Resumming soft and collinear contributions in deeply virtual Compton scattering, JHEP 10 (2012) 049 [arXiv:1207.4609] [INSPIRE].
T. Becher, M. Neubert and B.D. Pecjak, Factorization and momentum-space resummation in deep-inelastic scattering, JHEP 01 (2007) 076 [hep-ph/0607228] [INSPIRE].
M. Beneke, P. Falgari, S. Klein and C. Schwinn, Hadronic top-quark pair production with NNLL threshold resummation, Nucl. Phys. B 855 (2012) 695 [arXiv:1109.1536] [INSPIRE].
G. Sterman and M. Zeng, Quantifying comparisons of threshold resummations, JHEP 05 (2014) 132 [arXiv:1312.5397] [INSPIRE].
A.V. Belitsky and A.V. Radyushkin, Unraveling hadron structure with generalized parton distributions, Phys. Rept. 418 (2005) 1 [hep-ph/0504030] [INSPIRE].
S.B. Libby and G.F. Sterman, Mass divergences in two particle inelastic scattering, Phys. Rev. D 18 (1978) 4737 [INSPIRE].
J. Collins, Foundations of perturbative QCD, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 32 (2011) 1 [INSPIRE].
V.M. Braun, A.N. Manashov, S. Moch and J. Schoenleber, Axial-vector contributions in two-photon reactions: pion transition form factor and deeply-virtual Compton scattering at NNLO in QCD, Phys. Rev. D 104 (2021) 094007 [arXiv:2106.01437] [INSPIRE].
J. Gao, T. Huber, Y. Ji and Y.-M. Wang, Next-to-next-to-leading-order QCD prediction for the photon-pion form factor, Phys. Rev. Lett. 128 (2022) 062003 [arXiv:2106.01390] [INSPIRE].
S.A. Larin, The renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
V.M. Braun, A.N. Manashov, S. Moch and M. Strohmaier, Three-loop off-forward evolution kernel for axial-vector operators in Larin’s scheme, Phys. Rev. D 103 (2021) 094018 [arXiv:2101.01471] [INSPIRE].
G.P. Korchemsky and A.V. Radyushkin, Renormalization of the Wilson loops beyond the leading order, Nucl. Phys. B 283 (1987) 342 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2209.09015
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Schoenleber, J. Resummation of threshold logarithms in deeply-virtual Compton scattering. J. High Energ. Phys. 2023, 207 (2023). https://doi.org/10.1007/JHEP02(2023)207
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2023)207