Abstract
Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the vector flavor-nonsinglet contribution to deeply-virtual Compton scattering (DVCS). The analytic expression for the coefficient function in momentum fraction space is presented in the \( \overline{\mathrm{MS}} \) scheme. The corresponding next-to-next-to-leading order correction to the Compton form factor ℋ for a simple model of the generalized parton distribution appears to be rather large: a factor two smaller than the next-to-leading order correction, approximately ∼ 10% of the tree level result in the bulk of the kinematic range, for Q2 = 4 GeV2.
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15 February 2022
An Erratum to this paper has been published: https://doi.org/10.1007/JHEP02(2022)115
References
J. Dudek et al., Physics Opportunities with the 12 GeV Upgrade at Jefferson Lab, Eur. Phys. J. A 48 (2012) 187 [arXiv:1208.1244] [INSPIRE].
A. Accardi et al., Electron Ion Collider: The Next QCD Frontier : Understanding the glue that binds us all, Eur. Phys. J. A 52 (2016) 268 [arXiv:1212.1701] [INSPIRE].
D. Müller, D. Robaschik, B. Geyer, F.M. Dittes and J. Hořejši, Wave functions, evolution equations and evolution kernels from light ray operators of QCD, Fortsch. Phys. 42 (1994) 101 [hep-ph/9812448] [INSPIRE].
X.-D. Ji, Deeply virtual Compton scattering, Phys. Rev. D 55 (1997) 7114 [hep-ph/9609381] [INSPIRE].
A.V. Radyushkin, Scaling limit of deeply virtual Compton scattering, Phys. Lett. B 380 (1996) 417 [hep-ph/9604317] [INSPIRE].
M. Diehl, Generalized parton distributions, Phys. Rept. 388 (2003) 41 [hep-ph/0307382] [INSPIRE].
A.V. Belitsky and A.V. Radyushkin, Unraveling hadron structure with generalized parton distributions, Phys. Rept. 418 (2005) 1 [hep-ph/0504030] [INSPIRE].
A. Accardi et al., A Critical Appraisal and Evaluation of Modern PDFs, Eur. Phys. J. C 76 (2016) 471 [arXiv:1603.08906] [INSPIRE].
V.M. Braun, A.N. Manashov, S. Moch and M. Strohmaier, Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics, JHEP 06 (2017) 037 [arXiv:1703.09532] [INSPIRE].
S.J. Brodsky, P. Damgaard, Y. Frishman and G. Lepage, Conformal symmetry: exclusive processes beyond leading order, Phys. Rev. D 33 (1986) 1881 [INSPIRE].
D. Müller, Constraints for anomalous dimensions of local light cone operators in φ3 in six-dimensions theory, Z. Phys. C 49 (1991) 293 [INSPIRE].
D. Müller, Conformal constraints and the evolution of the nonsinglet meson distribution amplitude, Phys. Rev. D 49 (1994) 2525 [INSPIRE].
D. Müller, Restricted conformal invariance in QCD and its predictive power for virtual two photon processes, Phys. Rev. D 58 (1998) 054005 [hep-ph/9704406] [INSPIRE].
A.V. Belitsky and D. Müller, Predictions from conformal algebra for the deeply virtual Compton scattering, Phys. Lett. B 417 (1998) 129 [hep-ph/9709379] [INSPIRE].
A.V. Belitsky and D. Müller, Next-to-leading order evolution of twist-2 conformal operators: The Abelian case, Nucl. Phys. B 527 (1998) 207 [hep-ph/9802411] [INSPIRE].
A.V. Belitsky, A. Freund and D. Müller, Evolution kernels of skewed parton distributions: Method and two loop results, Nucl. Phys. B 574 (2000) 347 [hep-ph/9912379] [INSPIRE].
A.V. Belitsky and D. Müller, Broken conformal invariance and spectrum of anomalous dimensions in QCD, Nucl. Phys. B 537 (1999) 397 [hep-ph/9804379] [INSPIRE].
D. Müller, Next-to-next-to leading order corrections to deeply virtual Compton scattering: The Non-singlet case, Phys. Lett. B 634 (2006) 227 [hep-ph/0510109] [INSPIRE].
K. Kumericki, D. Müller, K. Passek-Kumericki and A. Schafer, Deeply virtual Compton scattering beyond next-to-leading order: the flavor singlet case, Phys. Lett. B 648 (2007) 186 [hep-ph/0605237] [INSPIRE].
K. Kumericki, D. Müller and K. Passek-Kumericki, Towards a fitting procedure for deeply virtual Compton scattering at next-to-leading order and beyond, Nucl. Phys. B 794 (2008) 244 [hep-ph/0703179] [INSPIRE].
V.M. Braun and A.N. Manashov, Evolution equations beyond one loop from conformal symmetry, Eur. Phys. J. C 73 (2013) 2544 [arXiv:1306.5644] [INSPIRE].
V.M. Braun, A.N. Manashov, S.O. Moch and M. Strohmaier, Conformal symmetry of QCD in d-dimensions, Phys. Lett. B 793 (2019) 78 [arXiv:1810.04993] [INSPIRE].
V.M. Braun, A.N. Manashov, S. Moch and M. Strohmaier, Two-loop conformal generators for leading-twist operators in QCD, JHEP 03 (2016) 142 [arXiv:1601.05937] [INSPIRE].
V.M. Braun, A.N. Manashov, S. Moch and M. Strohmaier, Two-loop evolution equations for flavor-singlet light-ray operators, JHEP 02 (2019) 191 [arXiv:1901.06172] [INSPIRE].
X.-D. Ji and J. Osborne, One loop QCD corrections to deeply virtual Compton scattering: The Parton helicity independent case, Phys. Rev. D 57 (1998) 1337 [hep-ph/9707254] [INSPIRE].
Y. Dokshitzer, G. Marchesini and G.P. Salam, Revisiting parton evolution and the large-x limit, Phys. Lett. B 634 (2006) 504 [hep-ph/0511302] [INSPIRE].
B. Basso and G.P. Korchemsky, Anomalous dimensions of high-spin operators beyond the leading order, Nucl. Phys. B 775 (2007) 1 [hep-th/0612247] [INSPIRE].
L.F. Alday, A. Bissi and T. Lukowski, Large spin systematics in CFT, JHEP 11 (2015) 101 [arXiv:1502.07707] [INSPIRE].
L.F. Alday and A. Zhiboedov, An Algebraic Approach to the Analytic Bootstrap, JHEP 04 (2017) 157 [arXiv:1510.08091] [INSPIRE].
V.M. Braun, A.N. Manashov and B. Pirnay, Finite-t and target mass corrections to DVCS on a scalar target, Phys. Rev. D 86 (2012) 014003 [arXiv:1205.3332] [INSPIRE].
J.A.M. Vermaseren, A. Vogt and S. Moch, The Third-order QCD corrections to deep-inelastic scattering by photon exchange, Nucl. Phys. B 724 (2005) 3 [hep-ph/0504242] [INSPIRE].
V.M. Braun and A.N. Manashov, Operator product expansion in QCD in off-forward kinematics: Separation of kinematic and dynamical contributions, JHEP 01 (2012) 085 [arXiv:1111.6765] [INSPIRE].
I.V. Anikin and A.N. Manashov, Higher twist nucleon distribution amplitudes in Wandzura-Wilczek approximation, Phys. Rev. D 89 (2014) 014011 [arXiv:1311.3584] [INSPIRE].
W.A. Bardeen, A.J. Buras, D.W. Duke and T. Muta, Deep Inelastic Scattering Beyond the Leading Order in Asymptotically Free Gauge Theories, Phys. Rev. D 18 (1978) 3998 [INSPIRE].
J.A.M. Vermaseren, Harmonic sums, Mellin transforms and integrals, Int. J. Mod. Phys. A 14 (1999) 2037 [hep-ph/9806280] [INSPIRE].
V.M. Braun, A.N. Manashov and B. Pirnay, Scale dependence of twist-three contributions to single spin asymmetries, Phys. Rev. D 80 (2009) 114002 [Erratum ibid. 86 (2012) 119902] [arXiv:0909.3410] [INSPIRE].
E. Panzer, Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals, Comput. Phys. Commun. 188 (2015) 148 [arXiv:1403.3385] [INSPIRE].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
E.B. Zijlstra and W.L. van Neerven, Order \( {\alpha}_s^2 \) QCD corrections to the deep inelastic proton structure functions F2 and FL, Nucl. Phys. B 383 (1992) 525 [INSPIRE].
J. Kuipers, T. Ueda, J.A.M. Vermaseren and J. Vollinga, FORM version 4.0, Comput. Phys. Commun. 184 (2013) 1453 [arXiv:1203.6543] [INSPIRE].
J. Ablinger, A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics, MSc Thesis, Linz U. (2009) [arXiv:1011.1176] [INSPIRE].
J. Ablinger, The package HarmonicSums: Computer Algebra and Analytic aspects of Nested Sums, PoS LL2014 (2014) 019 [arXiv:1407.6180] [INSPIRE].
J. Ablinger, J. Blümlein and C. Schneider, Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms, J. Math. Phys. 54 (2013) 082301 [arXiv:1302.0378] [INSPIRE].
B. Melic, B. Nizic and K. Passek, BLM scale setting for the pion transition form-factor, Phys. Rev. D 65 (2002) 053020 [hep-ph/0107295] [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].
D. Maître, HPL, a mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun. 174 (2006) 222 [hep-ph/0507152] [INSPIRE].
D. Maître, Extension of HPL to complex arguments, Comput. Phys. Commun. 183 (2012) 846 [hep-ph/0703052] [INSPIRE].
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Braun, V.M., Manashov, A.N., Moch, S. et al. Two-loop coefficient function for DVCS: vector contributions. J. High Energ. Phys. 2020, 117 (2020). https://doi.org/10.1007/JHEP09(2020)117
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DOI: https://doi.org/10.1007/JHEP09(2020)117