Abstract
QCD in non-integer d = 4 − 2ϵ space-time dimensions enjoys conformal invariance at the special fine-tuned value of the coupling. Counterterms for composite operators in minimal subtraction schemes do not depend on ϵ by construction, and therefore the renormalization group equations for composite operators in physical (integer) dimensions inherit conformal symmetry. This observation can be used to restore the complete evolution kernels that take into account mixing with the operators containing total derivatives from their eigenvalues (anomalous dimensions). Using this approach we calculate the two-loop (NLO) evolution kernels for the leading twist flavor-singlet operators in the position space (light-ray operator) representation. As the main result of phenomenological relevance, in this way we are able to confirm the evolution equations of flavor-singlet generalized hadron parton distributions derived earlier by Belitsky and Müller using a different approach.
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References
A. Accardi et al., Electron Ion Collider: The Next QCD Frontier, Eur. Phys. J. A 52 (2016) 268 [arXiv:1212.1701] [INSPIRE].
A. Accardi et al., A Critical Appraisal and Evaluation of Modern PDFs, Eur. Phys. J. C 76 (2016) 471 [arXiv:1603.08906] [INSPIRE].
A.V. Belitsky, A. Freund and D. Mueller, Evolution kernels of skewed parton distributions: Method and two loop results, Nucl. Phys. B 574 (2000) 347 [hep-ph/9912379] [INSPIRE].
D. Mueller, Constraints for anomalous dimensions of local light cone operators in \( \phi \) 3 in six-dimensions theory, Z. Phys. C 49 (1991) 293 [INSPIRE].
D. Mueller, Conformal constraints and the evolution of the nonsinglet meson distribution amplitude, Phys. Rev. D 49 (1994) 2525 [INSPIRE].
D. Mueller, 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. Mueller, Broken conformal invariance and spectrum of anomalous dimensions in QCD, Nucl. Phys. B 537 (1999) 397 [hep-ph/9804379] [INSPIRE].
A.V. Belitsky and D. Mueller, Next-to-leading order evolution of twist-2 conformal operators: The Abelian case, Nucl. Phys. B 527 (1998) 207 [hep-ph/9802411] [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. Braun and D. Mueller, Exclusive processes in position space and the pion distribution amplitude, Eur. Phys. J. C 55 (2008) 349 [arXiv:0709.1348] [INSPIRE].
X. Ji, Parton Physics on a Euclidean Lattice, Phys. Rev. Lett. 110 (2013) 262002 [arXiv:1305.1539] [INSPIRE].
Y.-Q. Ma and J.-W. Qiu, Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations, Phys. Rev. Lett. 120 (2018) 022003 [arXiv:1709.03018] [INSPIRE].
V.M. Braun and A.N. Manashov, Two-loop evolution equations for light-ray operators, Phys. Lett. B 734 (2014) 137 [arXiv:1404.0863] [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, Three-loop evolution equation for flavor-nonsinglet operators in off-forward kinematics, JHEP 06 (2017) 037 [arXiv:1703.09532] [INSPIRE].
A. Freund and M.F. McDermott, A Next-to-leading order QCD analysis of deeply virtual Compton scattering amplitudes, Phys. Rev. D 65 (2002) 074008 [hep-ph/0106319] [INSPIRE].
A. Freund and M. McDermott, A Detailed next-to-leading order QCD analysis of deeply virtual Compton scattering observables, Eur. Phys. J. C 23 (2002) 651 [hep-ph/0111472] [INSPIRE].
I.I. Balitsky and V.M. Braun, Evolution Equations for QCD String Operators, Nucl. Phys. B 311 (1989)541 [INSPIRE].
A. Vogt, S. Moch and J.A.M. Vermaseren, The Three-loop splitting functions in QCD: The Singlet case, Nucl. Phys. B 691 (2004) 129 [hep-ph/0404111] [INSPIRE].
A.P. Bukhvostov, G.V. Frolov, L.N. Lipatov and E.A. Kuraev, Evolution Equations for Quasi-Partonic Operators, Nucl. Phys. B 258 (1985) 601 [INSPIRE].
C. Becchi, A. Rouet and R. Stora, Renormalization of Gauge Theories, Annals Phys. 98 (1976)287 [INSPIRE].
S.D. Joglekar and B.W. Lee, General Theory of Renormalization of Gauge Invariant Operators, Annals Phys. 97 (1976) 160 [INSPIRE].
S.D. Joglekar, Local Operator Products in Gauge Theories. 1., Annals Phys. 108 (1977) 233 [INSPIRE].
S.D. Joglekar, Local Operator Products in Gauge Theories. 2., Annals Phys. 109 (1977) 210 [INSPIRE].
J.C. Collins, Renormalization, Cambridge Monographs on Mathematical Physics, Cambridge University Press (1984) [INSPIRE].
V.M. Braun, A.N. Manashov, S.O. Moch and M. Strohmaier, Conformal symmetry of QCD in d-dimensions, arXiv:1810.04993 [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].
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].
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. D 86 (2012) 119902] [arXiv:0909.3410] [INSPIRE].
V.P. Spiridonov, Anomalous Dimension of G 2μν and β Function, Preprint IYaI-P-0378 [INSPIRE].
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ArXiv ePrint: 1901.06172
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Braun, V.M., Manashov, A.N., Moch, S. et al. Two-loop evolution equations for flavor-singlet light-ray operators. J. High Energ. Phys. 2019, 191 (2019). https://doi.org/10.1007/JHEP02(2019)191
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DOI: https://doi.org/10.1007/JHEP02(2019)191