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 $$ \overline{\mathrm{MS}} $$ 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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A correction to this paper has been published: https://doi.org/10.1007/JHEP09(2020)117

I derive an all-order resummation formula for the logarithmically enhanced contributions proportional to $$ \frac{\alpha_s^n}{x\pm \xi } $$ α s n x ± ξ log $$ {\left(\frac{\xi \pm x}{2\xi}\right)}^k $$ ξ ± x 2 ξ 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.

I derive an all-order resummation formula for the logarithmically enhanced contributions proportional tothe N 3 LL accuracy, in the coefficient function of deeply-virtual-Compton scattering and the pion-photon transition form factor. The key observation is that the non-singlet coefficient function itself factorizes in the x → ±ξ limit, which allows for a resummation using renormalization group equations.