Resummation of threshold logarithms in deeply-virtual Compton scattering

I derive an all-order resummation formula for the logarithmically enhanced contributions proportional to $\frac{\alpha_s^n}{x \pm \xi} \log (\frac{\xi \pm x}{2\xi})^k$ in the 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 non-singlet coefficient function itself factorizes in the $x \rightarrow \pm \xi$ limit, which allows for a resummation using renormalization group equations

Two-loop coefficient functions in deeply virtual Compton scattering: flavor-singlet axial-vector and transversity case

We calculate the two-loop flavor-singlet axial-vector and gluon transversity coefficient functions for deeply virtual Compton scattering in QCD. We observe interesting properties regarding the transcendentality of the transversity coefficient function. Our results complete the calculation of the full next-to-next-to-leading order coefficient function in deeply virtual Compton scattering. Numerically, the two-loop corrections in the axial-vector and transversity channel are comparable to their vector counterpart at moderate skewness parameter {\xi} and hence indispensable for analyzing the upcoming high-precision data from the Electron-Ion Collider.Comment: 22 pages, 6 figures, 1 ancillary file "axial_and_transversity_CF.m'

Deeply-virtual Compton scattering at the next-to-next-to-leading order

Deeply-virtual Compton scattering gives access to the generalized parton distributions that encode the information on the transverse position of quarks and gluons in the proton in dependence in their longitudinal momentum. In anticipation of the high-precision experimental data in a broad kinematic range from the Electron-Ion Collider, we have calculated the two-loop, next-to-next-to-leading (NNLO) DVCS coefficient functions associated with the dominant Compton form factors $\mathcal H$ and $\mathcal E$ at large energies. The NNLO correction to the imaginary part of $\mathcal H$ appears to be rather large, up to factor two at the input scale $Q^2=4$ GeV$^2$ for simple GPD models, due to a cancellation between quark and gluon contributions.Comment: 9 pages, 3 figure

Breakdown of collinear factorization in the exclusive photoproduction of a π0γ \pi ^{0}\gamma pair with large invariant mass

We study the exclusive photoproduction of a $\pi ^{0}\gamma$ pair with large invariant mass $M_{\gamma \pi}^2$, which is sensitive to the exchange of either two quarks or two gluons in the $t$-channel. In this letter, we show that the process involving two-gluon exchanges does not factorize in the Bjorken limit at the leading twist. This can be explicitly demonstrated by the fact that there exist diagrams, which contribute at the leading twist, for which Glauber gluons remain trapped, due to the pinching of the contour integrations of both the plus and minus component of the Glauber gluon momentum. For the same reason, $\pi^0$-nucleon scattering to two photons also suffers from the same issue. On the other hand, we stress that there are no issues with respect to collinear factorization for the quark channels. By considering an analysis of all potential reduced diagrams of leading pinch surfaces, we argue that the quark channel is safe from Glauber pinches, and therefore, a collinear factorization in that case follows through without any problems. This means that processes where gluon exchanges are forbidden, such as the exclusive photoproduction of $\pi ^{\pm}\gamma$ and $\rho^{0,\,\pm} \gamma$, are unaffected by the factorization breaking effects we point out in this letter.Comment: 11 pages, 4 figure

Deeply Virtual Compton Scattering at Next-to-Next-to-Leading Order

Deeply virtual Compton scattering gives access to the generalized parton distributions that encode the information on the transverse position of quarks and gluons in the proton with dependence on their longitudinal momentum. In anticipation of the high-precision experimental data in a broad kinematic range from the Electron-Ion Collider, we have calculated the two-loop, next-to-next-to-leading order (NNLO) deeply virtual Compton scattering coefficient functions associated with the dominant Compton form factors H and E at large energies. The NNLO correction to the imaginary part of H appears to be rather large, up to factor 2 at the input scale Q2=4  GeV2 for simple generalized parton distribution models, due to a cancellation between quark and gluon contribution

Breakdown of collinear factorization in the exclusive photoproduction of a π0γ \pi ^{0}\gamma pair with large invariant mass

International audienceWe study the exclusive photoproduction of a $\pi ^{0}\gamma$ pair with large invariant mass $M_{\gamma \pi}^2$, which is sensitive to the exchange of either two quarks or two gluons in the $t$-channel. In this letter, we show that the process involving two-gluon exchanges does not factorize in the Bjorken limit at the leading twist. This can be explicitly demonstrated by the fact that there exist diagrams, which contribute at the leading twist, for which Glauber gluons remain trapped, due to the pinching of the contour integrations of both the plus and minus component of the Glauber gluon momentum. For the same reason, $\pi^0$-nucleon scattering to two photons also suffers from the same issue. On the other hand, we stress that there are no issues with respect to collinear factorization for the quark channels. By considering an analysis of all potential reduced diagrams of leading pinch surfaces, we argue that the quark channel is safe from Glauber pinches, and therefore, a collinear factorization in that case follows through without any problems. This means that processes where gluon exchanges are forbidden, such as the exclusive photoproduction of $\pi ^{\pm}\gamma$ and $\rho^{0,\,\pm} \gamma$, are unaffected by the factorization breaking effects we point out in this letter