Searcharxiv⌕ Search

arXiv subjects

A. N. Manashov

Publications and source records attributed to A. N. Manashov.

At least 19 recordsLinked to original sources
arXiv2026

Anomalous dimensions at small spins

In perturbation theory, the anomalous dimensions of twist-two operators have poles at negative or small positive integer values of spin and therefore must be resummed at these points. It was observed earlier that a certain quadratic combination of the anomalous dimensions remains finite at the right-most singularities, providing an efficient tool for resummation. In this paper, we analyze the small-spin behavior of the anomalous dimensions for all types of twist-two operators in the $O(N)$-symmetric $φ^4$ model at the four-loop level, in the complex $φ^3$ model at the three-loop level, and the Gross-Neveu-Yukawa model at the two-loop level. We find that the behavior of the anomalous dimensions at singular points is consistent with theoretical expectations, and we present expressions for the resummed anomalous dimensions.

hep-th↗
arXiv2026

Conformal moments of the two-loop coefficient functions in DVCS

We develop a new technique and calculate conformal (Gegenbauer) moments of the two-loop coefficient functions in Deeply Virtual Compton Scattering (DVCS). These results are necessary for the extraction of the generalized parton distributions from the experimental data to the NNLO accuracy within the Mellin-Barnes approach.

hep-ph↗
arXiv2025

The $γ^\ast\to ηγ$ and $γ^\ast\to η'γ$ form factors to NNLO accuracy in perturbative QCD

We use conformal symmetry to calculate the NNLO anomalous dimension matrix (three loops) for flavor-singlet axial-vector QCD operators for spin $N \le 8$ from a set of gauge-invariant two-point correlation functions. Combining this result with the recent calculation of the two-loop coefficient functions, we carry out the calculation of the $γγ^\ast\to η$ and $γγ^\ast\to η'$ form factors at large momentum transfers to the NNLO accuracy in perturbative QCD.

hep-ph↗
arXiv2025

Kinematic power corrections to DVCS to twist-six accuracy

We calculate $(\sqrt{-t}/Q)^k $ and $(m/Q)^k$ power corrections with $k\le 4$, where $m$ is the target mass and $t$ is the momentum transfer, to several key observables in Deeply Virtual Compton Scattering (DVCS). We find that the power expansion is well convergent up to $|t|/Q^2\lesssim 1/4$ for most of the observables, but is naturally organized in terms of $1/(Q^2+t)$ rather than the nominal hard scale $1/Q^2$. We also argue that target mass corrections remain under control and do not endanger QCD factorization for coherent DVCS on nuclei. These results remove an important source of uncertainties due to the frame dependence and violation of electromagnetic Ward identities in the QCD predictions for the DVCS amplitudes in the leading-twist approximation.

hep-ph↗
arXiv2024

Three-loop evolution kernel for transversity operator

We calculate quantum corrections to the symmetry generators for the transversity operators in quantum chromodynamics (QCD) in the two-loop approximation. Using this result, we obtain the evolution kernel for the corresponding operators at three loops. The explicit expression for the anomalous dimension matrix in the Gegenbauer basis is given for the first few operators.

hep-th↗
arXiv2023

Evolution equations for quark-gluon distributions in multi-color QCD and open spin chains

We study the scale dependence of the twist-3 quark-gluon parton distributions using the observation that in the multi-color limit the corresponding QCD evolution equations possess an additional integral of motion and turn out to be effectively equivalent to the Schrodinger equation for integrable open Heisenberg spin chain model. We identify the integral of motion of the spin chain as a new quantum number that separates different components of the twist-3 parton distributions. Each component evolves independently and its scale dependence is governed by anomalous dimension given by the energy of the spin magnet. To find the spectrum of the QCD induced open Heisenberg spin magnet we develop the Bethe Ansatz technique based on the Baxter equation. The solutions to the Baxter equation are constructed using different asymptotic methods and their properties are studied in detail. We demonstrate that the obtained solutions provide a good qualitative description of the spectrum of the anomalous dimensions and reveal a number of interesting properties. We show that the few lowest anomalous dimensions are separated from the rest of the spectrum by a finite mass gap and estimate its value.

hep-ph↗
arXiv2022

Next-to-leading-power kinematic corrections to DVCS: a scalar target

Using the recent results on the contributions of descendants of the leading twist operators to the operator product expansion of two electromagnetic currents we derive explicit expressions for the kinematic finite-$t$ and target mass corrections to the DVCS helicity amplitudes to the $1/Q^4$ power accuracy. The cancellation of IR divergences for kinematic corrections is demonstrated to all powers in the leading order of perturbation theory. We also argue that target mass corrections in the coherent DVCS from nuclei are small and do not invalidate the factorization theorem.

hep-ph↗
arXiv2022

NNLO anomalous dimension matrix for twist-two flavor-singlet operators

Conformal symmetry of QCD is restored at the Wilson-Fisher critical point in noninteger $4-2ε$ space-time dimensions. Correlation functions of multiplicatively renormalizable operators with different anomalous dimensions at the critical point vanish identically. We show that this property allows one to calculate off-diagonal parts of the anomalous dimension matrices for leading-twist operators from a set of two-point correlation functions of gauge-invariant operators which can be evaluated using standard computer algebra techniques. As an illustration, we present the results for the NNLO anomalous dimension matrix for flavor-singlet QCD operators for spin $N\le 8$.

hep-ph↗
arXiv2021

The axial-vector contributions in two-photon reactions: pion transition form factor and deeply-virtual Compton scattering at NNLO in QCD

Using the approach based on conformal symmetry we calculate the two-loop coefficient function for the axial-vector contributions to two-photon processes in the $\overline{\rm MS}$ scheme. This is the last missing element for the complete next-to-next-to-leading order (NNLO) calculation of the the pion transition form factor $γ^\astγ\to π$ in perturbative QCD. The corresponding high-statistics measurement is planned by the Belle II collaboration and will allow one to put strong constraints on the pion light-cone distribution amplitude. The calculated NNLO corrections prove to be rather large and have to be taken into account. The same coefficient function determines the contribution of the axial-vector generalized parton distributions to deeply-virtual Compton scattering which is investigated at the JLAB 12 GeV accelerator, by COMPASS at CERN, and in the future will be studied at the Electron Ion Collider EIC.

hep-ph↗
arXiv2021

Two-loop coefficient function for DVCS: Vector contributions

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 $\overline{\text{MS}}$ scheme. The corresponding next-to-next-to-leading order correction to the Compton form factor $\mathcal{H}$ 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 $\sim 10$\% of the tree level result in the bulk of the kinematic range, for $Q^2=4$ GeV$^2$.

hep-ph↗
arXiv2021

Three-loop off-forward evolution kernel for axial-vector operators in Larin's scheme

Evolution equations for leading twist operators in high orders of perturbation theory can be restored from the spectrum of anomalous dimensions and the calculation of the special conformal anomaly at one order less using conformal symmetry of QCD at the Wilson-Fisher critical point at non-integer $d=4-2ε$ space-time dimensions. In this work we generalize this technique to axial-vector operators. We calculate the corresponding three-loop evolution kernels in Larin's scheme and derive explicit expressions for the finite renormalization kernel that describes the difference to the vector case to restore the conventional ${\overline{\mathrm{MS}}}$-scheme. The results are directly applicable to deeply-virtual Compton scattering and the transition form factor $γ^*γ\toπ$.

hep-ph↗
arXiv2020

Two-photon processes in conformal QCD: Resummation of the descendants of leading-twist operators

Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two electromagnetic currents in QCD. Our expression resums contributions of all twists and to all orders in perturbation theory up to corrections proportional to the QCD $β$-function. At tree level and to twist-four accuracy, our result agrees with the expression derived earlier by a different method. The results are directly applicable to deeply-virtual Compton scattering and, e.g., $γγ^\ast$ annihilation in two mesons. As a byproduct, we derive a simple representation for the OPE of two scalar currents that is convenient for applications.

hep-ph↗
arXiv2020

Higher spin currents in the critical $O(N)$ vector model at $1/N^2$

We calculate the anomalous dimensions of higher spin singlet currents in the critical $O(N)$ vector model at order $1/N^2$. The results are shown to be in agreement with the four-loop perturbative computation in $ϕ^4$ theory in $4-2ε$ dimensions. It is known that the order $1/N$ anomalous dimensions of higher-spin currents happen to be the same in the Gross-Neveu and the critical vector model. On the contrary, the order $1/N^2$ corrections are different. The results can also be interpreted as a prediction for the two-loop computation in the dual higher-spin gravity.

hep-th↗
arXiv2019

Scale-dependence of the $B$-meson LCDA beyond leading order from conformal symmetry

We argue that the evolution kernel for the scale-dependence of the $B$-meson light-cone distribution amplitude (LCDA) can be written, to all orders in perturbation theory, in terms of the generator of special conformal transformations in a modified theory: QCD at critical coupling in non-integer $d\neq 4$ dimensions. Explicit expression for the eigenfunctions of the evolution kernel is derived that is valid, again, to all orders. From a practitioner's point of view the utility of this representation is that it allows to "save one loop" and obtain the evolution kernel to a given order of perturbation theory, up to a constant term, from the calculation of the conformal anomaly at one order less. This construction is verified by explicit calculation at two-loop level.

hep-ph↗
arXiv2019

Two-loop evolution equation for the B-meson distribution amplitude

We derive the two-loop evolution equation of the B-meson light-cone distribution amplitude which is the last missing element for the next-to-next-to-leading logarithmic resummation of QCD corrections to B decays in QCD factorization. We argue that the evolution kernel to all orders in perturbation theory can be written as a logarithm of the generator of special conformal transformations times the cusp anomalous dimension, up to a scheme-dependent overall constant. Up to this constant term, the evolution kernel to a given order in perturbation theory can be obtained from the calculation of special conformal anomaly at one order less.

hep-ph↗
arXiv2019

Two-loop evolution equations for flavor-singlet light-ray operators

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.

hep-ph↗
arXiv2018

Conformal symmetry of QCD in $d$-dimensions

QCD in $d=4-2ε$ space-time dimensions possesses a nontrivial critical point. Scale invariance usually implies conformal symmetry so that there are good reasons to expect that QCD at the critical point restricted to the gauge invariant subsector provides one with an example of a conformal field theory. The aim of this letter is to present a technical proof of this statement which is important both as a matter of principle and for applications.

hep-th↗