Related papers: On evolution kernels of twist-two operators
Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…
We propose a mechanism for calculating anomalous dimensions of higher-spin twist-two operators in N=4 SYM. We consider the ratio of the two-point functions of the operators and of their superconformal descendants or, alternatively, of the…
We discuss skewed parton distributions in the coordinate space. Solution of the corresponding LO evolution equation is constructed in terms of eigenfunctions of the evolution kernel and its relation to the conformal symmetry is explained.
We discuss the $Q^2$ dependence of the chiral-odd twist-3 distribution $e(x,Q^2)$. The anomalous dimension matrix for the corresponding twist-3 operators is calculated in the one-loop level. This study completes the calculation of the…
We outline a formalism used for a construction of two-loop flavor singlet exclusive evolution kernels in the MS bar scheme. The approach is based on the known pattern of conformal symmetry breaking in MS bar as well as constraints arising…
Anomalous dimensions of twist-two operators govern the scale evolution of parton distribution functions. For off-shell external states, the physical twist-two operators mix with unknown gauge-variant operators under renormalization. In this…
The big empirical success of group equivariant networks has led in recent years to the sprouting of a great variety of equivariant network architectures. A particular focus has thereby been on rotation and reflection equivariant CNNs for…
The results of a two-loop calculation in the Feynman gauge of both the DGLAP and the ERBL evolution kernels for transversely polarized distributions are presented. The structure of these evolution kernels is discussed in detail. In…
A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…
The factorization theorem for $q_T$ spectra in Drell-Yan processes, boson production and semi-inclusive deep inelastic scattering allows for the determination of the non-perturbative parts of transverse momentum dependent parton…
We present a calculation of the two-loop anomalous dimension for the transversity distribution $h_1(x,Q^2)$, $\gamma^{h(1)}_n$, in the MS scheme of the dimensional regularization. Because of the chiral-odd nature, $h_1$ does not mix with…
The method of 'covariant perturbation theory' allowed for the computation of the kernel of the evolution equation on a spin Riemannian manifold. The proposed axiomatic definition of the effective action introduces the universal scale…
We discuss the NLO evolution of quark transversity densities and of the parton distribution function for linearly polarized gluons in a linearly polarized hadron. A supersymmetric relation between the NLO evolution kernels for transversity…
We calculate non-singlet quark operator matrix elements of deep-inelastic scattering in the chiral limit including operators with total derivatives. This extends previous calculations with zero-momentum transfer through the operator vertex…
Based on the non-local light-ray operator technique, we develop an algorithm for the computational calculation of evolution kernels for higher-twist operators in leading order of the perturbation theory. We compute the evolution kernel for…
Hamiltonians of a wide-spread class of $G_{inv}$-invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of $sl(2)$ generators. It enables us to use standard variational…
We investigate the nonlinear evolution of cosmological perturbations in theories with scale-dependent perturbation growth, first in general and then focusing on Horndeski gravity. Within the framework of standard perturbation theory, we…
We constructed two sets of twist-3 correlation functions that are responsible for generating the novel single transverse-spin asymmetry in the QCD collinear factorization approach. We derive evolution equations for these universal…
Convolution is a fundamental operation in image processing and machine learning. Aimed primarily at maintaining image size, padding is a key ingredient of convolution, which, however, can introduce undesirable boundary effects. We present a…
We study the large-x behaviour of the physical evolution kernels for flavour non-singlet observables in deep-inelastic scattering, where x is the Bjorken variable, semi-inclusive e^+ e^- annihilation and Drell-Yan lepton-pair production.…