Related papers: Exclusive evolution kernels in two-loop order: par…
There has recently been surprising progress in understanding the spin and flavor dependence of deep inelastic structure functions in terms of the same physics needed in the simple quark models used for hadronic spectroscopy. However, the…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
We derive one-loop matching condition for non-singlet quark distributions in transverse-momentum cut-off scheme, including unpolarized, helicity and transversity distributions. The matching is between the quasi-distribution defined by…
The general evolution kernels of the twist 2 light-ray operators for unpolarized and polarized deep inelastic scattering are calculated in ${\cal O}(\alpha_s)$. From these evolution kernels a series of special evolution equations can be…
The overlap representation of skewed parton distributions is discussed and applications to wide-angle Compton scattering and electroproduction of mesons are presented. The amplitudes for these processes factorise into parton-level…
Parton evolution with the rapidity essentially is a branching diffusion process. We describe the fluctuations of the density of partons which affect the properties of QCD scattering amplitudes at moderately high energies. We arrive at…
Matrix theory, foundational in diverse fields such as mathematics, physics, and computational sciences, typically categorizes matrices based strictly on their invertibility-determined by a sharply defined singular or nonsingular…
The large-x behavior of the physical evolution kernels appearing in the second order evolution equations of the singlet F_2 structure function and of the F_{phi} structure function in phi-exchange DIS is investigated. The validity of a…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
We consider several kinds of quintessence models in the framework of scale factor duality. We show that this symmetry exists only for a very small number of quintessence potentials. We then apply the duality transformations found to several…
We prove that the complete kernel for the high energy evolution in QCD must be selfdual. The relevant duality transformation is formulated in precise mathematical terms and is shown to transform the charge density into the functional…
Using a recursive algorithm to solve the renormalization group equations of N=1 QCD (DGLAP), we describe the most general supersymmetric evolution of the parton distributions. The analysis involves the regular DGLAP evolution, a partial…
We discuss the evolution of the eight leading twist transverse momentum dependent parton distribution functions, which turns out to be universal and spin independent. By using the highest order perturbatively calculable ingredients at our…
Integrability of the differential constraints arising from the singularity analysis of two (1+1)-dimensional second-order evolution equations is studied. Two nonlinear ordinary differential equations are obtained in this way, which are…
In Exact Quantum Query model, almost all of the Boolean functions for which non-trivial query algorithms exist are symmetric in nature. The most well known techniques in this domain exploit parity decision trees, in which the parity of two…
Previously in \cite{Tao:2025fch}, we constructed the $\ell$-loop planar integrands using loop components and loop kernels by some recursion rules. In this paper, we propose a new formalism to express the loop kernel recursion. We define…
We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…
We construct unitary evolution operators on a phase space with power of two discretization. These operators realize the metaplectic representation of the modular group SL(2,Z_{2^n}). It acts in a natural way on the coordinates of the…
One can use more than one scale variable to specify the family of surfaces in the space of parton splitting parameters that define the evolution of a parton shower. Considering $e^+e^-$ annihilation, we use two variables, with shower…
We revisit the calculation of the evolution equations for four unpolarized twist-3 transverse momentum dependent (TMD) parton distribution functions (PDFs) at $\mathcal {O}(\alpha_s)$. Unlike the existing calculations in the literature,…