Related papers: The inverse Mellin transform via analytic continua…
We have derived the coefficients of the highest three 1/x-enhanced small-x logarithms of all timelike splitting functions and the coefficient functions for the transverse fragmentation function in one-particle inclusive e^+e^- annihilation…
In this article, the infinite series form of the probability densities of tempered stable and inverse tempered stable subordinators are obtained using Mellin transform. Further, the densities of the products and quotients of stable and…
We calculate the three-loop anomalous dimension of the non-singlet transverse operator from N=1 to N=15. Using some guess we have reconstructed a general form of three-loop anomalous dimension for arbitrary Mellin moment N. Obtained result…
Iterative algorithms are fundamental tools for approximating fixed-points of nonexpansive operators in real Hilbert spaces. Among them, Krasnosel'ski\u{\i}--Mann iteration and Halpern iteration are two widely used schemes. In this work, we…
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…
The theory of monotone operators plays a major role in modern optimization and many areas of nonlinera analysis. The central classes of monotone operators are matrices with a positive semidefinite symmetric part and subsifferential…
This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
We give a systematic study on the Hardy spaces of functions with values in the non-commutative $L^p$-spaces associated with a semifinite von Neumann algebra ${\cal}M.$ This is motivated by the works on matrix valued Harmonic Analysis…
Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix…
We introduce calculus-based formulas for the continuous Euler and homotopy operators. The 1D continuous homotopy operator automates integration by parts on the jet space. Its 3D generalization allows one to invert the total divergence…
We present the two-mass QCD contributions to the pure singlet operator matrix element at three loop order in x-space. These terms are relevant for calculating the structure function $F_2(x,Q^2)$ at $O(\alpha_s^3)$ as well as for the…
We report on the analytic calculation of the second-order QCD corrections to semi-inclusive hadron production in electron-positron annihilation. The calculation of the single-particle inclusive cross-section in time-like kinematics is…
The contributions $\propto n_f$ to the $O(\alpha_s^3)$ massive operator matrix elements describing the heavy flavor Wilson coefficients in the limit $Q^2 \gg m^2$ are computed for the structure function $F_2(x,Q^2)$ and transversity for…
It is often inevitable to introduce an indefinite-metric space in quantum field theory. There is a problem to determine the metric structure of a given representation space of field operators. We show the systematic method to determine such…
A new method is given for the model-space effective interaction. Introducing a new operator in place of the Q-box in the Krenciglowa-Kuo (KK) method, we derive a new equation for the effective interaction. This equation can be viewed as an…
A method for calculating phase-space master integrals for the decay process $1 \to n$ massless partons in QCD using integration-by-parts and differential equations techniques is discussed. The method is based on the appropriate choice of…
We present the analytic calculation of all master integrals for 3-, 4-, and 5-particle semi-inclusive cuts of four-loop massless propagators by means of differential equations. We fix the integration constants by reducing the semi-inclusive…
We describe the calculation of the two--loop massive operator matrix elements with massive external fermions in QED. We investigate the factorization of the $O(\alpha^2)$ initial state corrections to $e^+e^-$ annihilation into a virtual…
An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…