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The large double logarithm in loop-induced processes is one kind of logarithm at subleading power, which has a different origin from Sudakov double logarithms. We develop a method with soft-collinear effective theory to resum these large…

High Energy Physics - Phenomenology · Physics 2019-12-24 Jian Wang

We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some…

Number Theory · Mathematics 2024-01-30 Kam Cheong Au

In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.

Number Theory · Mathematics 2021-03-24 Rusen Li

We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…

High Energy Physics - Phenomenology · Physics 2013-12-16 T. Binoth , J. Ph. Guillet , G. Heinrich , E. Pilon , C. Schubert

We propose a new approach that allows for the separate numerical calculation of the real and imaginary parts of finite loop integrals. We find that at one-loop the real part is given by the Loop-Tree Duality integral supplemented with…

High Energy Physics - Phenomenology · Physics 2022-02-01 Dario Kermanschah

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive…

High Energy Physics - Theory · Physics 2011-09-13 A. T. Suzuki , E. S. Santos , A. G. M. Schmidt

We show that for a class of two-loop diagrams, the on-shell part of the integration-by-parts (IBP) relations correspond to exact meromorphic one-forms on algebraic curves. Since it is easy to find such exact meromorphic one-forms from…

High Energy Physics - Theory · Physics 2016-01-27 Alessandro Georgoudis , Yang Zhang

I present the two-loop self-energy functions for scalar bosons in a general renormalizable theory, within the approximation that vector bosons are treated as massless or equivalently that gauge symmetries are unbroken. This enables the…

High Energy Physics - Phenomenology · Physics 2008-11-26 Stephen P. Martin

In this paper, using Euler's function, we give a formula of all integral solutions to linear indeterminate equation with $s$-variables $a_1x_1+a_2x_2+...+a_sx_s=n$. It is a explicit formula of the coefficients $a_1$, $a_2$,..., $a_s$ and…

Analysis of PDEs · Mathematics 2011-03-09 Changjiang Zhu

Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence…

High Energy Physics - Phenomenology · Physics 2008-11-26 P. A. Baikov

We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…

High Energy Physics - Theory · Physics 2019-05-21 A. V. Kotikov , S. Teber

We present analytic results for one of two types of planar QED two-loop integrals for $\mu e$ scattering including finite lepton masses. No approximations are made, such that the results are valid not only in the limit of a small electron…

High Energy Physics - Phenomenology · Physics 2021-05-18 Matthias Heller

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

Mathematical Physics · Physics 2026-03-31 Umpei Miyamoto

We develop an alternative derivation of the renormalized expression for the one-loop soliton quantum mass corrections in (1+1)-dimensional scalar field theories. We regularize implicitly such quantity by subtracting and adding its…

High Energy Physics - Theory · Physics 2020-02-28 A. R. Aguirre , G. Flores-Hidalgo

We use a result on mixed Tate motives due to Goncharov (arXiv:alg-geom/9601021) to show that the symbol of an arbitrary one-loop 2m-gon integral in 2m dimensions may be read off directly from its Feynman parameterization. The algorithm…

High Energy Physics - Theory · Physics 2015-05-28 Marcus Spradlin , Anastasia Volovich

A simple formula for one-loop logarithmic divergences on the background of a two-dimensional curved space-time is derived for theories for which the second variation of the action is a nonminimal second order operator with small nonminimal…

High Energy Physics - Theory · Physics 2016-07-20 H. P. Popova , K. V. Stepanyantz

Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees…

Optimization and Control · Mathematics 2015-08-27 Sei Zhen Khong , Corentin Briat , Anders Rantzer

We present a program for the numerical evaluation of scalar integrals and tensor form factors entering the calculation of one-loop amplitudes which supports the use of complex masses in the loop integrals. The program is built on an earlier…

High Energy Physics - Phenomenology · Physics 2015-05-27 G. Cullen , J. -Ph. Guillet , G. Heinrich , T. Kleinschmidt , E. Pilon , T. Reiter , M. Rodgers

Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we compute the renormalized vacuum expectation value of several observables (in particular, of the stress-energy tensor and of the…

Mathematical Physics · Physics 2016-02-09 Davide Fermi , Livio Pizzocchero

In this paper, we consider a Carroll magnetic limit of a one-loop scalar effective action. We work on general static backgrounds and compute both divergent and finite parts of the effective action in this limit. We show, that the divergent…

High Energy Physics - Theory · Physics 2025-02-18 Dmitri Vassilevich