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Related papers: A fresh look on three-loop sum-integrals

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The recent introduced \textit{dressed coordinates} are studied in the path-integral approach. These coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and, it is shown that in this…

Atomic Physics · Physics 2007-05-23 R. Casana , G. Flores-Hidalgo , B. M. Pimentel

The three-gluon vertex is a basic object of interest in nonabelian gauge theory. It contains important structural information, in particular on infrared divergences, and also figures prominently in the Schwinger-Dyson equations. At the…

High Energy Physics - Phenomenology · Physics 2012-06-11 N. Ahmadiniaz , C. Schubert

The most efficient MC weights for the calculation of physical, canonical expectation values are not necessarily those of the canonical ensemble. The use of suitably generalized ensembles can lead to a much faster convergence of the…

Statistical Mechanics · Physics 2011-01-24 Bernd A. Berg

In this paper, we work out some explicit formulae for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. As applications of these formulae, we give new closed form representations of several quadratic…

Number Theory · Mathematics 2017-01-02 Ce Xu , Yingyue Yang , Jianwen Zhang

The gauge-boson sector of perturbative scalar electrodynamics is investigated in detail as a testing ground for resummation methods in hot gauge theories. It also serves as a simple non-trivial reference system for the non-Abelian gluon…

High Energy Physics - Phenomenology · Physics 2010-11-01 U. Kraemmer , A. K. Rebhan , H. Schulz

We present the transformation of several sums of positive integer powers of the sine and cosine into non-trigonometric combinatorial forms. The results are applied to the derivation of generating functions and to the number of the closed…

Number Theory · Mathematics 2016-04-04 Carlos M. da Fonseca , M. Lawrence Glasser , Victor Kowalenko

Negative dimensional integration method (NDIM) is a technique to deal with D-dimensional Feynman loop integrals. Since most of the physical quantities in perturbative Quantum Field Theory (pQFT) require the ability of solving them, the…

High Energy Physics - Theory · Physics 2009-10-30 Alfredo T. Suzuki , Alexandre G. M. Schmidt

I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of the angle allows for an…

General Mathematics · Mathematics 2022-12-26 Luca Guido Molinari

We recently presented a new method for the evaluation of one-loop amplitude of arbitrary scattering processes, in which the reduction to scalar integrals is performed at the integrand level. In this talk, we review the main features of the…

High Energy Physics - Phenomenology · Physics 2007-09-17 Giovanni Ossola

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

We present here a large collection of harmonic and quadratic harmonic sums, that can be useful in applied questions, e.g., probabilistic ones. We find closed-form formulae, that we were not able to locate in the literature.

Discrete Mathematics · Computer Science 2024-12-13 Krzysztof Bartoszek

Using sum rules, the dipolar terms can be eliminated from the commonly-used sum-over-states (SOS) expression for nonlinear susceptibilities. This new dipole-free expression is more compact, converges to the same results as the common SOS…

Optics · Physics 2009-11-11 Mark G. Kuzyk

The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.

Number Theory · Mathematics 2011-05-10 Zhong-hua Li

The system is described by three mass-shell constraints. After a nonlinear transformation of the momenta, the analytic form taken by admissible interactions (allowing compatibility) is characterized in terms of the new variables. These…

High Energy Physics - Phenomenology · Physics 2009-11-11 Philippe Droz-Vincent

In this paper, by using the method of Contour Integral Representations and the Theorem of Residues and integral representations of series, we discuss the analytic representa- tions of parametric Euler sums that involve harmonic numbers…

Number Theory · Mathematics 2017-01-16 Ce Xu

Given a boolean n by n matrix A we consider arithmetic circuits for computing the transformation x->Ax over different semirings. Namely, we study three circuit models: monotone OR-circuits, monotone SUM-circuits (addition of non-negative…

Computational Complexity · Computer Science 2013-04-24 Magnus Find , Mika Göös , Matti Järvisalo , Petteri Kaski , Mikko Koivisto , Janne H. Korhonen

In recent years a significant amount of research in quantum optics has been devoted to the analysis of atomic three-level systems and for many physical quantities the same effects have been predicted for different configurations. These…

Quantum Physics · Physics 2009-11-07 M. B. Plenio

The three-loop master integrals for ladder-box diagrams with one massive leg are computed from an eighty-five by eighty-five system of differential equations, solved by means of Magnus exponential. The results of the considered box-type…

High Energy Physics - Phenomenology · Physics 2015-06-22 Stefano Di Vita , Pierpaolo Mastrolia , Ulrich Schubert , Valery Yundin

Effective thermal masses of bosonic particles in a plasma play an important role in many different phenomena. We compute them in general supersymmetric models at leading order. The origin of different corrections is explicitly shown for the…

High Energy Physics - Phenomenology · Physics 2014-11-17 D. Comelli , J. R. Espinosa

To entirely determine the resulting functions of one-loop integrals it is necessary to find the correct analytic continuation to all relevant kinematical regions. We argue that this continuation procedure may be performed in a general and…

High Energy Physics - Theory · Physics 2015-06-26 L. Bruecher , J. Franzkowski , D. Kreimer