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In order to prepare the ground for evaluating classes of three-loop sum-integrals that are presently needed for thermodynamic observables, we take a fresh and systematic look on the few known cases, and review their evaluation in a unified…

High Energy Physics - Phenomenology · Physics 2015-06-05 Y. Schroder

We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three…

Differential Geometry · Mathematics 2009-02-16 M. Crampin , T. Mestdag

In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…

Symbolic Computation · Computer Science 2024-10-23 Hamid Rahkooy

Three-loop vertex diagrams in HQET needed for sum rules for B^0 - \bar{B}^0 mixing are considered. They depend on two residual energies. An algorithm of reduction of these diagrams to master integrals has been constructed. All master…

High Energy Physics - Phenomenology · Physics 2014-11-18 Andrey G. Grozin , Roman N. Lee

The third-order particle-hole ring diagrams are evaluated for a NN-contact interaction of the Skyrme type. The pertinent four-loop coefficients in the energy per particle $\bar E(k_f) \sim k_f^{5+2n}$ are reduced to double-integrals over…

Nuclear Theory · Physics 2017-08-23 N. Kaiser

We develop a coarse-graining procedure for two-dimensional models of fluctuating loops by mapping them to interface models. The result is an effective field theory for the scaling limit of loop models, which is found to be a Liouville…

Condensed Matter · Physics 2015-06-25 Jane' Kondev

An imaginary part of the false-vacuum energy density in a metastable system, i.e., the decay width due to quantum tunneling, might be reproduced by Borel resummation of vacuum bubble diagrams. We examine the convergence of this prescription…

High Energy Physics - Theory · Physics 2009-10-30 Hirofumi Yasuta

We present a simple method which simplifies the evaluation of the on-shell multiple box diagrams reducing them to triangle type ones. For the $L$-loop diagram one gets the expression in terms of Feynman parameters with $2L$-fold…

High Energy Physics - Theory · Physics 2015-06-18 D. I. Kazakov

Quantum field theories with purely virtual particles, or fakeons, require suitable modifications in one-loop integrals. We provide the expressions for the modified scalar integrals in the case of the bubble, triangle and box diagrams. The…

High Energy Physics - Phenomenology · Physics 2023-11-21 Aurora Melis , Marco Piva

The QCD free energy can be studied by dimensional reduction to a three-dimensional (3d) effective theory, whereby non-perturbative lattice simulations become less demanding. To connect to the original QCD a perturbative matching computation…

High Energy Physics - Lattice · Physics 2007-05-23 C. Torrero , F. Di Renzo , V. Miccio , M. Laine , Y. Schroder

An algorithm for the reduction of one-loop n-point tensor integrals to basic integrals is proposed. We transform tensor integrals to scalar integrals with shifted dimension and reduce these by recurrence relations to integrals in generic…

High Energy Physics - Phenomenology · Physics 2008-11-26 J. Fleischer , F. Jegerlehner , O. V. Tarasov

We propose a new set of Master Integrals which can be used as a basis for certain multiloop calculations in massless gauge field theories. In these theories we consider three-point Feynman diagrams with arbitrary number of loops. The…

High Energy Physics - Theory · Physics 2016-11-29 Julio Borja , Igor Kondrashuk

We study the 3D topology of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) single-modes, which includes bubbles, jets and saddle points. We present an analytic description of the interface as a whole, for arbitrary time-dependant…

Fluid Dynamics · Physics 2007-05-23 N. A. Inogamov , M. Tricottet , A. M. Oparin , S. Bouquet

Dimensional Reduction is applied to \qcd{} in order to compute various renormalization constants in the \drbar{} scheme at higher orders in perturbation theory. In particular, the $\beta$ function and the anomalous dimension of the quark…

High Energy Physics - Phenomenology · Physics 2009-11-11 R. Harlander , P. Kant , L. Mihaila , M. Steinhauser

It has been shown that for a certain special type of quantum graphs the random-matrix form factor can be recovered to at least third order in the scaled time \tau using periodic-orbit theory. Two types of contributing pairs of orbits were…

Chaotic Dynamics · Physics 2007-05-23 G. Berkolaiko

This is a status report of the evaluation of the three-loop corrections to the static QCD potential of a heavy quark and an antiquark. The families of Feynman integrals that appear in the evaluation are described. To reduce any integral of…

High Energy Physics - Phenomenology · Physics 2015-05-13 Alexander V. Smirnov , Vladimir A. Smirnov , Matthias Steinhauser

A three-wave Budden model with two resonance layers is constructed that allows recirculation of energy fluxes along a quadrangle in ray phase space. The transmission, reflection, and conversion coefficients for this extended Budden problem…

Plasma Physics · Physics 2007-05-23 A. J. Brizard , A. N. Kaufman , E. R. Tracy

The three-dimensional Couette flow between parallel plates is addressed using mixed lattice Boltzmann models which implement the half-range and the full-range Gauss-Hermite quadratures on the Cartesian axes perpendicular and parallel to the…

Fluid Dynamics · Physics 2018-12-26 Victor E. Ambrus , Victor Sofonea

The three-loop form factors in massless QCD can be expressed as a linear combination of master integrals. Besides a number of master integrals which factorise into products of one-loop and two-loop integrals, one finds 16 genuine three-loop…

High Energy Physics - Phenomenology · Physics 2010-04-05 T. Gehrmann , G. Heinrich , T. Huber , C. Studerus

Belokurov-Usyukina loop reduction method has been proposed in 1983 to reduce a number of rungs in triangle ladder-like diagram by one. The disadvantage of the method is that it works in d=4 dimensions only and it cannot be used for…

High Energy Physics - Theory · Physics 2015-06-05 Ivan Gonzalez , Igor Kondrashuk