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Related papers: Three-loop vacuum integrals with arbitrary masses

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With a key improvement, the auxiliary mass flow method is now able to compute Feynman integrals encountered in cutting-edge collider processes. We have successfully applied it to compute some integrals involved in two-loop electroweak…

High Energy Physics - Phenomenology · Physics 2022-03-16 Xiao Liu , Yan-Qing Ma

The three-loop QCD contributions to the vacuum polarization functions of the $Z$ and $W$ bosons at zero momentum are calculated. The top quark is considered to be massive and the other quarks massless. Using these results, we calculate the…

High Energy Physics - Phenomenology · Physics 2011-01-13 L. Avdeev , J. Fleischer , S. Mikhailov , O. Tarasov

We introduce a new framework for perturbatively computing equilibrium thermodynamic properties of cosmological phase transitions to high loop orders, using the full four-dimensional resummed thermal effective potential and avoiding the…

High Energy Physics - Phenomenology · Physics 2025-07-10 Pablo Navarrete , Risto Paatelainen , Kaapo Seppänen , Tuomas V. I. Tenkanen

We obtain finite parts (as well as $\epsilon$-pole parts) of massive three-loop vacuum diagrams with three-point and/or four-point interaction vertices by reducing them to tetrahedron diagrams with both massive and massless lines, whose…

High Energy Physics - Theory · Physics 2014-11-18 J. -M. Chung , B. K. Chung

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 calculate analytically the two-loop triangle integrals entering the $\mathcal{O}(\alpha\alpha_s)$ corrections to the $HZV$ vertex with $V=Z^*,\gamma^*$ using the method of differential equations. Our result provides a prototype to study…

High Energy Physics - Phenomenology · Physics 2019-10-23 Yuxuan Wang , Xiaofeng Xu , Li Lin Yang

We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding…

High Energy Physics - Phenomenology · Physics 2018-07-17 J. Blümlein , A. De Freitas , M. van Hoeij , E. Imamoglu , P. Marquard , C. Schneider

A unified formulation of one-loop tensor integrals is proposed for systematical calculations of finite volume corrections. It is shown that decomposition of the one-loop tensor integrals into a series of tensors accompanied by tensor…

High Energy Physics - Phenomenology · Physics 2022-12-28 Ze-Rui Liang , De-Liang Yao

We use variational perturbation theory to calculate various universal amplitude ratios above and below T_c in minimally subtracted phi^4-theory with N components in three dimensions. In order to best exhibit the method as a powerful…

Condensed Matter · Physics 2009-10-31 H. Kleinert , B. Van den Bossche

Hypergeometric function method is proposed to calculate the scalar integrals of Feynman diagrams. For the scalar integral of three-loop vacuum diagram with four-propagator, we verify the equivalency of Feynman parametrization and the…

High Energy Physics - Phenomenology · Physics 2019-09-04 Zhi-Hua Gu , Hai-Bin Zhang

Explicit formulas for solutions of recurrence relations for 3--loop vacuum integrals are generalized for the $n$-loop case.

High Energy Physics - Phenomenology · Physics 2008-02-03 P. A. Baikov

``Three-mass triangles'' are a class of integral functions appearing in one-loop gauge theory amplitudes. We discuss how the complex analytic properties and singularity structures of these amplitudes can be combined with generalised…

High Energy Physics - Phenomenology · Physics 2008-11-26 N. E. J. Bjerrum-Bohr , David C. Dunbar , Warren B. Perkins

Measurements of electroweak precision observables at future electron-positron colliders, such as the CEPC, FCC-ee, and ILC, will be sensitive to physics at multi-TeV scales. To achieve this sensitivity, precise predictions for the Standard…

High Energy Physics - Phenomenology · Physics 2021-04-07 Lisong Chen , Ayres Freitas

We study systematically the decomposition of the Weinberg operator at three-loop order. There are more than four thousand connected topologies. However, the vast majority of these are infinite corrections to lower order neutrino mass…

High Energy Physics - Phenomenology · Physics 2019-06-19 Ricardo Cepedello , Renato M. Fonseca , Martin Hirsch

In this article we present a high-precision evaluation of the expansions in $\e=(4-d)/2$ of (up to) four-loop scalar vacuum master integrals, using the method of difference equations developed by S. Laporta. We cover the complete set of…

High Energy Physics - Phenomenology · Physics 2009-11-11 Y. Schroder , A. Vuorinen

In this article, we present analytical expansion results of two single mass scale four-loop vacuum integrals in d=3-2*ep dimensions. After finding hypergeometric representations with half-integer coefficients, we use algorithms which we…

High Energy Physics - Phenomenology · Physics 2009-03-24 E. Bejdakic

In this paper we calculate at high-precision the expansions in e=(4-D)/2 of the master integrals of 4-loop vacuum bubble diagrams with equal masses, using a method based on the solution of systems of difference equations. We also show that…

High Energy Physics - Phenomenology · Physics 2009-11-07 Stefano Laporta

This PhD thesis is concerned with one-loop virtual electroweak corrections to arbitrary processes in the high-energy limit. Complete results are presented for the leading and subleading logarithms of large ratios of energy scales to mass…

High Energy Physics - Phenomenology · Physics 2007-05-23 Stefano Pozzorini

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

We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon,…

High Energy Physics - Phenomenology · Physics 2009-10-31 T. Binoth , G. Heinrich