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Related papers: Planar master integrals for four-loop form factors

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We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…

High Energy Physics - Phenomenology · Physics 2020-12-30 S. Abreu , H. Ita , F. Moriello , B. Page , W. Tschernow , M. Zeng

We consider the massless two-loop two-point function with arbitrary powers of the propagators and derive a representation, from which we can obtain the Laurent expansion to any desired order in the dimensional regularization parameter eps.…

High Energy Physics - Phenomenology · Physics 2009-11-10 Isabella Bierenbaum , Stefan Weinzierl

We calculate the complete quark and gluon cusp anomalous dimensions in four-loop massless QCD analytically from first principles. In addition, we determine the complete matter dependence of the quark and gluon collinear anomalous…

High Energy Physics - Phenomenology · Physics 2020-05-12 Andreas von Manteuffel , Erik Panzer , Robert M. Schabinger

The inclusive four-particle phase space integral of any $1\to 4$ matrix element in massless QCD contains divergences due to the soft and collinear emission of up to two particles in the final state. We show that any term appearing in this…

High Energy Physics - Phenomenology · Physics 2008-11-26 A. Gehrmann-De Ridder , T. Gehrmann , G. Heinrich

We present the values of the complete set of planar four-point Master Integrals needed for massive Bhabha scattering in the limit of fixed angle and high energy at the two-loop level. The integrals have been calculated using direct…

High Energy Physics - Phenomenology · Physics 2010-04-05 M. Czakon , J. Gluza , T. Riemann

We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary…

High Energy Physics - Phenomenology · Physics 2025-01-15 Yuanche Liu , Antonela Matijašić , Julian Miczajka , Yingxuan Xu , Yongqun Xu , Yang Zhang

We present numerical results which are needed to evaluate all non-trivial master integrals for four-loop massless propagators, confirming the recent analytic results of[1]and evaluating an extra order in $\ep$ expansion for each master…

High Energy Physics - Phenomenology · Physics 2014-11-20 A. V. Smirnov , M. Tentyukov

In a recent paper we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines.…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Binoth , G. Heinrich

We compute three-loop corrections of $\mathcal{O}(\alpha_{s}^3)$ to form factors with one massive and one massless quark coupling to an external vector, axialvector, scalar, pseudoscalar, or tensor current. We obtain analytic results for…

High Energy Physics - Phenomenology · Physics 2024-09-24 Matteo Fael , Tobias Huber , Fabian Lange , Jakob Müller , Kay Schönwald , Matthias Steinhauser

We evaluate a Laurent expansion in dimensional regularization parameter $\epsilon=(4-d)/2$ of all the master integrals for four-loop massless propagators up to transcendentality weight twelve, using a recently developed method of one of the…

High Energy Physics - Theory · Physics 2015-05-30 R. N. Lee , A. V. Smirnov , V. A. Smirnov

Higher order calculations in perturbative Quantum Field Theories often produce coupled linear systems of differential equations which factorize to first order. Here we present an algorithm to solve such systems in terms of iterated…

High Energy Physics - Phenomenology · Physics 2020-08-26 J. Ablinger , J. Blümlein , P. Marquard , N. Rana , C. Schneider

We consider the maximal cut of a three-loop four point function with massless kinematics. By applying Groebner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an…

High Energy Physics - Phenomenology · Physics 2015-06-05 Simon Badger , Hjalte Frellesvig , Yang Zhang

We develop a coordinate space renormalization of massless Quantum Electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier…

High Energy Physics - Phenomenology · Physics 2009-10-22 Peter E. Haagensen , Jose I. Latorre

We show that direct Feynman-parametric loop integration is possible for a large class of planar multi-loop integrals. Much of this follows from the existence of manifestly dual-conformal Feynman-parametric representations of planar loop…

High Energy Physics - Theory · Physics 2022-08-24 Jacob L. Bourjaily , Andrew J. McLeod , Matt von Hippel , Matthias Wilhelm

A summary of the calculation of the color-planar and complete light quark contributions to the massive three-loop form factors is presented. Here a novel calculation method for the Feynman integrals is used, solving general uni-variate…

High Energy Physics - Phenomenology · Physics 2019-06-14 J. Ablinger , J. Blümlein , P. Marquard , N. Rana , C. Schneider

New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…

High Energy Physics - Theory · Physics 2010-04-05 A. P. Isaev

Among the unitarity cuts of 4-loop massless propagators two kinds are currently fully known: the 2-particle cuts with 3 loops corresponding to form-factors, and the 5-particle phase-space integrals. In this paper we calculate master…

High Energy Physics - Phenomenology · Physics 2020-01-29 Vitaly Magerya , Andrey Pikelner

We carry out a systematic investigation of all the 2-loop integrals occurring in the electron vertex in QED in the continuous $D$-dimensional regularization scheme, for on-shell electrons, momentum transfer $t=-Q^2$ and finite squared…

High Energy Physics - Phenomenology · Physics 2008-11-26 R. Bonciani , P. Mastrolia , E. Remiddi

We compute the master integrals for massless two-loop vertex graphs with three off-shell legs. These master integrals are relevant for the QCD corrections to H to V*V* (where V = W, Z) and for two-loop studies of the triple gluon (and…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. G. Birthwright , E. W. N. Glover , P. Marquard

We compute the three-loop non-singlet corrections to the photon-quark form factors taking into account the full dependence on the virtuality of the photon and the quark mass. We combine the method of differential equations in an effective…

High Energy Physics - Phenomenology · Physics 2022-05-11 Matteo Fael , Fabian Lange , Kay Schoenwald , Matthias Steinhauser