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Related papers: Mellin$-$Barnes Transformation for Two-Loop Master…

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We explore the large set of linear transformations of Srivastava's $H_C$ triple hypergeometric function. This function has been recently linked to the massive one-loop conformal scalar 3-point Feynman integral. We focus here on the class of…

Mathematical Physics · Physics 2022-05-13 S. Friot , G. Suchet-Bernard

We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph $G$ to evaluate to multiple zeta values. The criterion depends…

Algebraic Geometry · Mathematics 2009-03-24 Francis Brown

We obtain for the first time the two-loop amplitudes for Higgs plus three gluons in Higgs effective field theory including dimension-seven operators. This provides the S-matrix elements for the top mass corrections for Higgs plus a jet…

High Energy Physics - Theory · Physics 2018-09-11 Qingjun Jin , Gang Yang

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

In our previous paper [Nucl.Phys. B 870 (2013) 243], we showed that multi-fold Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions may be reduced to two-fold MB transforms. The MB transforms were written there as polynomials…

High Energy Physics - Theory · Physics 2015-06-15 Bernd Kniehl , Igor Kondrashuk , Eduardo A. Notte-Cuello , Ivan Parra Ferrada , Marko Rojas-Medar

We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…

High Energy Physics - Phenomenology · Physics 2015-06-19 Jakob Ablinger , Johannes Blümlein , Clemens Raab , Carsten Schneider , Fabian Wißbrock

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of…

High Energy Physics - Phenomenology · Physics 2011-08-17 D. J. Broadhurst , J. Fleischer , O. V. Tarasov

New method of calculation of master integrals using differential equations and asymptotical expansion is presented. This method leads to the results exact in space-time dimension $D$ having the form of the convergent power series. As an…

High Energy Physics - Phenomenology · Physics 2009-11-11 A. V. Bogdan , R. N. Lee

We present the calculation of the master integrals needed for the two-loop QCDxEW corrections to $ q + \bar{q} \to l^- + l^+$ and $ q + \bar{q}' \to l^- + \overline{\nu} \, , $ for massless external particles. We treat W and Z bosons as…

High Energy Physics - Phenomenology · Physics 2016-10-12 Roberto Bonciani , Stefano Di Vita , Pierpaolo Mastrolia , Ulrich Schubert

Massive on-shell operator matrix elements and self-energy diagrams with outer gluon lines are calculated analytically at $O(\alpha_s^2)$, using Mellin-Barnes integrals and representations through generalized hypergeometric functions. This…

High Energy Physics - Phenomenology · Physics 2008-11-26 I. Bierenbaum , J. Blümlein , S. Klein

We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\bar\psi\Gamma\psi$, where $\Gamma$ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider…

High Energy Physics - Lattice · Physics 2008-11-26 A. Skouroupathis , H. Panagopoulos

A general one-loop scattering amplitude may be expanded in terms of master integrals. The coefficients of the master integrals can be obtained from tree-level input in a two-step process. First, use known formulas to write the coefficients…

High Energy Physics - Phenomenology · Physics 2009-01-14 Ruth Britto , Bo Feng , Gang Yang

The status of numerical evaluations of Mellin-Barnes integrals is discussed, in particular, the application of the quasi-Monte Carlo integration package QMC to the efficient calculation of multi-dimensional integrals.

High Energy Physics - Phenomenology · Physics 2019-12-25 Ievgen Dubovyk , Janusz Gluza , Tord Riemann

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

The computational technique of $N$-fold Mellin-Barnes (MB) integrals, presented in a companion paper by the same authors, is used to derive sets of series representations of the massive one-loop conformal 3-point Feynman integral in various…

High Energy Physics - Theory · Physics 2021-05-19 B. Ananthanarayan , Sumit Banik , Samuel Friot , Shayan Ghosh

We present a construction kit for calculating two-loop beta functions in N=1 supersymmetric theories for the operators of the superpotential using supergraph techniques. In particular, it allows to compute the beta functions for every…

High Energy Physics - Phenomenology · Physics 2009-11-07 Stefan Antusch , Michael Ratz

This paper is devoted to the calculation by Mellin-Barnes transform of a especial class of integrals. It contains double integrals in the position space in d = 4-2e dimensions, where e is parameter of dimensional regularization. These…

High Energy Physics - Theory · Physics 2010-06-01 Pedro Allendes , Natanael Guerrero , Igor Kondrashuk , Eduardo A. Notte Cuello

Methods developed by the Bielefeld-DESY-Dubna collaboration in recent years are: DIANA (DIagram ANAlyser), a program to produce ``FORM input'' for Feynman diagrams, starting from the Feynman rules; methods to calculate scalar diagrams:…

High Energy Physics - Phenomenology · Physics 2007-05-23 J. Fleischer , O. L. Veretin

A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…

High Energy Physics - Phenomenology · Physics 2015-06-03 F. Yuasa , E. de Doncker , N. Hamaguchi , T. Ishikawa , K. Kato , Y. Kurihara , J. Fujimoto , Y. Shimizu

We present the analytic calculation of two-loop master integrals that are relevant for $tW$ production at hadron colliders. We focus on the integral families with only one massive propagator. After choosing a canonical basis, the…

High Energy Physics - Phenomenology · Physics 2021-12-08 Long-Bin Chen , Jian Wang