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Among the unitarity cuts of massless 4-loop propagators two classes have remained unknown until recently: 2-loop 3-particle cuts, and 1-loop 4-particle cuts. In this article we shall discuss the calculation that completes the master…

High Energy Physics - Phenomenology · Physics 2019-12-16 Vitaly Magerya , Andrey Pikelner

I obtain identities satisfied by the 3-loop self-energy master integrals with four or five propagators with generic masses, including the derivatives with respect to each of the squared masses and the external momentum invariant. These…

High Energy Physics - Phenomenology · Physics 2023-03-29 Stephen P. Martin

We compute the master integrals containing one massive propagator entering the two-loop electroweak form factor, i.e. the process f fbar --> X, where f fbar is an on-shell massless fermion pair and X is a singlet particle under SU(2)L x…

High Energy Physics - Phenomenology · Physics 2009-11-10 U. Aglietti , R. Bonciani

We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter $\epsilon=(4-d)/2$ up to transcendentality weight twelve, using a recently developed method of one of…

High Energy Physics - Theory · Physics 2011-08-17 R. N. Lee , A. V. Smirnov , V. A. Smirnov

We compute epsilon-expansions around 4 dimensions of a complete set of master integrals for momentum space five-loop massless propagator integrals in dimensional regularization, up to and including the first order with contributions of…

High Energy Physics - Phenomenology · Physics 2021-10-04 Alessandro Georgoudis , Vasco Gonçalves , Erik Panzer , Raul Pereira , Alexander V. Smirnov , Vladimir A. Smirnov

We calculate analytically the three-loop planar master integrals relevant for heavy-to-light form factors using the method of differential equations. After choosing a proper canonical basis, the boundary conditions are easy to be…

High Energy Physics - Phenomenology · Physics 2018-10-24 Long-Bin Chen , Jian Wang

We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the…

High Energy Physics - Phenomenology · Physics 2020-05-20 Johannes Henn , Bernhard Mistlberger , Vladimir A. Smirnov , Pascal Wasser

We study multi-propagator angular integrals, a class of phase-space integrals relevant to processes with multiple observed final states and a test-bed for transferring loop-integral technology to phase space integrals without reversed…

High Energy Physics - Phenomenology · Physics 2025-10-17 Juliane Haug , Vladimir A. Smirnov , Fabian Wunder

We give explicit expressions (or at least an algorithm of obtaining such expressions) of the coefficients of the Laurent series expansions of the Euler-Zagier multiple zeta-functions at any integer points. The main tools are the…

Number Theory · Mathematics 2016-01-25 Kohji Matsumoto , Tomokazu Onozuka , Isao Wakabayashi

We present for numerical use the analytic continuations to complex arguments of those basic Mellin transforms, which build the harmonic sums contributing to the 3--loop anomalous dimensions. Eight new basic functions contribute in addition…

High Energy Physics - Phenomenology · Physics 2010-04-05 Johannes Blümlein , Sven-Olaf Moch

The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three…

High Energy Physics - Phenomenology · Physics 2011-09-29 T. Gehrmann , E. Remiddi

Three loop ladder and $V$-topology diagrams contributing to the massive operator matrix element $A_{Qg}$ are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable…

High Energy Physics - Phenomenology · Physics 2016-04-20 J. Ablinger , A. Behring , J. Blümlein , A. De Freitas , A. von Manteuffel , C. Schneider

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by…

High Energy Physics - Phenomenology · Physics 2020-09-23 D. Chicherin , T. Gehrmann , J. M. Henn , P. Wasser , Y. Zhang , S. Zoia

We use dimensional recurrence relations and analyticity to calculate four-loop propagator-type master integrals in the heavy-quark effective theory. Compared to previous applications of the DRA method, we apply a new technique of fixing…

High Energy Physics - Phenomenology · Physics 2023-03-01 Roman N. Lee , Andrey F. Pikelner

The dimensionally regularized massless on-shell planar triple box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t in a Laurent expansion in the…

High Energy Physics - Phenomenology · Physics 2009-11-10 V. A. Smirnov

We present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integrand-decomposition. In the asymptotic limit, the coefficients of the master…

High Energy Physics - Phenomenology · Physics 2015-06-04 Pierpaolo Mastrolia , Edoardo Mirabella , Tiziano Peraro

We present Forcer, a new FORM program for the calculation of four-loop massless propagators. The basic framework is similar to that of the Mincer program for three-loop massless propagators: the program reduces Feynman integrals to a set of…

High Energy Physics - Phenomenology · Physics 2016-12-21 T. Ueda , B. Ruijl , J. A. M. Vermaseren

Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines…

High Energy Physics - Phenomenology · Physics 2017-08-23 J. Ablinger , J. Blümlein , A. De Freitas , A. Hasselhuhn , C. Schneider , F. Wißbrock

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

We apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. After a set of master integrals has been found using the integration-by-parts method, the crucial point of…

High Energy Physics - Theory · Physics 2015-06-16 Johannes M. Henn , Alexander V. Smirnov , Vladimir A. Smirnov