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Related papers: Two-loop Master Integrals with the Simplified Diff…

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By employing the method of differential equations, we compute the various types of two-loop master integrals involved in CP-even heavy quarkonium exclusive production and decays. All the integrals presented in this paper can be casted into…

High Energy Physics - Phenomenology · Physics 2017-06-28 Long-Bin Chen , Yi Liang , Cong-Feng Qiao

This is a sequel of our previous paper where we described an algorithm to find a solution of differential equations for master integrals in the form of an $\epsilon$-expansion series with numerical coefficients. The algorithm is based on…

High Energy Physics - Phenomenology · Physics 2018-08-15 Roman N. Lee , Alexander V. Smirnov , Vladimir A. Smirnov

We outline the computational details to obtain mixed EW-QCD corrections to on-shell production of a single vector boson at the LHC at two-loop level. We use the method of differential equation to obtain the pure virtual, real-virtual and…

High Energy Physics - Phenomenology · Physics 2019-12-24 Roberto Bonciani , Federico Buccioni , Narayan Rana , Alessandro Vicini

Variational integrators applied to degenerate Lagrangians that are linear in the velocities are two-step methods. The system of modified equations for a two-step method consists of the principal modified equation and one additional equation…

Numerical Analysis · Mathematics 2019-01-30 Mats Vermeeren

We perform analytical reductions of one-loop tensor integrals with 5 and 6 legs to scalar master integrals. They are based on the use of recurrence relations connecting integrals in different space-time dimensions. The reductions are…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Diakonidis , J. Fleischer , J. Gluza , K. Kajda , T. Riemann , J. B. Tausk

The differential equation in the external invariant p^2 satisfied by the master integral of the general massive 2-loop 4-denominator self-mass diagram is exploited and the expansion of the master integral at p^2=0 is obtained analytically.…

High Energy Physics - Phenomenology · Physics 2010-04-05 M. Caffo , H. Czyz , A. Grzelinska , E. Remiddi

The factorisation of QCD matrix elements in the limit of two external partons becoming collinear is described by process-independent splitting amplitudes, which can be expanded systematically in perturbation theory. Working in conventional…

High Energy Physics - Phenomenology · Physics 2015-06-23 Claude Duhr , Thomas Gehrmann , Matthieu Jaquier

Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to…

High Energy Physics - Phenomenology · Physics 2016-04-18 T. Gehrmann , J. M. Henn , N. A. Lo Presti

A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2…

High Energy Physics - Phenomenology · Physics 2007-05-23 J. Fleischer , M. Yu. Kalmykov , A. V. Kotikov

We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential…

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

We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.

High Energy Physics - Theory · Physics 2016-02-02 Bernd A. Kniehl , Oleg V. Tarasov

We present the Master Integrals needed for the calculation of the two-loop QCD corrections to the forward-backward asymmetry of a quark-antiquark pair produced in electron-positron annihilation events. The abelian diagrams entering in the…

High Energy Physics - Phenomenology · Physics 2009-11-10 R. Bonciani , P. Mastrolia , E. Remiddi

We compute the two-loop crossed six-line vertex master integral with two massive lines in dimensional regularisation, and give the result up to the finite part in D-4. We focus in particular on the purely analytical calculation of the…

High Energy Physics - Phenomenology · Physics 2009-03-27 T. Huber

At small inter-parton distances, double parton distributions receive their dominant contribution from the splitting of a single parton. We compute this mechanism at next-to-leading order in perturbation theory for all colour configurations…

High Energy Physics - Phenomenology · Physics 2021-09-01 Markus Diehl , Jonathan R. Gaunt , Peter Ploessl

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 describe in some detail the present features of an automatic loop calculation program as well as the integration techniques that go into it. The program, called XLOOPS 1.0, allows one to calculate massive one- and two-loop Feynman…

High Energy Physics - Phenomenology · Physics 2009-09-25 A. Frink , J. G. Körner , J. B. Tausk

We consider the two-loop corrections to the $HW^+W^-$ vertex at order $\alpha\alpha_s$. We construct a canonical basis for the two-loop integrals using the Baikov representation and the intersection theory. By solving the $\epsilon$-form…

High Energy Physics - Phenomenology · Physics 2022-01-07 Chichuan Ma , Yuxuan Wang , Xiaofeng Xu , Li Lin Yang , Bin Zhou

In modern quantum field theory, one of the most important tasks is the calculation of loop integrals. Loop integrals appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. Even though…

High Energy Physics - Theory · Physics 2020-06-24 Maxim Bezuglov

As the new-generation precision experiments such as MOLLER and P2 look for physics beyond Standard Model, it is becoming increasingly important to evaluate the higher-order electroweak radiative corrections to a sub-percent level of…

High Energy Physics - Theory · Physics 2019-12-11 A. Aleksejevs , S. Barkanova

By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the…

High Energy Physics - Phenomenology · Physics 2018-05-23 Long-Bin Chen , Jun Jiang , Cong-Feng Qiao