# Libra: A package for transformation of differential systems for multiloop integrals

@article{Lee2021LibraAP, title={Libra: A package for transformation of differential systems for multiloop integrals}, author={Roman N. Lee}, journal={Comput. Phys. Commun.}, year={2021}, volume={267}, pages={108058} }

## 13 Citations

Non-planar elliptic vertex

- Physics
- 2021

We consider the problem of obtaining higher order in regularization parameter analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of…

Integral representation for three-loop banana graph

- Physics
- 2021

It has recently been shown that two-loop kite-type diagrams can be computed analytically in terms of iterated integrals with algebraic kernels. This result was obtained using a new integral…

Master integrals for bipartite cuts of three-loop photon self energy

- Physics
- 2020

We calculate master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed…

Two-loop amplitude for mixed QCD-EW corrections to $gg \to Hg$

- Physics
- 2021

We report on the two-loop amplitude computation for the mixed QCD-electroweak corrections to the process gg → Hg, with exact dependence on the electroweak boson masses. This amplitude has been…

Differential Equations and Feynman Integrals

- PhysicsTexts & Monographs in Symbolic Computation
- 2021

The role of differential equations in the process of calculating Feynman integrals is shown. An example of a diagram is given, in the calculation of which the method of differential equations was…

Massive two-loop heavy particle diagrams

- PhysicsPhysical Review D
- 2022

We determine the master integrals for vertex and propagator diagrams that appear in effective field theories containing heavy fields. The integrals involve at least one heavy line, and the standard…

Real corrections to Higgs boson pair production at NNLO in the large top quark mass limit

- PhysicsJournal of High Energy Physics
- 2022

In this paper we consider the next-to-next-to-leading order total cross section of Higgs boson pair production in the large top quark mass limit and compute four expansion terms in 1 / m t 2 $$…

The four-loop
N
$$ \mathcal{N} $$
= 4 SYM Sudakov form factor

- Physics
- 2022

We present the Sudakov form factor in full color N $$ \mathcal{N} $$ = 4 supersymmetric Yang- Mills theory to four loop order and provide uniformly transcendental results for the relevant master…

Charge asymmetry in electron/positron energy loss in nuclear Bremsstrahlung

- PhysicsJournal of High Energy Physics
- 2021

Abstract
We calculate the leading Coulomb correction to the Bremsstrahlung energy loss in the electron-nucleus collisions for arbitrary energy of the incoming particle. This correction determines…

Fermionic corrections to quark and gluon form factors in four-loop QCD

- PhysicsPhysical Review D
- 2021

Roman N. Lee, Andreas von Manteuffel, Robert M. Schabinger, Alexander V. Smirnov, Vladimir A. Smirnov, and Matthias Steinhauser Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia…

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A bstractWe present an algorithm of the reduction of the differential equations for master integrals the Fuchsian form with the right-hand side matrix linearly depending on dimensional regularization…

Differential equations for Feynman graph amplitudes

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epsilon : A tool to find a canonical basis of master integrals

- Mathematics, Computer ScienceComput. Phys. Commun.
- 2017

Multiloop integrals in dimensional regularization made simple.

- Mathematics, MedicinePhysical review letters
- 2013

It is argued that a good choice of basis for (multi)loop integrals can lead to significant simplifications of the differential equations, and criteria for finding an optimal basis are proposed.

Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form

- Mathematics, PhysicsComput. Phys. Commun.
- 2017

Normalized Fuchsian form on Riemann sphere and differential equations for multiloop integrals

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We consider the question of reducibility of the differential system to normalized Fuchsian form on the Riemann sphere. The differential equations for the multiloop integrals in $\epsilon$-form…

Four-loop quark form factor with quartic fundamental colour factor

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A bstractWe analytically compute the four-loop QCD corrections for the colour structure (dFabcd)2 to the massless non-singlet quark form factor. The computation involves non-trivial non-planar…

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The multiple ζ-values were invented and studied by Euler [E] and then forgotten. They showed up again in such different subjects as quantum groups [Dr] (the Drinfeld associator), Zagier’s studies…