35 research outputs found
Multi-loop Integrand Reduction with Computational Algebraic Geometry
We discuss recent progress in multi-loop integrand reduction methods.
Motivated by the possibility of an automated construction of multi-loop
amplitudes via generalized unitarity cuts we describe a procedure to obtain a
general parameterisation of any multi-loop integrand in a renormalizable gauge
theory. The method relies on computational algebraic geometry techniques such
as Gr\"obner bases and primary decomposition of ideals. We present some results
for two and three loop amplitudes obtained with the help of the Macaulay2
computer algebra system and the Mathematica package BasisDet.Comment: Contribution to the 15th International Workshop on advanced computing
and analysis techniques (ACAT 2013), 16-21 May, Beijing, China. 8 pages, 2
figure
Multi-loop integrand reduction techniques
We review recent progress in D-dimensional integrand reduction algorithms for
two loop amplitudes and give examples of their application to non-planar
maximal cuts of the five-point all-plus helicity amplitude in QCD.Comment: 8 pages, Contribution to the proceedings of Loops and Legs in Quantum
Field Theory, 27 April - 2 May 2014, Weimar, German
Two-loop QCD-EW master integrals for Z plus jet production at large transverse momentum
The production of electroweak Z bosons that decay to neutrinos and recoil against jets with large transverse momentum p is an important background process to searches for dark matter at the Large Hadron Collider (LHC). To fully benet from opportunities offered by the future high-luminosity LHC, the theoretical description of the pp → Z + j process should be extended to include mixed QCD-electroweak corrections. The goal of this paper is to initiate the computation of such corrections starting with the calculation of the Feynman integrals needed to describe two-loop QCD-electroweak contributions to qq̅ → Z + g scattering amplitudes. Making use of the hierarchy between the large transverse momenta of the recoiling jet, relevant for heavy dark matter searches, and the Z boson mass m, we present the relevant master integrals as a series expansion in m/p
Two-Loop QCD-EW Master Integrals for Z Plus Jet Production at Large Transverse Momentum
The production of electroweak bosons that decay to neutrinos and recoil
against jets with large transverse momentum is an important
background process to searches for dark matter at the Large Hadron Collider
(LHC). To fully benefit from opportunities offered by the future
high-luminosity LHC, the theoretical description of the process
should be extended to include mixed QCD-electroweak corrections. The goal of
this paper is to initiate the computation of such corrections starting with the
calculation of the Feynman integrals needed to describe two-loop
QCD-electroweak contributions to scattering amplitudes.
Making use of the hierarchy between the large transverse momenta of the
recoiling jet, relevant for heavy dark matter searches, and the boson mass
, we present the relevant master integrals as a series expansion in
.Comment: 23 pages, 5 figures, analytical results included as ancillary file
Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
We elaborate on the recent idea of a direct decomposition of Feynman
integrals onto a basis of master integrals on maximal cuts using intersection
numbers. We begin by showing an application of the method to the derivation of
contiguity relations for special functions, such as the Euler beta function,
the Gauss hypergeometric function, and the Appell function.
Then, we apply the new method to decompose Feynman integrals whose maximal cuts
admit 1-form integral representations, including examples that have from two to
an arbitrary number of loops, and/or from zero to an arbitrary number of legs.
Direct constructions of differential equations and dimensional recurrence
relations for Feynman integrals are also discussed. We present two novel
approaches to decomposition-by-intersections in cases where the maximal cuts
admit a 2-form integral representation, with a view towards the extension of
the formalism to -form representations. The decomposition formulae computed
through the use of intersection numbers are directly verified to agree with the
ones obtained using integration-by-parts identities.Comment: 115 pages, 29 figures; references added; additional examples added;
matches published versio
The complete set of two-loop master integrals for Higgs + jet production in QCD
In this paper we complete the computation of the two-loop master integrals
relevant for Higgs plus one jet production initiated in arXiv:1609.06685,
arXiv:1907.13156, arXiv:1907.13234. We compute the integrals by defining
differential equations along contours in the kinematic space, and by solving
them in terms of one-dimensional generalized power series. This method allows
for the efficient evaluation of the integrals in all kinematic regions, with
high numerical precision. We show the generality of our approach by considering
both the top- and the bottom-quark contributions. This work along with
arXiv:1609.06685, arXiv:1907.13156, arXiv:1907.13234 provides the full set of
master integrals relevant for the NLO corrections to Higgs plus one jet
production, and for the real-virtual contributions to the NNLO corrections to
inclusive Higgs production in QCD in the full theory.Comment: 32 pages, references added, minor revisio