Collider physics at the precision frontier

https://doi.org/10.1016/j.cpc.2022.108565

AMFlow: A Mathematica package for Feynman integrals computation via auxiliary mass flow

We present an analytic computation of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up to two loops in QCD. We reconstruct the analytic form of the finite remainders from numerical evaluations over finite fields including all colour contributions. Compact expressions are found using the pentagon function basis. We provide a fast and stable implementation for the colour- and helicity-summed interference between the one-loop and two-loop finite remainders in C++ as part of the NJet library.

/pdf/virtual-qcd-corrections-to-gluon-initiated-diphoton-plus-jet-pmh07e03nh.pdf

Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders

We calculate all planar contributions to the two-loop massless helicity amplitudes for the process $$ q\overline{q} $$
 → γγγ. The results are presented in fully analytic form in terms of the functional basis proposed recently by Chicherin and Sotnikov. With this publication we provide the two-loop contributions already used by us in the NNLO QCD calculation of the LHC process pp → γγγ [Chawdhry et al. (2019)]. Our results agree with a recent calculation of the same amplitude [Abreu et al. (2020)] which was performed using different techniques. We combine several modern computational techniques, notably, analytic solutions for the IBP identities, finite-field reconstruction techniques as well as the recent approach [Chen (2019)] for efficiently projecting helicity amplitudes. Our framework appears well-suited for the calculation of two-loop multileg amplitudes for which complete sets of master integrals exist.

/pdf/two-loop-leading-color-helicity-amplitudes-for-three-photon-3i4awuyj67.pdf

Two-loop leading-color helicity amplitudes for three-photon production at the LHC

We present an analytic computation of the two-loop QCD corrections to $u\overline{d}\ensuremath{\rightarrow}{W}^{+}b\overline{b}$ for an on-shell $W$ boson using the leading color and massless bottom quark approximations. We perform an integration-by-parts reduction of the unpolarized squared matrix element using finite field reconstruction techniques and identify an independent basis of special functions that allows an analytic subtraction of the infrared and ultraviolet poles. This basis is valid for all planar topologies for five-particle scattering with an off-shell leg.

Two-Loop QCD Corrections to W b b ¯ Production at Hadron Colliders

We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas’ multivariate partial fraction algorithm, and provide a modern implementation based on the computer algebra system Singular. Furthermore, we observe that for an integral basis with uniform transcendental (UT) weights, the denominators of IBP reduction coefficients with respect to the UT basis are either symbol letters or polynomials purely in the spacetime dimension D. With a UT basis, the partial fraction algorithm is more efficient both with respect to its performance and the size reduction. We show that in complicated examples with existence of a UT basis, the IBP reduction coefficients size can be reduced by a factor of as large as ∼ 100. We observe that our algorithm also works well for settings without a UT basis.

/pdf/ibp-reduction-coefficients-made-simple-4kxmxf9und.pdf

IBP reduction coefficients made simple

We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas' multivariate partial fraction algorithm, and provide a modern implementation based on the computer algebra system Singular. Furthermore, We observe that for an integral basis with uniform transcendental (UT) weights, the denominators of IBP reduction coefficients with respect to the UT basis are either symbol letters or polynomials purely in the spacetime dimension $D$. With a UT basis, the partial fraction algorithm is more efficient both with respect to its performance and the size reduction. We show that in complicated examples with existence of a UT basis, the IBP reduction coefficients size can be reduced by a factor of as large as $\sim 100$. We observe that our algorithm also works well for settings without a UT basis.

/pdf/ibp-reduction-coefficients-made-simple-3zf848oi2a.pdf

https://link.springer.com/content/pdf/10.1007/JHEP10(2022)165.pdf

A study of Feynman integrals with uniform transcendental weights and their symbology

In this work, we present the package {\sc NeatIBP}, which automatically generates small-size integration-by-parts (IBP) identities for Feynman integrals. Based on the syzygy and module intersection techniques, the generated IBP identities' propagator degree is controlled and thus the size of the system of IBP identities is shorter than that generated by the standard Laporta algorithm. This package is powered by the computer algebra systems {\sc Mathematica} and {\sc Singular}, and the library {\sc SpaSM}. It is parallelized on the level of Feynman integral sectors. The generated small-size IBP identities can subsequently be used for either finite field reduction or analytic reduction. We demonstrate the capabilities of this package on several multi-loop IBP examples.

NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals

In this paper, we show that with the state-of-art module intersection IBP reduction method and our improved Leinartas' algorithm, IBP relations for very complicated Feynman integrals can be solved and the analytic reduction coefficients can be dramatically simplified. We develop a large scale parallel implementation of our improved Leinartas' algorithm, based on the \textsc{Singular}/\textsc{GPI-Space} framework. We demonstrate our method by the reduction of two-loop five-point Feynman integrals with degree-five numerators, with a simple and sparse IBP system. The analytic reduction result is then greatly simplified by our improved Leinartas' algorithm to a usable form, with a compression ratio of two order of magnitudes. We further discover that the compression ratio increases with the complexity of the Feynman integrals.

Zihao Wu

Papers

IBP reduction coefficients made simple

IBP reduction coefficients made simple

A study of Feynman integrals with uniform transcendental weights and their symbology

NeatIBP 1.0, A package generating small-size integration-by-parts relations for Feynman integrals

Two-loop five-point integration-by-parts relations in a usable form.