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

We further exploit the relation between tropical Grassmannians and Gr(4, n) cluster algebras in order to make and refine predictions for the singularities of scattering amplitudes in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory at higher multiplicity n ≥ 8. As a mathematical foundation that provides access to square-root symbol letters in principle for any n, we analyse infinite mutation sequences in cluster algebras with general coefficients. First specialising our analysis to the eight-particle amplitude, and comparing it with a recent, closely related approach based on scattering diagrams, we find that the only additional letters the latter provides are the two square roots associated to the four-mass box. In combination with a tropical rule for selecting a finite subset of variables of the infinite Gr(4, 9) cluster algebra, we then apply our results to obtain a collection of 3, 078 rational and 2, 349 square-root letters expected to appear in the nine-particle amplitude. In particular these contain the alphabet found in an explicit 2-loop NMHV symbol calculation at this multiplicity.

Section: Jhep10(2021)007mentioning

confidence: 99%

Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry

Henke¹,

Παπαθανασίου²

2021

“…Furthermore, we implement our expressions in a publicly available C++ library that allows one to evaluate these contributions efficiently and in a stable manner, making our results readily available for a future full calculation of the corresponding NNLO QCD corrections. 1 Our work builds on a number of recent technical advances that have paved the way to the calculation of two-loop scattering amplitudes for 2 → 3 processes with phenomenological applications [32][33][34][35][36][37]. We employ the known pure two-loop master integrals [21,26,38,39], which can be written in terms of a special set of multi-valued transcendental functions -the so-called pentagon functions [40,41].…”

Section: Jhep07(2021)095mentioning

confidence: 99%

Leading-color two-loop QCD corrections for three-jet production at hadron colliders

Abreu

Cordero

Ita

et al. 2021

We present the complete set of leading-color two-loop contributions required to obtain next-to-next-to-leading-order (NNLO) QCD corrections to three-jet production at hadron colliders. We obtain analytic expressions for a generating set of finite remainders, valid in the physical region for three-jet production. The analytic continuation of the known Euclidean-region results is determined from a small set of numerical evaluations of the amplitudes. We obtain analytic expressions that are suitable for phenomenological applications and we present a C++ library for their efficient and stable numerical evaluation.

“…The number of (independent) rational functions for each colour/charge structure can be found in table 1. The appearance of these simpler rational structures has already been discussed in the literature [37,[43][44][45][46] and they have been utilized for expressing the amplitudes in a more compact from. On the other hand, it seems to us that the possible JHEP07(2021)164 true structure behind these independent rational functions has not yet been fully explored and we hope to return to this in a future publication.…”

Section: Jhep07(2021)164mentioning

confidence: 99%

“…The last few years have seen many advances in the calculation of multi-loop integrals and amplitudes . Two-loop 5-point amplitudes are at the frontier of current amplitude calculations and have been the subject of particularly intense research [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. That research has notably led to the calculation of the 2-loop QCD leading-colour amplitude for qq → γγγ [40,42,43], which in turn has enabled, for the first time, the computation of the Next-to-Next-to-Leading-Order (NNLO) QCD corrections for a 2 → 3 process [40,47].…”

Section: Introductionmentioning

confidence: 99%

Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC

Chawdhry

Czakon

Mitov

et al. 2021