Two-loop leading colour helicity amplitudes for W±γ + j production at the LHC

Badger, Simon; Hartanto, Heribertus Bayu; Kryś, Jakub; Zoia, Simone

doi:10.1007/jhep05(2022)035

Cited by 30 publications

(29 citation statements)

References 84 publications

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“…At next-to-next-to-leading order (NNLO) the required two-loop amplitudes still need to be derived on a process-by-process basis. To date, full NNLO predictions for 2 → 2 processes are widely available (see [18][19][20][21][22][23][24][25][26][27] for recent progress 1 ), while for 2 → 3 processes only a few two-loop amplitudes [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] and pioneering NNLO results [45][46][47][48] exist. The complexity and the status of NLO calculations for loop-induced processes is similar, with an increasing number of 2 → 2 predictions [49][50][51][52][53] and first results for 2 → 3 processes [54].…”

Section: Jhep05(2022)161mentioning

confidence: 99%

Two-loop tensor integral coefficients in OpenLoops

Pozzorini

Schär

Zoller

2022

J. High Energ. Phys.

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We present a new and fully general algorithm for the automated construction of the integrands of two-loop scattering amplitudes. This is achieved through a generalisation of the open-loops method to two loops. The core of the algorithm consists of a numerical recursion, where the various building blocks of two-loop diagrams are connected to each other through process-independent operations that depend only on the Feynman rules of the model at hand. This recursion is implemented in terms of tensor coefficients that encode the polynomial dependence of loop numerators on the two independent loop momenta. The resulting coefficients are ready to be combined with corresponding tensor integrals to form scattering probability densities at two loops. To optimise CPU efficiency we have compared several algorithmic options identifying one that outperforms naive solutions by two orders of magnitude. This new algorithm is implemented in the OpenLoops framework in a fully automated way for two-loop QED and QCD corrections to any Standard Model process. The technical performance is discussed in detail for several 2 → 2 and 2 → 3 processes with up to order 105 two-loop diagrams. We find that the CPU cost scales linearly with the number of two-loop diagrams and is comparable to the cost of corresponding real-virtual ingredients in a NNLO calculation. This new algorithm constitutes a key building block for the construction of an automated generator of scattering amplitudes at two loops.

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Section: Jhep05(2022)161mentioning

confidence: 99%

Two-loop tensor integral coefficients in OpenLoops

Pozzorini

Schär

Zoller

2022

J. High Energ. Phys.

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“…Going beyond purely massless two-loop five-point amplitudes, first analytic results with one external mass (we will refer to it as one-mass kinematics here) have started to appear [18][19][20][21][22]. A steep increase in complexity has been observed.…”

Section: Publicmentioning

confidence: 99%

Status of double virtual NNLO QCD corrections for high multiplicity processes

Sotnikov¹

2022

Preprint

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Pushing the reach of NNLO QCD predictions to 2 → 3 production processes is one of the pillars of precision phenomenology program at the LHC. In this talk we will overview recent results and developments in the calculation of two-loop five-point amplitudes contributing towards achieving this goal. We will discuss challenges encountered in advancing the state-of-the-art beyond the class of massless five-point scattering. We will then present a basis set of transcendental functions sufficient to express any planar two-loop five-particle scattering amplitude with one external massive leg. This basis greatly facilitates derivation of compact analytic form of scattering amplitudes, and opens a possibility of their fast and reliable numerical evaluation. Applications for phenomenology of electroweak boson production can be reasonably anticipated in the near future.

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“…Many such predictions require the computation of two-loop QCD scattering amplitudes with five external particles. In recent years, we have seen impressive advances in computational techniques that have allowed the calculation of many two-loop amplitudes involving five massless particles [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] as well as a number involving four massless and a single massive particle [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Constructing Compact Ansätze for Scattering Amplitudes

Laurentis¹,

Page²

2022

Preprint

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In these proceedings, we discuss the recent approach of Ref. [1] for the construction of compact Ansätze for scattering amplitudes. The method builds powerful constraints on the analytic structure of the rational functions in amplitudes from numerical tests of their behavior close to singularity surfaces. We discuss how we systematically understand these surfaces and how the singular behavior of the rational function can be incorporated into an Ansatz using techniques from algebraic geometry. To perform the numerical sampling, we make use of 𝑝-adic numbers, a number-theoretical field that can be considered a cousin of finite fields. The 𝑝-adic numbers admit a non-trivial absolute value, as well as analytic functions such as the 𝑝-adic logarithm. We provide a detailed example of the approach applied to an NMHV tree amplitude and discuss the efficacy when applied to the two-loop leading-color amplitude for three-photon production at hadron colliders.

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Two-loop leading colour helicity amplitudes for W±γ + j production at the LHC

Cited by 30 publications

References 84 publications

Two-loop tensor integral coefficients in OpenLoops

Two-loop tensor integral coefficients in OpenLoops

Status of double virtual NNLO QCD corrections for high multiplicity processes

Constructing Compact Ansätze for Scattering Amplitudes

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