Three-loop helicity amplitudes for diphoton production in gluon fusion

Piotr, Bargiela,; Caola, Fabrizio; Manteuffel, Andreas von; Tancredi, Lorenzo

doi:10.1007/jhep02(2022)153

Cited by 23 publications

(20 citation statements)

References 64 publications

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“…First calculations at this order were completed for Higgs boson production [1][2][3][4][5][6] and the Drell-Yan process [4,7]. Even 2 → 2 reactions may become feasible at this order in the not-too-far future as first results for 3-loop dijet production amplitudes have become available [8,9]. One of the dominant remaining theoretical uncertainties associated to such N3LO calculations is now related to the lack of knowledge of the 4-loop splitting functions, which determine the evolution of the parton densities at the relevant perturbative order, and which are known completely only up to three loops [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Section: Jhep05(2022)177 1 Introductionmentioning

confidence: 99%

Renormalization of gluonic leading-twist operators in covariant gauges

Falcioni

Herzog

2022

J. High Energ. Phys.

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We provide the all-loop structure of gauge-variant operators required for the renormalisation of Green’s functions with insertions of twist-two operators in Yang-Mills theory. Using this structure we work out an explicit basis valid up to 4-loop order for an arbitrary compact simple gauge group. To achieve this we employ a generalised gauge symmetry, originally proposed by Dixon and Taylor, which arises after adding to the Yang-Mills Lagrangian also operators proportional to its equation of motion. Promoting this symmetry to a generalised BRST symmetry allows to generate the ghost operator from a single exact operator in the BRST-generalised sense. We show that our construction complies with the theorems by Joglekar and Lee. We further establish the existence of a generalised anti-BRST symmetry which we employ to derive non-trivial relations among the anomalous dimension matrices of ghost and equation-of-motion operators. For the purpose of demonstration we employ the formalism to compute the N = 2, 4 Mellin moments of the gluonic splitting function up to 4 loops and its N = 6 Mellin moment up to 3 loops, where we also take advantage of additional simplifications of the background field formalism.

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Section: Jhep05(2022)177 1 Introductionmentioning

confidence: 99%

Renormalization of gluonic leading-twist operators in covariant gauges

Falcioni

Herzog

2022

J. High Energ. Phys.

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“…An important recent success of the Ansatz approach is the calculation of a plethora of two-loop, five-point scattering amplitudes -both for fully massless configurations [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and for configurations involving one massive particle [5,[23][24][25]. Furthermore, we have also seen ground-breaking computations of three-loop four-point amplitudes made possible by these tools [26][27][28].…”

Section: Introductionmentioning

confidence: 93%

Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry

Laurentis¹,

Page²

2022

Preprint

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Rational coefficients of special functions in scattering amplitudes are known to simplify on singular surfaces, often diverging less strongly than the naïve expectation. To systematically study these surfaces and rational functions on them, we employ tools from algebraic geometry. We show how the divergences of a rational function constrain its numerator to belong to symbolic powers of ideals associated to the singular surfaces. To study the divergences of the coefficients, we make use of p-adic numbers, closely related to finite fields. These allow us to perform numerical evaluations close to the singular surfaces in a stable manner and thereby characterize the divergences of the coefficients. We then use this information to construct low-dimensional Ansätze for the rational coefficients. As a proof-of-concept application of our algorithm, we reconstruct the two-loop 0 → q qγγγ pentagon-function coefficients with fewer than 1000 numerical evaluations.

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“…To be able to perform computations for 2 → 2 processes at N 3 LO, three-loop 2 → 2 amplitudes and two-loop 2 → 3 amplitudes are required. While first results are becoming available [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45], a systematic approach to the computation of the required multi-loop amplitudes is currently still missing, in part also due to a lack of understanding of the relevant special functions, see section 3.2. State of the art computations rely on impressive developments of efficient algorithms for the calculation of amplitudes and a continued effort to deepen our understanding of QFT.…”

Section: Multi-loop Scattering Amplitudesmentioning

confidence: 99%

The Path forward to N$^3$LO

Caola¹,

Chen²,

Duhr³

et al. 2022

Preprint

Self Cite

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The LHC experiments will achieve percent level precision measurements of processes key to some of the most pressing questions of contemporary particle physics: What is the nature of the Higgs boson? Can we successfully describe the interaction of fundamental particles at high energies? Is there physics beyond the Standard Model at the LHC? The capability to predict and describe such observables at next-to-nextto-next-to-leading order (N 3 LO) in QCD perturbation theory is paramount to fully exploit these experimental measurements. We describe the current status of N 3 LO predictions and highlight their importance in the upcoming precision phase of the LHC. Furthermore, we identify key conceptual and mathematical developments necessary to see wide-spread N 3 LO phenomenology come to fruition.

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Three-loop helicity amplitudes for diphoton production in gluon fusion

Cited by 23 publications

References 64 publications

Renormalization of gluonic leading-twist operators in covariant gauges

Renormalization of gluonic leading-twist operators in covariant gauges

Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry

The Path forward to N$^3$LO

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