Long-distance singularities in multi-leg scattering amplitudes

Gardi, Einan; Almelid, Øyvind; Duhr, Claude

doi:10.48550/arxiv.1606.05697

Cited by 2 publications

(3 citation statements)

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“…[78], (see also Ref. [410]) and verified by an explicit amplitude calculation in N = 4 Super-Yang-Mills 33 It is interesting here to note the close analogy between Eq. (5.32) and the factorisation of ultraviolet singularities in field correlators, Eq.…”

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confidence: 61%

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The infrared structure of perturbative gauge theories

et al. 2023

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supporting

confidence: 61%

“…[202,245], and exploited for explicit calculations up to 3 loops in Refs. [78,410,486]. In this approach, one introduces the infrared regulator at the level of individual Wilson lines, forcing an exponential suppression of gluon emission at large distances by means of the definition Φ (m)…”

Section: Computing the Infrared Anomalous Dimension Matrixmentioning

confidence: 99%

The infrared structure of perturbative gauge theories

et al. 2023

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“…And generalized higher-loop structures were conjectured based on the dipole-formula in [117,118]. Later, concrete three-loop computations revealed that the dipole-formula is not complete and new non-dipole contributions begin to appear at three-loop order [87,119,120].…”

Section: Structure Of Ir Divergences and Finite Remaindersmentioning

confidence: 99%

Full-color three-loop three-point form factors in N=4 SYM

Lin,

Yang,

Zhang

2021

Preprint

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We present the detailed computation of full-color three-loop three-point form factors of both stress-tensor supermultiplet and a length-three operator in N " 4 SYM. The integrands are constructed based on the color-kinematics duality and generalized unitarity method. An interesting observation is that the CK-dual integrands contain a large number of free parameters. We discuss the origin of these free parameters in detail and check that they cancel after simplifying the integrands. We further perform a numerical evaluation of the integrals at a special kinematics point by using public packages FIESTA and pySecDec based on the sector-decomposition approach. While such a three-loop computation requires large computational resources, we find that one can significantly simplify the numerical computation by expressing the integrands in terms of uniformly transcendental integrals. Given the full-color numerical results, we are able to check the non-planar infrared divergences where the non-dipole terms firstly appear at three loops. The numerical planar finite remainder for the stress-tensor supermultiplet is consistent with the computation from form factor bootstrap. We also obtain for the first time the numerical three-loop non-planar remainder for the stress-tensor supermultiplet, as well as the three-loop remainder for the length-three operator.12 Interestingly, at three-loop level, color factors similar to C a,b in (4.4) contain Nc-subleading parts, such as Nc f a 1 a 2 a 3 . Only after summing up Ca and C b does the subleading parts cancel.13 Note that in (3.14), the summation over σ includes σi P S3{Z3. Here we are only left with σe P S3, since the summation on σi has been taken into account in organizing integrals in pairs to get the N 3 c da 1 a 2 a 3 color factor.

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Long-distance singularities in multi-leg scattering amplitudes

Cited by 2 publications

References 0 publications

The infrared structure of perturbative gauge theories

The infrared structure of perturbative gauge theories

Full-color three-loop three-point form factors in N=4 SYM

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