The four-loop six-gluon NMHV ratio function

Dixon, Lance J.; Hippel, Matt von; McLeod, Andrew J.

doi:10.1007/jhep01(2016)053

Cited by 142 publications

(233 citation statements)

References 174 publications

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“…See [39,40] for applications of such a bootstrap approach to six-point amplitudes in N = 4 SYM. In the latter theory, the kinematic dependence of the c i is related, at least conjecturally, to leading singularities [41], simplifying the above ansatz.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD

2016

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Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to derive an analytical expression for the two-loop fivegluon all-plus-helicity amplitude. After subtracting terms that are related to the universal infrared and ultraviolet pole structure, we obtain a remarkably simple and compact finite remainder function, consisting only of dilogarithms.PACS numbers: 12.38BxThe precise theoretical description of scattering reactions of elementary particles relies on the perturbation theory expansion of the scattering amplitudes describing the process under consideration. In this expansion, higher perturbative orders correspond to more and more virtual particle loops. At present, one-loop corrections can be computed to scattering amplitudes of arbitrary multiplicity, while two-loop corrections are known only for selected two-to-one annihilation or two-to-two scattering processes.For many experimental observables at higher multiplicity, a substantial increase in statistical precision can be expected from the CERN LHC in the near future. Perturbative predictions beyond one loop will be in demand for many precision applications of these data, for example in improved extractions of standard model parameters or in search for indirect signatures of new high-scale physics in precision observables.Progress on multiloop corrections to high-multiplicity amplitudes requires significant advances in two directions. Feynman-diagrammatic approaches to the computation of these amplitudes yield enormously large expressions that contain many thousands of different Feynman integrals. These integrals are related among each other through Poincaré invariance and symmetries, such that only a limited set of independent so-called master integrals will remain in the final answer for a scattering amplitude. To express a generic two-loop multiparton amplitude in terms of the relevant master integrals (ideally circumventing the large algebraic complexity at intermediate stages that is generated by working in terms of Feynman diagrams) is a yet outstanding problem. A particular example where the reduction to a basis set of integrals was achieved [1, 2] is the two-loop five-gluon helicity amplitude with all helicities positive. In this case, the application of on-shell techniques led to a particularly compact integrand, which motivated a specific choice of basis integrals (which do not necessarily form a minimal set in the sense of being master integrals). In [1], these integrals were evaluated numerically for selected kinematical points. Although this specific helicity amplitude is not contributing to the second-order correction to the three-jet cross section (due to its vanishing at tree level), it provides an ideal testing laboratory for new calculational concepts and methods that will carry over to the general helicity case, as previously in the case for the four-point tw...

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Section: Discussion and Outlookmentioning

confidence: 99%

Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD

2016

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“…[93]). At weak coupling, it was found to simplify the six-point multi-particle factorization limit [11], self-crossing limit [73] and NMHVQ relations [35], before its role in applying the six-point Steinmann relations was noticed [15]. We will see its advantages as well in our seven-point analysis.…”

Section: )mentioning

confidence: 83%

“…Starting at six points, the BDS ansatz receives corrections from finite functions of dual conformal invariants [25,26,28,29]. The correction to the maximally helicity violating (MHV) amplitude has traditionally been expressed in terms of a (BDS) remainder function [10,12,25,26,30], while the correction to the next-to-maximally helicity violating (NMHV) amplitude has traditionally been expressed in terms of the infrared-finite NMHV ratio function [11,[31][32][33][34][35].…”

Section: Jhep02(2017)137mentioning

confidence: 99%

Heptagons from the Steinmann cluster bootstrap

Dixon

Drummond

Harrington

et al. 2017

J. High Energ. Phys.

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Abstract:We reformulate the heptagon cluster bootstrap to take advantage of the Steinmann relations, which require certain double discontinuities of any amplitude to vanish. These constraints vastly reduce the number of functions needed to bootstrap seven-point amplitudes in planar N = 4 supersymmetric Yang-Mills theory, making higher-loop contributions to these amplitudes more computationally accessible. In particular, dual superconformal symmetry and well-defined collinear limits suffice to determine uniquely the symbols of the three-loop NMHV and four-loop MHV seven-point amplitudes. We also show that at three loops, relaxing the dual superconformal (Q) relations and imposing dihedral symmetry (and for NMHV the absence of spurious poles) leaves only a single ambiguity in the heptagon amplitudes. These results point to a strong tension between the collinear properties of the amplitudes and the Steinmann relations.

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“…A leading-order strong-coupling analysis is also possible [37,38], but even more remarkably, the building blocks in question can also be obtained to all loops [39] by means of analytic continuation from a collinear limit where the dynamics is governed by an integrable flux tube [40][41][42][43][44][45][46][47][48][49][50][51], see also [52][53][54]. These developments render the MRK as one of the best sources of 'boundary data' [54][55][56][57] for determining the six-gluon amplitude in general kinematics through five loops, by exploiting its analytic structure with the help of the bootstrap method [30,[58][59][60][61][62].…”

Section: Jhep06(2018)116mentioning

confidence: 99%

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

Duca

Druc

Drummond

et al. 2018

J. High Energ. Phys.

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Abstract:We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2 → 5 amplitude in planar N = 4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N -particle MHV amplitude in this region to a function, we specialize to N = 7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the wellstudied six-gluon case. As an application of our results, we explicitly compute the sevengluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively.

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The four-loop six-gluon NMHV ratio function

Cited by 142 publications

References 174 publications

Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD

Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD

Heptagons from the Steinmann cluster bootstrap

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

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