A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory

Badger, Simon; Mogull, Gustav; Ochirov, A.; O’Connell, Donal

doi:10.1007/jhep10(2015)064

Cited by 89 publications

(124 citation statements)

References 133 publications

(187 reference statements)

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“…An obvious next step consists in calculating the loop integrals in the nonplanar case (the method for finding an appropriate integral basis [10] does not rely on planarity) and applying them to the all-plus loop integrand that was found very recently [2].…”

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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“…The six-dimensional spinor-helicity formalism has been extensively developed in Ref. [65], and used in the context of multi-loop generalized unitarity for producing analytic results for five-and sixpoint two-loop all-plus amplitudes in (non-supersymmetric) Yang-Mills theory [64,66,67].…”

Section: Sdf: Six-dimensional Formalismmentioning

confidence: 99%

“…This setup has been used for the calculation of planar five-and six-point two-loop amplitudes in Yang-Mills theory presented in Refs. [64,66,67], as well as for the first application of multivariate reconstruction techniques to generalized unitarity presented in Ref. [68].…”

Section: Applications To Integrand Reduction Via Generalized Unitaritymentioning

confidence: 99%

To $${d}$$ d , or not to $${d}$$ d : recent developments and comparisons of regularization schemes

et al. 2017

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“…Recently the leading in color component of the two-loop all-plus five-point amplitude has been computed in QCD [5,6] using d-dimensional unitarity techniques. Subsequently this amplitude was presented in a very elegant and compact form [7].…”

Section: Introductionmentioning

confidence: 99%