Perturbative expansion of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>8</mml:mn></mml:math>Supergravity

Dunbar, David C.; Ettle, James H.; Perkins, Warren B.

doi:10.1103/physrevd.83.065015

Cited by 35 publications

(70 citation statements)

References 59 publications

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“…The expression (9) for the finite remainder agrees with the very recent result of [42], which uncovered a typo in the original version of our manuscript. This work was supported in part by the Schweizer Nationalfonds under grant 200020-162487, as well as by the European Commission through the ERC Advanced Grant "MC@NNLO" (340983).…”

Section: Acknowledgmentssupporting

confidence: 78%

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: Acknowledgmentssupporting

confidence: 78%

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

2016

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“…The duality and double-copy property have also been confirmed in one-and two-loop five-point amplitudes in N = 8 supergravity [33]. For less-than-maximal supergravities, the double-copy property has been checked explicitly for the one-loop four-and five-graviton amplitudes of N = 4, 5, 6 supergravity [56] by showing it matches known results [57]. In the two-loop four-graviton amplitudes in these theories, it has been verified to be consistent with the known infrared divergences and other properties [58].…”

Section: A Duality Between Color and Kinematicssupporting

confidence: 52%

Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes

et al. 2012

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We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N = 4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D = 11/2, the same dimension as for N = 4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N = 8 supergravity as the subleading-in-1/N 2 c single-trace divergence in N = 4 super-Yang-Mills theory.

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“…This amplitude is well studied and has been computed in refs. [26][27][28]. The double-copy construction of this amplitude is particularly simple.…”

Section: One-loop Examplementioning

confidence: 99%

“…These examples are based on the one-and two-loop N = 4 supergravity amplitudes previously obtained in refs. [26][27][28][29].…”

Section: Jhep05(2017)137mentioning

confidence: 99%

Manifesting enhanced cancellations in supergravity: integrands versus integrals

Bern

Enciso

Parra-Martinez

et al. 2017

J. High Energ. Phys.

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Examples of 'enhanced ultraviolet cancellations' with no known standardsymmetry explanation have been found in a variety of supergravity theories. By examining one-and two-loop examples in four-and five-dimensional half-maximal supergravity, we argue that enhanced cancellations in general cannot be exhibited prior to integration. In light of this, we explore reorganizations of integrands into parts that are manifestly finite and parts that have poor power counting but integrate to zero due to integral identities. At two loops we find that in the large loop-momentum limit the required integral identities follow from Lorentz and SL(2) relabeling symmetry. We carry out a nontrivial check at four loops showing that the identities generated in this way are a complete set. We propose that at L loops the combination of Lorentz and SL(L) symmetry is sufficient for displaying enhanced cancellations when they happen, whenever the theory is known to be ultraviolet finite up to (L − 1) loops.

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Perturbative expansion ofN<8Supergravity

Cited by 35 publications

References 59 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

Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes

Manifesting enhanced cancellations in supergravity: integrands versus integrals

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