Maximal unitarity at two loops

“…(See also recent work on a different organization of higher-loop integrals [84][85][86].) In previous papers, we have considered double boxes with no external masses [79] or with one, two, or three external masses [80]. In this article, we extend the GDO construction to planar double boxes with four external masses.…”

Section: Introductionmentioning

confidence: 99%

“…(1.1). In previous papers [79,80], we showed how to extract the coefficients of double-box master integrals using multidimensional contours around global poles. In this paper, we recast this operation as applying generalized discontinuity operators (GDOs).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Maximal unitarity for the four-mass double box

2014

Self Cite

View full text Add to dashboard Cite

We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, VV → VV. In this formalism, the two-loop amplitude is expanded over a basis of integrals. We obtain formulas for the coefficients of the double-box integrals, expressing them as products of tree-level amplitudes integrated over specific complex multidimensional contours. The contours are subject to the consistency condition that integrals over them annihilate any integrand whose integral over real Minkowski space vanishes. These include integrals over parity-odd integrands and total derivatives arising from integration-by-parts (IBP) identities. We find that, unlike the zero-through three-mass cases, the IBP identities impose no constraints on the contours in the four-mass case. We also discuss the algebraic varieties connected with various double-box integrals and show how discrete symmetries of these varieties largely determine the constraints.

show abstract

“…We will find the two coefficients to be both zero, which is consistent In order to explain the machinery that we use at five loops, we briefly review the treatment in Ref. [66] of IBP relations needed to demonstrate the ultraviolet finiteness of half-maximal supergravity at two loops in D = 5, and in addition give a more intuitive treatment by computing cut integrals [46,47,68,69] following the method of Ref. [47].…”

Section: Maximal Cut Integration Check In D = 22/5mentioning

confidence: 99%

Five-loop four-point integrand of N=8 supergravity as a generalized double copy

Bern¹,

Carrasco

Chen³

et al. 2017

Phys. Rev. D

117

127

View full text Add to dashboard Cite

We use the recently developed generalized double-copy procedure to construct an integrand for the five-loop four-point amplitude of N = 8 supergravity. This construction starts from a naive double copy of the previously computed corresponding amplitude of N = 4 super-Yang-Mills theory. This is then systematically modified by adding contact terms generated in the context of the method of maximal unitarity cuts. For the simpler generalized cuts, whose corresponding contact terms tend to be the most complicated, we derive a set of formulas relating the contact contributions to the violations of the dual Jacobi identities in the relevant gauge-theory amplitudes.For more complex generalized unitarity cuts, which tend to have simpler contact terms associated with them, we use the method of maximal cuts more directly. The five-loop four-point integrand is a crucial ingredient towards future studies of ultraviolet properties of N = 8 supergravity at five loops and beyond. We also present a nontrivial check of the consistency of the integrand, based on modern approaches for integrating over the loop momenta in the ultraviolet region.

show abstract

Maximal unitarity at two loops

Cited by 120 publications

References 102 publications

Differential equations for Feynman integrals beyond multiple polylogarithms

Differential equations for Feynman integrals beyond multiple polylogarithms

Maximal unitarity for the four-mass double box

Five-loop four-point integrand of N=8 supergravity as a generalized double copy

Contact Info

Product

Resources

About