Analytic results for two-loop Yang-Mills

Recent Developments in computing very specific helicity amplitudes in two loop QCD are presented. The techniques focus upon the singular structure of the amplitude rather than on a diagramatic and integration approachComment: Talk presented at 13th International Symposium on Radiative Corrections, 24-29 September, 2017,St. Gilgen, Austria, 9 page

Two-loop n-point all-plus helicity amplitude

We propose a compact analytic expression for the polylogarithmic part of the $n$-point two-loop all-plus helicity amplitude in gauge theory

Two-loop gravity amplitudes from four dimensional unitarity

We compute the polylogarithmic parts of the two-loop four and five-graviton amplitudes where the external helicities are positive and express these in a simple compact analytic form. We use these to extract the $\ln(\mu^2)$ terms from both the four and five-point amplitudes and show that these match the same $R^3$ counterterm

Analytic all-plus-helicity gluon amplitudes in QCD

We detail the calculation of two-loop all-plus helicity amplitudes for pure Yang-Mills theory.The four dimensional unitarity methods and augmented recursion techniques we have developed, together with a knowledge of the singular structure of the amplitudesallow us to compute thesein compact analytic forms.Specifically we present the computation and analytic results for the six- and seven-gluon leading colour two-loop amplitudes these being the first QCD two-loop amplitudes beyond five-points

Diagrammar in an extended theory of gravity

We show how the S-matrix of an extended theory of gravity defined by itsthree-point amplitudes can be constructed by demanding factorisation. Theresultant S-matrix has tree amplitudes obeying the same soft singularitytheorems as Einstein gravity including the sub-sub-leading terms

Graviton particle statistics and coherent states from classical scattering amplitudes

In the two-body scattering problem in general relativity, we study the final graviton particle distribution using a perturbative approach. We compute the mean, the variance and the factorial moments of the distribution from the expectation value of the graviton number operator in the KMOC formalism. For minimally coupled scalar particles, the leading deviation from the Poissonian distribution is given by the unitarity cut involving the six-point tree amplitude with the emission of two gravitons. We compute this amplitude in two independent ways. First, we use an extension of the Cheung-Remmen parametrization that includes minimally coupled scalars. We then repeat the calculation using on-shell BCFW-like techniques, finding complete agreement. In the classical limit, this amplitude gives a purely quantum contribution, proving that we can describe the final semiclassical radiation state as a coherent state at least up to order $\mathcal{O}(G^4)$ for classical radiative observables. Finally, we give general arguments about why we expect this to hold also at higher orders in perturbation theory.Comment: 44 pages, 12 figures; v3: published in JHEP, final versio

Proving the dimension-shift conjecture

International audienceWe prove the conjecture made by Bern, Dixon, Dunbar, and Kosower that describes a simple dimension shifting relationship between the one-loop structure of N = 4 MHV amplitudes and all-plus helicity amplitudes in pure Yang-Mills theory. The proof captures all orders in dimensional regularisation using unitarity cuts, by combining massive spinor-helicity with Coulomb-branch supersymmetry. The form of these amplitudes can be given in terms of pentagon and box integrals using a generalised D-dimensional unitarity technique which captures the full amplitude to all multiplicities

The dimension-shift conjecture for one-loop amplitudes

International audienceA conjecture made by Bern, Dixon, Dunbar, and Kosower asserts a simple dimension shifting relationship between the one-loop structure of $\mathcal{N}$ = 4 MHV amplitudes and all-plus helicity amplitudes in pure Yang-Mills theory. We prove this conjecture to all orders in dimensional regularisation using unitarity cuts, and evaluate the form of these simplest one-loop amplitudes using a generalised D-dimensional unitarity technique which captures the full amplitude to all multiplicities

The two-loop n-point all-plus helicity amplitude

Abstract We propose a compact analytic expression for the polylogarithmic part of the n-point two-loop all-plus helicity amplitude in gauge theory

The two-loop n-point all-plus helicity amplitude

Abstract We propose a compact analytic expression for the polylogarithmic part of the n-point two-loop all-plus helicity amplitude in gauge theory