Scattering of gravitons and spinning massive states from compact numerators

Abstract

We provide a new efficient diagrammatic tool, in the context of the scattering equations, for computation of covariant D-dimensional tree-level n-point amplitudes with pairs of spinning massive particles using compact exponential numerators. We discuss how this framework allows non-integer spin extensions of recurrence relations for amplitudes developed for integer spin. Our results facilitate the on-going program for generating observables in classical general relativity from on-shell tree amplitudes through the Kawai-Lewellen-Tye relations and generalized unitarity.

Generalizations of the double-copy: the KLT bootstrap

“…The double-copy is a very efficient method for computing gravity amplitudes that is playing an increasingly important role in modern gravity computations; for example, one of the recent exciting applications is to gravitional-wave physics [29,[49][50][51][52][53][54][55][56]. A fully systematic understanding of the double-copy is still an open question.…”

Post-Minkowskian radial action from soft limits and velocity cuts

“…Systematic algebraic construction of numerators for gluon in the scattering equation framework was pioneered by Fu, Du, Huang, and Feng in [51] and in refs. [52,53] developed into diagrammatic methods. Provided the scattering equation prescription for the colour-ordered multi-gluon amplitude in [48,54] and following the construction in [53] for tree-level amplitudes, the Yang-Mills multi-gluon amplitude (with Yang-Mills coupling at unity) has the form…”

“…[52,53] developed into diagrammatic methods. Provided the scattering equation prescription for the colour-ordered multi-gluon amplitude in [48,54] and following the construction in [53] for tree-level amplitudes, the Yang-Mills multi-gluon amplitude (with Yang-Mills coupling at unity) has the form…”

“…, n − 1), n) are numerator expressions containing ith gluon polarisation vectors ζ i and momenta k i . In contrast to the numerators developed in [51] we will as suggested in [53] average over reference orderings since it provides a computational advantage. Integration over the scattering equations can be done numerically but for arriving at analytic expressions one can explore the one-to-one link between integration measures and integrands in scattering equations and traditional string theory [55] and use it to formulate scattering equation integration rules [56][57][58][59].…”

“…As explained in [48,53] Thus the amplitude for emission of gravitons from a massive scalar can be written…”