Abstract
Color-kinematics duality in the adjoint has proven key to the relationship between gauge and gravity theory scattering amplitude predictions. In recent work, we demonstrated that at four-point tree-level, a small number of color-dual EFT building blocks could encode all higher-derivative single-trace massless corrections to gauge and gravity theories compatible with adjoint double-copy. One critical aspect was the trivialization of building higher-derivative color-weights — indeed, it is the mixing of kinematics with non-adjoint-type color-weights (like the permutation-invariant d4) which permits description via adjoint double-copy. Here we find that such ideas clarify the predictions of local five-point higher-dimensional operators as well. We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators. These may then be suitably mapped, through another double-copy, to higher-derivative corrections in gravity.
Highlights
Identifying independent higher-derivative operators and calculating their predictions in the form of on-shell scattering amplitudes can be technically challenging, especially in gauge and gravity theories
We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators
The task of calculating gravitational amplitudes has been remarkably simplified by the discovery of color-dual double copy structure [14, 15], exploiting the fact that gravity predictions are entirely encoded by the kinematic information of gauge theory amplitudes [16,17,18]
Summary
Identifying independent higher-derivative operators and calculating their predictions in the form of on-shell scattering amplitudes can be technically challenging, especially in gauge and gravity theories. The cornerstone of our strategy is to target the construction of higher-derivative color weights, which mix both color structure and scalar kinematics into single numerator factors that obey adjoint relations Their adjoint properties render them appropriate building blocks for adjoint double copy with vector kinematic weights (such as from Yang-Mills) to generate gauge and gravity corrections. All order construction via relaxed adjoint for odd-multiplicity in the specific case of five points is treated in detail in this paper, but we expect this to generalize to all odd multiplicity In this manuscript, we demonstrate that such a simple scalar structure allows the constructive building of higher-derivative adjoint-type color-weight corrections at five-point tree level. We discuss our approach for discovering functional algebraic composition rules in appendix A, tabulate our explicit color-basis for five points in appendix B, offer a pedagogic example of operator matching in appendix C, as well as the explicit composition formulae relevant at five points in appendix D
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