Abstract
We consider a broad class of massive four dimensional effective theories describing an infinite tower of charged massive spin 1 states, interacting with massless spin 1 and spin 0. The spectrum is chosen to be the same as that appears in the Kaluza-Klein theory reduction of 5d Yang-Mills to ensure the absence of any spurious poles in a possible double copy formulation. The effective theories are characterized by multiple different couplings between different fields which are unconstrained by symmetries and low energy criteria. Remarkably, by demanding that the scattering amplitudes preserve colour-kinematics duality for different scattering processes, required for the existence of a massive double copy, we find that our 4d Lagrangian is fixed uniquely to the Kaluza-Klein compactification of 5d Yang-Mills theory together with its known double copy consistent higher derivative operators.
Highlights
Are well established for massless theories, while the double copy for massive theories is far less understood
In this work we aim to explore whether there are other consistent effective field theories (EFTs) for interacting massive spin-1 states, which still respect colour-kinematics duality, for which there is a possibility of developing a double-copy
We find that if we demand the naive extension of colour-kinematics (CK) duality for massive states proposed in [53, 54] to an array of scattering amplitudes with different external states, the huge freedom in our EFT coupling constant space is reduced, and to the order we have calculated, namely up to 5pt amplitudes and order 1/Λ4 in an EFT expansion, the unique solution which allows for CK duality is the Kaluza-Klein compactification of the 5d theory
Summary
Poles and the conditions necessary to remove them. To double copy an n-point tree level gauge theory amplitude, An, first we need to write it in the following form: An =. In other words the massive double copy formalism developed in [53, 54] assumes that all algebraic relations between partial amplitudes and propagators that are true in massless theories, compatible with the colour-kinematics duality, should still hold for massive ones This general procedure straightforwardly generalizes to higher n-pt functions. As mentioned in the introduction, known example of theories with massive states that will automatically satisfy the above spectral conditions (2.9) and (2.14) are Kaluza-Klein theories obtained by compatifying 5d massless theories obeying the colour-kinematics duality The reason for this is that the massive propagator Dij can always be interpreted as a massless propagator in 5 dimensions for a specific choice of 5d momenta. As long as the latter are satisfied, it is possible to solve for v, for ∆n, and determine new kinematic factors n + ∆n which do respect CK duality, from which a double copy theory may be constructed given via the standard prescription: Mn ∝ (n + ∆n)T D−1(n + ∆n)
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