Abstract
We use on-shell methods to calculate tree-level effective field theory (EFT) amplitudes, with no reference to the EFT operators. Lorentz symmetry, unitarity and Bose statistics determine the allowed kinematical structures. As a by-product, the number of independent EFT operators simply follows from the set of polynomials in the Mandelstam invariants, subject to kinematical constraints. We demonstrate this approach by calculating several amplitudes with a massive, SM-singlet, scalar (h) or vector (Z′) particle coupled to gluons. Specifically, we calculate hggg, hhgg and Z′ggg amplitudes, which are relevant for the LHC production and three-gluon decays of the massive particle. We then use the results to derive the massless-Z′ amplitudes, and show how the massive amplitudes decompose into the massless-vector plus scalar amplitudes. Amplitudes with the gluons replaced by photons are straightforwardly obtained from the above.
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Shadmi, Y., Weiss, Y. Effective field theory amplitudes the on-shell way: scalar and vector couplings to gluons. J. High Energ. Phys. 2019, 165 (2019). https://doi.org/10.1007/JHEP02(2019)165
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DOI: https://doi.org/10.1007/JHEP02(2019)165