Effective Field Theory for Heavy Vector Resonances Coupled to the Standard Model

We construct an effective field theory describing the decays of a heavy vector resonance $V$ into Standard Model particles. The effective theory is built using an extension of Soft-Collinear Effective Theory called SCET$_{\rm BSM}$, which provides a rigorous framework for parameterizing decay matrix elements with manifest power counting in the ratio of the electroweak scale and the mass of the resonance, $\lambda \sim v\mathrm{/}{m}_V$. Using the renormalization-group evolution of the couplings in the effective Lagrangian, large logarithms associated with this scale ratio can be resummed to all orders. We consider in detail the two-body decays of a heavy $Z^{\mathrm{\prime }}$ boson and of a Kaluza-Klein gluon at leading and subleading order in $\lambda$. We illustrate the matching onto SCET${}_{\mathrm{B}\mathrm{S}\mathrm{M}}$ with a concrete example of a UV-complete new-physics model.