Abstract
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 SCETBSM, 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, λ∼v/mV. 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′ boson and of a Kaluza-Klein gluon at leading and subleading order in λ. We illustrate the matching onto SCETBSM with a concrete example of a UV-complete new-physics model.
Highlights
That can be adapted to any specific new-physics scenario with only little effort
The effective theory is built using an extension of Soft-Collinear Effective Theory called SCETBSM, 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, λ ∼ v/mV
In refs. [5, 6], the original formulation of SCET has been extended to an effective theory called SCETBSM, which describes light SM fields coupled to a field describing a hypothetical new heavy resonance with mass much above the electroweak scale
Summary
We give a brief overview of the necessary ingredients of SCET relevant to this paper, referring the reader to [5] for a more detailed discussion. Since some of the low-energy degrees of freedom can have large momentum components (of order E), derivatives acting on (anti-)collinear fields are not necessarily power-suppressed, and the most general effective Lagrangian contains an infinite number of operators with arbitrary powers of large derivatives. They can be traded for nonlocalities of the composite operators and their Wilson coefficients along light-like directions, over which the Lagrangian is integrated. Operators in the EFT can contain derivatives ∂μ acting on the fields, but only those derivatives corresponding to small momentum components can appear, which again gives rise to a suppression in powers of λ. This mode will be replaced by the Higgs vacuum expectation value (VEV), i.e
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