Effective Field Theory after a New-Physics Discovery

Abstract

When a new heavy particle is discovered at the LHC or at a future high-energy collider, it will be interesting to study its decays into Standard Model particles using an effective field-theory framework. We point out that the proper effective theory can not be constructed as an expansion in local, higher-dimensional operators; rather, it must be based on non-local operators defined in soft-collinear effective theory (SCET). For the interesting case where the new resonance is a gauge-singlet spin-0 boson, which is the first member of a new sector governed by a mass scale $M$, we show how a consistent scale separation between $M$ and the electroweak scale $v$ is achieved up to next-to-next-to-leading order in the expansion parameter $\lambda \sim v/M$. The Wilson coefficients in the effective Lagrangian depend in a non-trivial way on the mass of the new resonance and the masses of yet undiscovered heavy particles. Large logarithms of the ratio $M/v$ can be systematically resummed using the renormalization group. We develop a SCET toolbox, with which it is straightforward to construct the relevant effective Lagrangians for new heavy particles with other charges and spin.

arXiv comment37 pages plus appendix, 7 figures. Changes in v2: sign in the second line of eq. (76) corrected, superfluous subscript in the third line of eq. (72) removed, other minor modifications. Version accepted for publication in JHEP. Changes in v3: typos in eqs. (42) and (72) corrected, missing diagrams added in Fig. 3 and eq. (81), several references updated

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