Effective Field Theory after a New-Physics Discovery

TL;DR

This paper develops a non-local effective field theory framework using soft-collinear effective theory (SCET) for analyzing decays of new heavy particles discovered at colliders, enabling systematic scale separation and resummation of large logarithms.

Contribution

It introduces a SCET-based approach for constructing effective theories of new heavy particles, moving beyond local operator expansions, and provides tools for systematic analysis up to NNLO.

Findings

Proper effective theory is non-local, based on SCET.

Achieves scale separation between new physics scale and electroweak scale up to NNLO.

Provides a systematic resummation method for large logarithms of mass ratios.

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.