  We propose the creation of a Light Exotics Effective Field Theory (LEX-EFT)
catalog. LEX-EFT is a generic framework to capture all interactions between the
Standard Model (SM) and all (or at least a large class of) theoretically
allowed exotic states beyond the Standard Model (bSM), indexed by their SM and
bSM charges. These states are light enough to be on or nearly on shell in some
collider processes. This framework, which subsumes beyond the Standard Model
paradigms as generally as possible, is meant to extend recent successful
implementations of bSM EFTs and complement e.g. the Standard Model Effective
Field Theory (SMEFT), which can capture the off-shell effects of exotic fields.
In this work, we review a general method for the construction of a complete
list of gauge-invariant operators involving SM interactions with light exotics
via iterative tensor product decomposition, up to the desired order in mass
dimension. Each operator is characterized by specific Clebsch-Gordan
coefficients determined by the charge flow; we show how this charge flow
affects the range of EFT validity and cross sections associated with an
effective operator. We create an example catalog of exotic scalars coupling to
SM gauge boson pairs, and we highlight some operators with exotic weak
$\mathrm{SU}(2)_{\text{L}}$ charges that can produce spectacular LHC
phenomenology. We further demonstrate the utility of the LEX-EFT approach with
several examples of effects on kinematic distributions and cross sections that
would not be captured by EFTs agnostic to the exotic degrees of freedom and may
evade the main inclusive collider searches tailored to the existing preferred
set of standard bSM theories.
