The phenomenological cornucopia of SU(3) exotica

We introduce an effort to catalog the gauge-invariant interactions of Standard Model (SM) particles and new fields in a variety of representations of the SM color gauge group $\text{SU}(3)_{\text{c}}$. In this first installment, we direct this effort toward fields in the six-dimensional (sextet, $\boldsymbol{6}$) representation. We consider effective operators of mass dimension up to seven (comprehensively up to dimension six), featuring both scalar and fermionic color sextets. We use an iterative tensor-product method to identify the color invariants underpinning such operators, emphasizing structures that have received little attention to date. In order to demonstrate the utility of our approach, we study a simple but novel model of color-sextet fields at the Large Hadron Collider (LHC). We compute cross sections for an array of new production channels enabled by our operators, including single-sextet production and sextet production in association with photons or leptons. We also discuss dijet-resonance constraints on a sextet fermion. This example shows that there remains a wide array of fairly minimal but well motivated and unexplored models with extended strong sectors as we await the high-luminosity LHC.