Collider constraints and new tests of color octet vectors

We analyze the collider sensitivity for new colored resonances in $t\bar{t}$, $b \bar{b}$, and $jj$ final states. While searches in the single production channel are model-dependent, the pair production rate is model independent and the existing $(JJ)(JJ)$ and $4t$ searches impose strong constraints on the relevant branching fractions, where $J = j$ or $b$. We point out the missing, complementary searches in the mixed decay modes, $t\bar{t}(jj)$, $t\bar{t}(b\bar{b})$, and $(b\bar{b})(jj)$. We propose analysis strategies for the $t\bar{t}(jj)$ and $t\bar{t}(b\bar{b})$ decays and find their sensivity surpasses that of existing searches when the decay widths to tops and light jets are comparable. If no other decays are present, collective lower limits on the resonance mass can be set at 1.5~TeV using 37~fb$^{-1}$ of 13~TeV data.