Consistency and Interpretation of the LHC (Di-)Di-Jet Excesses

ATLAS observed a limit for {the cross section of di-jets resonances, which is weaker than expected for a} mass slightly below $\approx$1\TeV. In addition, CMS reported hints for the (non-resonant) pair production of di-jet resonances $X$ via a particle $Y$ at a very similar mass range with a local (global) significance of 3.6\,$\sigma$ (2.5\,$\sigma$) at $m_X\approx950\,$GeV. In this article we show that using the preferred range for $m_X$ from the ATLAS analysis, one can reinterpret the CMS analysis of di-di-jets in terms of a resonant search with $Y\to XX$, with a significantly reduced look-elsewhere effect, finding an excess for $m_Y\!\approx\!3.6$\TeV with a significance of $4.0\,\sigma$ ($3.2\,\sigma$) locally (globally). We present two possible UV completions capable of explaining the (di-)di-jet excesses, one containing two scalar di-quarks, the other one involving heavy gluons based on an $SU(3)_1\!\times\! SU(3)_2\!\times\! SU(3)_3$ gauge symmetry, spontaneously broken to $SU(3)$ color. In the latter case, non-perturbative couplings are required, pointing towards a composite or extra-dimensional framework. In fact, using 5D-AdS space-time, one obtains the correct mass ratio for $m_X/m_Y$, assuming the $X$ is the lowest lying resonance, and predicts a third (di-)di-jet resonance with a mass around $\approx2.2$\TeV.