Low Scale Composite Higgs Model and 1.8 $\sim$ 2 TeV Diboson Excess

We consider a simple solution to explain the recent diboson excess observed by ATALS and CMS Collaborations in models with custodial symmetry $SU(2)_L \times SU(2)_R \rightarrow SU(2)_c$. The $SU(2)_L$ triplet vector boson $\rho$ with mass range of $1.8 \sim 2$ TeV would be produced through the Drell-Yan process with sizable diboson decay branching to account for the excess. The other $SU(2)_L \times SU(2)_R$ bidoublet axial vector boson $a$ would cancel all deviations of electroweak obervables induced by $\rho$ even if the SM fermions mix with some heavy vector like (composite) fermions which couple to $\rho$ ("non-universally partially composite"), therefore allows arbitrary couplings between each SM fermion and $\rho$. We present our model in the "General Composite Higgs" framework with $SO(5) \times U(1)_X \rightarrow SO(4) \times U(1)_X$ breaking at scale $f$ and demand the first Weinberg sum rule and positive gauge boson form factors as the theoretical constraints. We find that our model can fit the diboson excess very well if the left-handed SM light quarks, charged leptons and tops have zero, zero/moderately small and moderate/large composite components for reasonable values of $g_\rho$ and $f$. The correlation between tree level $S$ parameter and the $h \rightarrow Z \gamma$ suggest a large $a$ contribution to $h \rightarrow Z \gamma$ and it is indeed a $\mathcal{O}(1)$ effect in our parameter space which provides a strong hint for our scenario if this diboson excess is confirmed by the $13 \sim 14$ TeV LHC Run II.