Interpreting the 3 TeV $WH$ Resonance as a $W'$ boson

Motivated by a local $3.2-3.4$ sigma resonance in $WH$ and $ZH$ in the ATLAS Run 2 data, we attempt to interpret the excess in terms of a $W'$ boson in a $SU(2)_1 \times SU(2)_2 \times U(1)_X$ model. We stretch the deviation from the alignment limit of the Equivalence Theorem, so as to maximize $WH$ production while keeping the $WZ$ production rate below the experimental limit. We found a viable though small region of parameter space that satisfies all existing constraints on $W' \to jj, t \bar b, WZ$, as well as the precision Higgs data. The cross section of $W' \to WH$ that we obtain is about $5-6$ fb.