A 2 TeV $W_R$, Supersymmetry, and the Higgs Mass

A recent ATLAS search for diboson resonances and a CMS search for $eejj$ resonances which both show excesses with significance around 3 sigma have generated interest in $SU(2)_R$ gauge extensions of the Standard Model with a $W'$ mass around 2 TeV. We investigate the possibility that an $SU(2)_R$ gauge extension of the MSSM compatible with an explanation of the diboson anomaly might give rise to a significant enhancement of the Higgs mass above the MSSM tree level bound $m_{h, \text{tree}} < 90 \; \text{GeV}$ due to non-decoupling D-terms. This model contains a vector-like charge -1/3 $SU(2)_R$ singlet quark for each generation which mixes significantly with the $SU(2)_R$ doublet quarks, affecting the $W_R$ phenomenology. We find that it is possible to achieve $m_{h, \text{tree}} > 110 \; \text {GeV}$, and this requires that the $Z'$ mass is close to 3 TeV.