$R$ -parity violating supersymmetry and the 125 GeV Higgs boson signals

We observe the impact of $R$-parity violating super symmetry (RPV SUSY) on the 125 GeV Higgs production and decay modes at the LHC. We assume a heavy SUSY spectrum with multi-TeV squarks and SU(2) scalar singlets as well as the decoupling limit in the SUSY Higgs sector. In this case the lightest CP-even Higgs is SM-like when $R$-parity is conserved. In contrast, we show that when $R$-parity violating interactions are added to the SUSY framework, significant deviations may occur in some production and decay channels of the 125 GeV Higgs-like state. Indeed, we assume a single-flavor (mostly third generation) Bilinear RPV (BRPV) interactions, which generate Higgs-sneutrino mixing, lepton-chargino mixing and neutrino-neutralino mixing, and find that notable deviations of $O$(20-30%) may be expected in the Higgs signal strength observables in some channels, e.g., in $pp\text{→}h\text{→}{\text{μ}}^{+}{\text{μ}}^{-}$, ${\text{τ}}^{+}{\text{τ}}^{-}$. Moreover, we find that new and detectable signals associated with BRPV Higgs decays to gauginos, $h\text{→}{\text{ν}}_{\text{τ}}$$\widetilde{\text{χ}}$${}_2^0$ and $h\text{→}{\text{τ}}^{\text{±}}{\text{χ}}_2^{\text{∓}}$, may also arise in this scenario. These decays yield a typical signature of $h\text{→}{\text{τ}}^{\text{±}}{\text{ℓ}}^{\text{∓}}$ + Ɇ${}_T$ ($\text{ℓ}=e,\text{μ},\text{τ}$) that can be much larger than in the SM, and may also be accompanied by an $O$(20-30%) enhancement in the diphoton signal $pp\text{→}h\text{→}\text{γ}\text{γ}$. We also examine potential interesting signals of Trilinear $R$-parity violation (TRPV) interactions in the production and decays of the Higgs-sneutrino BRPV mixed state (assuming it is the 125 GeV scalar) and show that, in this case also, large deviations up to $O$(100%) are expected in e.g., $pp\text{→}h\text{→}{\text{μ}}^{+}{\text{μ}}^{-},{\text{τ}}^{+}{\text{τ}}^{-}$, which are sensitive to the BRPV × TRPV coupling product.