<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math>-parity violating supersymmetric explanation for the CDF<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi><mml:mi>j</mml:mi><mml:mi>j</mml:mi></mml:math>excess

Recently the CDF Collaboration reported a statistically significant excess in the distribution of the dijet invariant mass between 120--160 GeV in $Wjj$ event sample in $4.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data and later confirmed with $7.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data, which has generated considerable interest. We offer a possible explanation of this observation in the general framework of minimal supersymmetric standard model with $R$-parity violation through resonance production of ${\stackrel{\texttildelow{}}{\ensuremath{\nu}}}_{\ensuremath{\tau}}$ decaying into the LSP ${\stackrel{\texttildelow{}}{\ensuremath{\tau}}}_{1}$ and $W$ boson. We also give the predictions of this scenario for the LHC operating at 7 TeV center of mass energy.