Probing Supersymmetric Dark Matter and the Electroweak Sector using Vector Boson Fusion Processes: A Snowmass Whitepaper

Vector boson fusion (VBF) processes at the Large Hadron Collider (LHC) provide a unique opportunity to search for new physics with electroweak couplings. Two studies are presented: (i) A search of supersymmetric dark matter in the final state of two VBF jets and large missing transverse energy is presented at 14 TeV. Prospects for determining the dark matter relic density are studied for the cases of Wino and Bino-Higgsino dark matter. The LHC could probe Wino dark matter with mass up to approximately 600 GeV with a luminosity of 1000 fb$^{-1}$. (ii) A search for the chargino/neutralino system in the final state of two VBF jets, missing transverse energy and two $\tau$'s (light stau case) and light lepton $e$ and $\mu$ (light slepton case). The $5 \sigma$ mass reach at 300 fb$^{-1}$ (1000 fb$^{-1}$) of LHC14 for inclusive and opposite-sign $\tau$ pairs are 250 GeV (300 GeV) and 200 GeV (250 GeV), respectively, for $\Delta M \, = \, m_{\tilde{\tau}_1} - m_{\neu{1}} \, = \, 30$ GeV. For $\Delta M \, = \, 15$ GeV, the $3 \sigma$ mass reach at 300 fb$^{-1}$ (1000 fb$^{-1}$) of LHC14 for inclusive $\tau$ pairs is 180 GeV. The $5 \sigma$ mass reach at 300 fb$^{-1}$ (1000 fb$^{-1}$) of LHC14 for inclusive and opposite-sign $\mu$ pairs are approximately 350 GeV (400 GeV) and 300 GeV (350 GeV), respectively. The mass reaches in the same-sign final state cases are similar to those in the opposite-sign cases.