Studies of the VBF $H\rightarrow\tau_l\tau_{had}$ analysis at High Luminosity LHC conditions

This note documents projections for the measurement of Standard Model $H\rightarrow \tau\tau$ in the vector boson fusion production channel for the High Luminosity LHC (HL-LHC). The projections are based on the Run-I analysis. It is assumed that the HL-LHC will deliver an integrated luminosity of 3000 $\text{fb}^{-1}$, a center-of-mass energy of 14 TeV and an average number of overlapping $pp$ collisions of $<\mu> = 140$. Only the VBF production is targeted, and the analysis requires one tau to decay leptonically and the other hadronically. The projected uncertainty on the signal strength is $24\%$ when theory uncertainties are ignored and $10\%$ ($5\%$) background (signal) uncertainties are assumed. If the tracking coverage is extended, the projected uncertainty on the signal strength is as low as $8\%$.