A mass reconstruction technique for a heavy resonance decaying to $\tau^+\tau^-$

For a resonance decaying to $\tau^+\tau^-$, it is difficult to reconstruct its mass accurately because of the presence of neutrinos in the decay products of the $\tau$ leptons. If the resonance is heavy enough, we show that its mass can be well determined by the momentum component of the $\tau$ decay products perpendicular to the velocity of the $\tau$ lepton, $p_{\perp}$, and the mass of the visible/invisible decay products, $m_{vis/inv}$, for $\tau$ decaying to hadrons/leptons. By sampling all kinematically allowed values of $p_{\perp}$ and $m_{vis/inv}$ according to their joint probability distributions determined by the MC simulations, the mass of the mother resonance is assumed to lie at the position with the maximal probability. Since $p_{\perp}$ and $m_{vis/inv}$ are invariant under the boost in the $\tau$ lepton direction, the joint probability distributions are independent upon $\tau$'s origin. Thus this technique is able to determine the mass of an unknown resonance with no efficiency loss. It is tested using the MC simulations of the physics processes $pp \to Z/h(125)/h(750)+X\to \tau\tau+X$ at 13~TeV. The ratio of the full width at half maximum and the peak value of the reconstructed mass distribution is found to be 20\%-40\% using the information of missing transverse energy.