$M_{T2}$ as a probe of CP phase in $h \rightarrow \tau \tau$ at the LHC

We propose to utilize the transverse mass variable $M_{T2}$ and it's descendant $M_{2Cons}$ for constraining the CP admixture of the tau lepton Yukawa coupling at the LHC. We have considered the tau lepton pair produced from the Higgs boson with each tau decays to a charged pion and a neutrino, $\tau^{\pm} \rightarrow \pi^{\pm} \nu_{\tau}$. Recently, for this channel, the LHC has employed the impact parameter method to measure the CP mixing angle of tau lepton Yukawa coupling with large uncertainty. The observables we propose here can be measured in the lab frame without the impact parameter measurement and in turn, give a complementary probe of the CP admixture of tau lepton Yukawa. The CP mixing angle, with our method, can be constrained up to 17$^{\circ}$ (7$^{\circ}$) with 300 (3000) $fb^{-1}$ of integrated luminosity at the 14 LHC.