Probing $CP$ Violation in $h\to {\tau }^{-}{\tau }^{+}$ at the LHC

We propose a novel method to reconstruct event by event the full kinematics of the cascade decay process, $h\to {\tau }^{+}{\tau }^{-}\to ({\pi }^{+}\overline{\nu })({\pi }^{-}\nu )$, which allows us to measure the ${\tau }^{+}{\tau }^{-}$ spin correlation, a measure of the $CP$ property of the Higgs boson. By noting that the ${\tau }^{\pm }$ momenta lie on the plane spanned by the accurately measured impact parameter and momentum vectors of charged pions, we can obtain the most likely momenta of the two missing neutrinos by using the probability distribution functions of the ${\overrightarrow{\cancel{p}}}_T$ vector and the location of the primary vertex. A simple detector level simulation shows an excellent agreement between the reconstructed and the true kinematics, both in the ${\tau }^{+}{\tau }^{-}$ and the ${\pi }^{+}{\pi }^{-}$ rest frames. The method can be tested in $Z\to {\tau }^{+}{\tau }^{-}$ events, which should exhibit no correlation.

Figure 1

The reconstructed azimuthal angle distribution of $Z\to {\tau }^{+}{\tau }^{-}$ events after the smearing in the impact parameter. The black solid line denotes the case without $|{\overrightarrow{b}}_{{\pi }^{\pm },T}^{\mathrm{obs}}|$ cut, the pink dotted line denotes $\min (|{\overrightarrow{b}}_{{\pi }^{\pm },T}^{\mathrm{obs}}|)>25\mu \mathrm{m}$, and the green solid line shows $\min (|{\overrightarrow{b}}_{{\pi }^{\pm },T}^{\mathrm{obs}}|)>50\mu \mathrm{m}$. The data points correspond to an integrated luminosity $3{\mathrm{ab}}^{-1}$.

Figure 2

Correlations between the true and reconstructed azimuthal angle difference for the SM Higgs (${\xi }_{h\tau \tau }=0$) after the cut $|{\overrightarrow{b}}_{{\pi }^{\pm },T}^{\mathrm{obs}}|>50\mu \mathrm{m}$. The 422 data points correspond to an integrated luminosity $3{\mathrm{ab}}^{-1}$.

Figure 3

Distributions of the reconstructed azimuthal angle difference for the $h\to {\tau }^{+}{\tau }^{-}\to {\pi }^{+}{\pi }^{-}\nu \overline{\nu }$ events with ${\xi }_{h\tau \tau }=0$ (blue solid line) and ${\xi }_{h\tau \tau }=\pi /4$ (pink dashed line) after the cut $|{\overrightarrow{b}}_{{\pi }^{\pm },T}^{\mathrm{obs}}|>50\mu \mathrm{m}$. The data points correspond to an integrated luminosity $3{\mathrm{ab}}^{-1}$.

Figure 4

The $\mathrm{\Delta }{\varphi }^{\mathrm{rec}}$ distribution of the signal and background and the result of fitting. The blue solid line show the signal events of ${\xi }_{h\tau \tau }=0$, the green solid line shows the background events. The red solid histogram shows their sum. The red solid curve shows our fit. The dashed line and histograms are for ${\xi }_{h\tau \tau }=\pi /4$. In both cases, we use the same background events. We require $|{\overrightarrow{b}}_{{\pi }^{\mp },T}^{\mathrm{obs}}|>50\mu \mathrm{m}$. The data points correspond to an integrated luminosity $3{\mathrm{ab}}^{-1}$.