Measurement of the $\tau$-lepton Lifetime at Belle

The lifetime of the $\tau$ lepton is measured using the process $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$, where both $\tau$ leptons decay to $3\pi {\nu }_{\tau }$. The result for the mean lifetime, based on $711{\mathrm{fb}}^{-1}$ of data collected with the Belle detector at the $\mathrm{\Upsilon }(4S)$ resonance and $60\mathrm{MeV}$ below, is $\tau =\mathbf{(}290.17\pm 0.53(\text{stat})\pm 0.33(\text{syst})\mathbf{)}\times {10}^{-15}\mathrm{s}$. The first measurement of the lifetime difference between ${\tau }^{+}$ and ${\tau }^{-}$ is performed. The upper limit on the relative lifetime difference between positive and negative $\tau$ leptons is $|\mathrm{\Delta }\tau |/\tau <7.0\times {10}^{-3}$ at 90% C.L.

Figure 1

The schematic view of the ${\tau }^{+}{\tau }^{-}$ event in the laboratory frame.

Figure 2

The measured proper time $t$ distribution for the data (filled circles with errors). The black line (passing through these circles) is the result of the fit by Eq. (4). The first histogram below the data circles (red histogram) is the MC prediction for the sum of the $uds$ and $\gamma \gamma$ background contributions. The magenta line near this histogram is the contribution of the $uds+\gamma \gamma$ obtained in the fit by Eq. (4). The lowest (blue) histogram is the MC prediction for the sum of the charm and beauty background contributions. The blue line (passing through this histogram) is the smoothed distribution of the charm and beauty contributions that is used in the fit. The distribution of residuals $[(data-fit)/error]$ for the fit is shown in the bottom panel.