Branching Fractions of $\tau$ Leptons to Three Charged Hadrons

From electron-positron collision data collected with the CLEO detector operating at Cornell Electron Storage Ring near $\sqrt{s}=10.6\mathrm{G}\mathrm{e}\mathrm{V}$, improved measurements of the branching fractions for $\tau$ decays into three explicitly identified hadrons and a neutrino are presented as $\mathcal{B}({\tau }^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau })=(9.13\pm 0.05\pm 0.46)\%$, $\mathcal{B}({\tau }^{-}\to K^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau })=(3.84\pm 0.14\pm 0.38)\times {10}^{-3}$, $\mathcal{B}({\tau }^{-}\to K^{-}{K}^{+}{\pi }^{-}{\nu }_{\tau })=(1.55\pm 0.06\pm 0.09)\times {10}^{-3}$, and $\mathcal{B}({\tau }^{-}\to K^{-}{K}^{+}{K}^{-}{\nu }_{\tau })<3.7\times {10}^{-5}$ at 90% C.L., where the uncertainties are statistical and systematic, respectively.

Figure 1

Kaon (solid circles) and pion (open circles) identification efficiencies (top) and fake rates (bottom) as a function of their momenta for tracks already within $|\cos \theta |<0.83$ as determined from $D^0\to K^{-}{\pi }^{+}$ decays. Error bars are statistical only.

Figure 2

Three-hadron masses from data (solid circles) and MC, $\tau$-pair background (short dashes), $q\overline{q}$ background (long dashes), sum of background and signal (solid lines), for (a) ${\tau }^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$, (b) ${\tau }^{-}\to K^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$, (c) ${\tau }^{-}\to K^{-}{K}^{+}{\pi }^{-}{\nu }_{\tau }$, and (d) ${\tau }^{-}\to K^{-}{K}^{+}{K}^{-}{\nu }_{\tau }$.

Figure 3

Mass distributions for two oppositely charged hadrons showing the data (solid circles) and MC [$\tau$-pair background (short dashes), $q\overline{q}$ background (long dashes), sum of background and signal (solid lines)] for (a) ${\tau }^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$ (two entries per event), (b),(c) ${\tau }^{-}\to K^{-}{K}^{+}{\pi }^{-}{\nu }_{\tau }$, ($K^{+}{K}^{-}$ and $K^{+}{\pi }^{-}$ masses, respectively), and (d),(e) ${\tau }^{-}\to K^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$ (${\pi }^{+}{\pi }^{-}$ and $K^{-}{\pi }^{+}$ masses, respectively).