Measurement of the kaon content of three-prong τ decays

We present branching fraction measurements of three-prong decays of the ${\mathrm{\tau }}^{\mathrm{-}}$ lepton based on data from the TPC/Two-Gamma detector at SLAC PEP. The decays are classified according to the identities of the charged tracks to give simultaneous measurements of B[${\mathrm{\tau }}^{\mathrm{-}}$→${\nu }_{\mathrm{\tau }}$ ${\mathit{K}}^{\mathrm{-}}$${\mathrm{\pi }}^{+}$${\mathrm{\pi }}^{\mathrm{-}}$]=0.${58}_{\mathrm{-}0.13}^{+0.15\mathrm{}}$% and B[${\mathrm{\tau }}^{\mathrm{-}}$→${\nu }_{\mathrm{\tau }}$ ${\mathit{K}}^{\mathrm{-}}$${\mathit{K}}^{+}$${\mathrm{\pi }}^{\mathrm{-}}$]=0.${15}_{\mathrm{-}0.07}^{+0.09\mathrm{}}$%, and upper limits of B[${\mathrm{\tau }}^{\mathrm{-}}$→${\nu }_{\mathrm{\tau }}$${\mathrm{\pi }}^{\mathrm{-}}$${\mathit{K}}^{+}$${\mathrm{\pi }}^{\mathrm{-}}$]<0.25%, B[${\mathrm{\tau }}^{\mathrm{-}}$→${\nu }_{\mathrm{\tau }}$ ${\mathit{K}}^{\mathrm{-}}$${\mathrm{\pi }}^{+}$${\mathit{K}}^{\mathrm{-}}$]<0.09%, and B[${\mathrm{\tau }}^{\mathrm{-}}$→${\nu }_{\mathrm{\tau }}$ ${\mathit{K}}^{\mathrm{-}}$${\mathit{K}}^{+}$${\mathit{K}}^{\mathrm{-}}$]<0.21%, where additional neutrals may be present in each case. The branching fractions are normalized to the world average three-prong topological branching fraction and there is an estimated 20% systematic error in addition to the listed statistical errors. We find the mass distributions in the ${\mathit{K}}^{\mathrm{-}}$${\mathrm{\pi }}^{+}$${\mathrm{\pi }}^{\mathrm{-}}$ decay are consistent with ${\mathit{K}}_1$ dominance, and obtain branching fractions of B[${\mathrm{\tau }}^{\mathrm{-}}$→${\nu }_{\mathrm{\tau }}$ ${\mathit{K}}_1^{\mathrm{-}}$(1270)]=0.${41}_{\mathrm{-}0.35}^{+0.41\mathrm{}}$% and B[${\mathrm{\tau }}^{\mathrm{-}}$→${\nu }_{\mathrm{\tau }}$ ${\mathit{K}}_1^{\mathrm{-}}$(1400)]=0.${76}_{\mathrm{-}0.33}^{+0.40\mathrm{}}$%.