Measurement of the ${\tau }^{-}\to \eta {\pi }^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$ branching fraction and a search for a second-class current in the ${\tau }^{-}\to {\eta }^{\prime }(958){\pi }^{-}{\nu }_{\tau }$ decay

The ${\tau }^{-}\to \eta {\pi }^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$ decay with the $\eta \to \gamma \gamma$ mode is studied using $384{\mathrm{fb}}^{-1}$ of data collected by the BABAR detector. The branching fraction is measured to be $(1.60\pm 0.05\pm 0.11)\times {10}^{-4}$. It is found that ${\tau }^{-}\to f_1(1285){\pi }^{-}{\nu }_{\tau }\to \eta {\pi }^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$ is the dominant decay mode with a branching fraction of $(1.11\pm 0.06\pm 0.05)\times {10}^{-4}$. The first error on the branching fractions is statistical and the second systematic. Note that no particle identification algorithm is applied to the charged tracks to distinguish pions from kaons. In addition, a 90% confidence level upper limit on the branching fraction of the ${\tau }^{-}\to {\eta }^{\prime }(958){\pi }^{-}{\nu }_{\tau }$ decay is measured to be $7.2\times {10}^{-6}$. This last decay proceeds through a second-class current and is expected to be forbidden in the limit of isospin symmetry.

Figure 1

The invariant masses of the (a) $\gamma \gamma$, and (b) $\eta {\pi }^{-}{\pi }^{+}{\pi }^{-}$ final states are shown. The dark shaded histograms show the simulated signal events, the lightly shaded histograms show the simulated $\tau$ background, and the unshaded histograms show the simulated $q\overline{q}$ background. All selection criteria are applied. In (b) the cut requirement on the invariant mass of the $\eta {\pi }^{-}{\pi }^{+}{\pi }^{-}$ system is not imposed and the invariant mass of the $\gamma \gamma$ system is between 0.50 and $0.58\mathrm{GeV}/c^2$.

Figure 2

The invariant masses of the (a) $\eta {\pi }^{-}{\pi }^{+}$ and (b) $\eta {\pi }^{\pm }$ final states are shown. The dark shaded histograms show the simulated signal events, the lightly shaded histograms show the simulated $\tau$ background, and the unshaded histograms show the simulated $q\overline{q}$ background. Note that (a) and (b) have two entries per event. All selection criteria are applied. In (b), it is required that the invariant mass of the associated $\eta {\pi }^{-}{\pi }^{+}$ system is between 1.23 and $1.32\mathrm{GeV}/c^2$.

Figure 3

Plot (a) shows the invariant mass of the $\gamma \gamma$ system. Plot (b) shows the invariant mass of the data $\eta {\pi }^{-}{\pi }^{+}$ system. The points represent the data, the solid line is the fit function, and the dashed line shows the background.

Figure 4

Fit to the ${\eta }^{\prime }(958)$ region of the $\eta {\pi }^{-}{\pi }^{+}$ invariant mass spectrum. The fit uses a Gaussian distribution for the peak summed with a linear function for the background. The events are tagged with muons or electrons and all selection criteria have been applied.