Measurement of the spectral function for the ${\tau }^{-}\to K^{-}{K}_S{\nu }_{\tau }$ decay

The decay ${\tau }^{-}\to K^{-}{K}_S{\nu }_{\tau }$ has been studied using $430\times {10}^6$ $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ events produced at a center-of-mass energy around 10.6 GeV at the PEP-II collider and studied with the BABAR detector. The mass spectrum of the $K^{-}{K}_S$ system has been measured and the spectral function has been obtained. The measured branching fraction $\mathcal{B}({\tau }^{-}\to K^{-}{K}_S{\nu }_{\tau })=(0.739\pm 0.011(\mathrm{stat})\pm 0.020(\mathrm{syst}))\times {10}^{-3}$ is found to be in agreement with earlier measurements.

Figure 1

Schematic view of the $\tau$ decay chains in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ events selected for this analysis. Lepton $l^{+}$ can be electron or muon.

Figure 2

The $K_S$ candidates decay length distribution for data (points with errors), ${\tau }^{+}{\tau }^{-}$ simulation events (solid histogram), and $\tau$ background simulation (dashed histogram). The vertical line indicates the boundary of the selection condition.

Figure 3

Distributions of the total energy of photons in the event for data (points with errors), ${\tau }^{+}{\tau }^{-}$ and $q\overline{q}$ simulation events (solid histogram), $\tau$ background simulation (empty triangles with errors) and $q\overline{q}$ background simulation (dashed histogram). The vertical line indicates the boundary of the selection condition.

Figure 4

Selection efficiency as a function of the $K^{-}{K}_S$ invariant mass, according to simulation.

Figure 5

Efficiency correction factor for adjusting the simulation PID efficiency to match the efficiency measured on data, as a function of the $K^{-}{K}_S$ mass for signal events.

Figure 6

The ${\pi }^{+}{\pi }^{-}$ mass spectrum for $K_S$ candidates in data (points with errors) and signal simulation (histogram). Between the two vertical lines there is a signal region used in the procedure of non-$K_S$ background subtraction.

Figure 7

The $m_{K^{-}{K}_S}$ spectra for data (points with errors), ${\tau }^{+}{\tau }^{-}$ simulation events (solid histogram), and $\tau$ background simulation (dashed histogram). The non-$K_S$ background is subtracted.

Figure 8

The probabilities ${\epsilon }_s$ and ${\epsilon }_b$ used in Eqs. (6a) and (6b) as functions of the $K^{-}{K}_S$ mass, measured on simulated events.

Figure 9

Two-photon invariant mass spectrum of ${\pi }^0$ candidates in data. The curve corresponds to the fit function, described in text.

Figure 10

Measured $m_{K^{-}{K}_S}$ spectra for signal events (top) and $\tau$ background events with ${\pi }^0$ (bottom) in comparison with the $\tau$ signal (${\tau }_S$) and $\tau$ background (${\tau }_b$) Monte Carlo simulation.

Figure 11

$K^{-}{K}_S$ mass spectra near the end point $M_{K^{-}{K}_S}=m_{\tau }$ for selected data and $q\overline{q}$ simulated events without (top) and with (bottom) a ${\pi }^0$ candidate. The vertical line indicates the $\tau$ mass.

Figure 12

Normalized $K^{-}{K}_S$ invariant mass spectrum for the ${\tau }^{-}\to K^{-}{K}_S{\nu }_{\tau }$ decay measured in this work (filled circles) compared to the CLEO measurement [7] (empty squares). Only statistical uncertainties are shown.

Figure 13

Measured spectral function for the ${\tau }^{-}\to K^{-}{K}_S{\nu }_{\tau }$ decay. Only statistical uncertainties are shown.