Study of $\tau$ Decays to Four-Hadron Final States with Kaons

The rare $\tau$ lepton decays to four explicitly identified hadrons have been studied with the CLEO detector at the Cornell Electron Storage Ring using $(7.56\pm 0.15){\mathrm{fb}}^{-1}$ of data collected near $\sqrt{s}=10.58\mathrm{GeV}$. The first statistically significant measurements of $\mathcal{B}({\tau }^{-}\to K^{-}{\pi }^{+}{\pi }^{-}{\pi }^0{\nu }_{\tau },\mathrm{\text{excluding}}{K}^0)=(7.4\pm 0.8\pm 1.1)\times {10}^{-4}$ and $\mathcal{B}({\tau }^{-}\to K^{-}{K}^{+}{\pi }^{-}{\pi }^0{\nu }_{\tau })=(5.5\pm 1.4\pm 1.2)\times {10}^{-5}$ are presented, including the first observation of the decay ${\tau }^{-}\to K^{-}\omega {\nu }_{\tau }$ with branching fraction, $(4.1\pm 0.6\pm 0.7)\times {10}^{-4}$. We publish the first upper limit for $\mathcal{B}({\tau }^{-}\to K^{-}{K}^{+}{K}^{-}{\pi }^0{\nu }_{\tau })<4.8(6.1)\times {10}^{-6}$ at 90% (95%) confidence level. We measure for the first time the invariant mass distributions, which together with the branching fraction measurements are important ingredients that can be used to extract the standard model parameters, the strange quark mass, and the Cabibbo-Kobayashi-Maskawa element $V_{us}$.

Figure 1

Four-hadron invariant mass spectra for ${\tau }^{-}\to K^{-}{\pi }^{+}{\pi }^{-}{\pi }^0{\nu }_{\tau }(\mathrm{ex}.\omega )$ (a), $K^{-}\omega {\nu }_{\tau }$ (c), and $K^{-}{K}^{+}{\pi }^{-}{\pi }^0{\nu }_{\tau }$ (e) events. The histograms show the expectations, including $\tau$-migration Monte Carlo (dashed) and hadronic (shaded) background events. The dotted histogram in (c) shows the contribution of $K_1(1270)$. The reproduction of the spectra above the $\tau$ mass by the high-mass tagged sample indicates the validity of the hadronic background estimate. The distributions in (b),(d),(f) show the corresponding background- and efficiency-corrected spectra. Data points in (a) below $1.3\mathrm{GeV}/c^2$ are consistent with the background expectation and also below the production threshold in the $K^{-}{a}_1^0$ model, hence are not displayed in (b). Error bars are statistical only; (b),(d),(f) include errors in backgrounds and efficiencies.

Figure 2

Two- and three-hadron invariant mass spectra (a) $K^{-}{\pi }^{+}$, (b) $K^{-}{\pi }^0$, (c) $K^{-}{\pi }^{+}{\pi }^{-}$, (d) ${\pi }^{-}{\pi }^{+}$, (e) ${\pi }^{+}{\pi }^0$, and (f) ${\pi }^{-}{\pi }^0$, in non-$\omega$ resonant ${\tau }^{-}\to K^{-}{\pi }^{+}{\pi }^{-}{\pi }^0{\nu }_{\tau }$ events. The histograms show the expectation including $\tau$-migration Monte Carlo events (dashed) and hadronic background (shaded). Error bars are statistical only.

Figure 3

${\pi }^{+}{\pi }^{-}{\pi }^0$ invariant mass spectrum in ${\tau }^{-}\to K^{-}{\pi }^{+}{\pi }^{-}{\pi }^0{\nu }_{\tau }$ events. The histogram shows the expectation using an equal mixture of $K_1(1400)$ and $K_1(1270)$, including $\tau$-migration Monte Carlo events (dashed) and hadronic background (shaded). Error bars are statistical only.