Measurement of the $B^0\to {D^{*}}^{-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ branching fraction

Using a sample of $(470.9\pm 2.8)\times 10^{6}B\overline{B}$ pairs, we measure the decay branching fraction $\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})=(7.26\pm 0.11\pm 0.31)\times {10}^{-3}$, where the first uncertainty is statistical and the second is systematic. Our measurement will be helpful in studies of lepton universality by measuring $\mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })$ using ${\tau }^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\overline{\nu }}_{\tau }$ decays, normalized to $\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})$.

Figure 1

The $m_{\mathrm{ES}}$ distribution of $B^0$ candidates for data (points), MC simulations (histograms), and the unbinned extended-maximum-likelihood fit to the data (curves). The MC distributions are shown as stacked histograms. The $B^0\to D^{*-}{D}_s^{+}$ with $D_s^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$ decays are part of the MC signal. The MC signal contribution is normalized such that its stacked histogram has the same integral as the data. The components of the MC simulations and the fit are described in the legend. The $m_{\mathrm{ES}}$ peak of the MC signal is slightly above that of the data. This shift has a negligible effect on the signal yield.

Figure 2

The background-subtracted invariant-mass spectrum of the $3\pi$ system. The indicated mass value of the $a_1^{+}$ is obtained from Ref. [4]. The $B^0\to D^{*-}{D}_s^{+}$, $D_s^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}$ decay, which is removed in the final result, is visible in the spectrum. The spectrum is obtained prior to the efficiency correction. The inset shows the distribution around the $D_s^{+}$ region.

Figure 3

The reconstruction efficiency as a function of $3\pi$ invariant mass using MC-simulated events. The uncertainties are statistical.