Improved measurements of the branching fractions for $B^0\to {\pi }^{+}{\pi }^{-}$ and $B^0\to K^{+}{\pi }^{-}$, and a search for $B^0\to K^{+}{K}^{-}$

We present measurements of the branching fractions for the charmless two-body decays $B^0\to {\pi }^{+}{\pi }^{-}$ and $B^0\to K^{+}{\pi }^{-}$, and a search for the decay $B^0\to K^{+}{K}^{-}$. We include the effects of final-state radiation from the daughter mesons for the first time, and quote branching fractions for the inclusive processes $B^0\to h^{+}{h}^{\prime -}n\gamma$, where $h$ and $h^{\prime }$ are pions or kaons. The maximum value of the sum of the energies of the $n$ undetected photons, $E_{\gamma }^{\max }$, is mode-dependent. Using a data sample of approximately $227\times {10}^6$ $\mathit{{\rm Y}}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at SLAC, we measure: $\mathcal{B}(B^0\to {\pi }^{+}{\pi }^{-}n\gamma ;E_{\gamma }^{\max }=150\mathrm{MeV})=(5.1\pm 0.4\pm 0.2)\times {10}^{-6}$, $\mathcal{B}(B^0\to K^{+}{\pi }^{-}n\gamma ;E_{\gamma }^{\max }=105\mathrm{MeV})=(18.1\pm 0.6\pm 0.6)\times {10}^{-6}$, $\mathcal{B}(B^0\to K^{+}{K}^{-}n\gamma ;E_{\gamma }^{\max }=59\mathrm{MeV})<0.5\times {10}^{-6}(90\%\mathrm{\text{confidence level}})$, where the first uncertainty is statistical and the second is systematic. Theoretical calculations can be used to extrapolate from the above measurements the nonradiative branching fractions, ${\mathcal{B}}^0$. Using one such calculation, we find: ${\mathcal{B}}^0(B^0\to {\pi }^{+}{\pi }^{-})=(5.5\pm 0.4\pm 0.3)\times {10}^{-6}$, ${\mathcal{B}}^0(B^0\to K^{+}{\pi }^{-})=(19.1\pm 0.6\pm 0.6)\times {10}^{-6}$, ${\mathcal{B}}^0(B^0\to K^{+}{K}^{-})<0.5\times {10}^{-6}(90\%\mathrm{\text{confidence level}})$. Meaningful comparison between theory and experiment, as well as combination of measurements from different experiments, can be performed only in terms of these nonradiative quantities.

Figure 1

Data distributions (points with error bars) of $m_{\mathrm{ES}}$, $\Delta E$, and $\mathcal{F}$ for signal ${\pi }^{+}{\pi }^{-}$ (a,b,c), signal $K^{+}{\pi }^{-}$ (d,e,f) and background for the three channels (g,h,i), using the weighting technique described in the text. Solid curves represent the corresponding PDFs used in the fit. The distribution of $\Delta E$ for signal $K^{+}{\pi }^{-}$ events is shifted due to the assignment of the pion mass for all tracks.

Figure 2

(Color online) Distribution of the likelihood ratio ${\mathcal{L}}_S/\sum _{}^{}{\mathcal{L}}_i$, where ${\mathcal{L}}_S$ is the likelihood for each event to be a signal ${\pi }^{+}{\pi }^{-}$ (left), $K^{+}{\pi }^{-}$ (middle), or $K^{+}{K}^{-}$ (right) event. The points with error bars show the distribution obtained on the fitted data sample, while the histograms show the distributions obtained by generating signal (dark shaded, red) and background (light shaded, yellow) events directly from the PDFs.