Measurement of branching fractions and rate asymmetries in the rare decays $B\to K^{(*)}{\ell }^{+}{\ell }^{-}$

In a sample of $471\times {10}^6$ $B\overline{B}$ events collected with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ collider we study the rare decays $B\to K^{(*)}{\ell }^{+}{\ell }^{-}$, where ${\ell }^{+}{\ell }^{-}$ is either $e^{+}{e}^{-}$ or ${\mu }^{+}{\mu }^{-}$. We report results on partial branching fractions and isospin asymmetries in seven bins of dilepton mass-squared. We further present $CP$ and lepton-flavor asymmetries for dilepton masses below and above the $J/\psi$ resonance. We find no evidence for $CP$ or lepton-flavor violation. The partial branching fractions and isospin asymmetries are consistent with the Standard Model predictions and with results from other experiments.

Figure 1

Lowest-order Feynman diagrams for $b\to s{\ell }^{+}{\ell }^{-}$.

Figure 2

Examples of new physics loop contributions to $b\to s{\ell }^{+}{\ell }^{-}$: (a) charged Higgs ($H^{-}$); (b) squark $(\tilde{t},\tilde{c},\tilde{u})$ and chargino (${\chi }^{-}$); (c) squark $(\tilde{b},\tilde{s},\tilde{d})$ and gluino ($\tilde{g}$) or neutralino (${\chi }^0$).

Figure 3

The (a) $B\overline{B}$ and (b) $q\overline{q}$ $e^{+}{e}^{-}$ BDT outputs for simulated events in the low $s$ region. Shown are the distributions for $B\overline{B}$ background (red dashed line), $q\overline{q}$ background (red dotted line), and signal (blue solid line) event samples, normalized to unit area.

Figure 4

Expected statistical significance of the number of fitted signal events as a function of BDT interval lower bounds for $B^0\to K^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ in bin $s_2$. The star marks the optimized pair of lower bounds.

Figure 5

The $m_{\mathrm{ES}}$ spectrum in bin $s_4$ for all $K{\ell }^{+}{\ell }^{-}$ modes combined showing data (points with error bars), the total fit (blue solid line), signal component (black short-dashed line), combinatorial background (magenta long-dashed line), hadrons misidentified as muons (green dash-dotted line), and the sum of cross-feed and peaking components (red dotted line).

Figure 6

The (a) $m_{\mathrm{ES}}$ and (b) $m_{K\pi }$ mass spectra in bin $s_1$ for all four $K^{*}{\ell }^{+}{\ell }^{-}$ modes combined showing data (points with error bars), the total fit (blue solid lines), signal component (black short-dashed lines), combinatorial background (magenta long-dashed lines), hadrons misidentified as muons (green dash-dotted lines), and the sum of cross-feed and peaking components (red dotted lines).

Figure 7

Partial branching fractions for the (a) $K{\ell }^{+}{\ell }^{-}$ and (b) $K^{*}{\ell }^{+}{\ell }^{-}$ modes as a function of $s$ showing BABAR measurements (red triangles), Belle measurements [27] (open squares), CDF measurements [28] (blue solid squares), and the SM prediction from the Ali et al. model [5] with $B\to K^{(*)}$ form factors [31] (magenta dashed lines). The magenta solid lines show the theory uncertainties. The vertical yellow shaded bands show the vetoed $s$ regions around the $J/\psi$ and $\psi (2S)$.

Figure 8

Total branching fractions for the $K{\ell }^{+}{\ell }^{-}$ and $K^{*}{\ell }^{+}{\ell }^{-}$ modes (red triangles) compared with Belle [27] (open squares) and CDF [28] (blue solid squares) measurements and with predictions from the Ali et al. [5] (light gray bands), and Zhong, Wu, and Wang [6] (dark gray bands) models.

Figure 9

(a),(c) $m_{\mathrm{ES}}$ and (b),(d) $m_{K\pi }$ fits for ${\mathcal{A}}_{CP}$ in the (a),(b) $\overline{B}$ and (c),(d) $B$ low $s$ region for all four $K^{*}{\ell }^{+}{\ell }^{-}$ modes combined. Data (points with error bars) are shown together with total fit (blue solid lines), combinatorial background (magenta long-dashed lines), signal (black short-dashed lines), hadronic background (green dash-dotted lines), and the sum of cross-feed and peaking background (red dotted lines).

Figure 10

$CP$ asymmetries ${\mathcal{A}}_{CP}$ for $K{\ell }^{+}{\ell }^{-}$ modes (red solid triangles) and $K^{*}{\ell }^{+}{\ell }^{-}$ modes (red open circles) as a function of $s$. The vertical yellow shaded bands show the vetoed $s$ regions around the $J/\psi$ and $\psi (2S)$.

Figure 11

$m_{\mathrm{ES}}$ fits for ${\mathcal{R}}_K$ in the (a) $K{e}^{+}{e}^{-}$ and (b) $K{\mu }^{+}{\mu }^{-}$ modes in the high $s$ region. Data (points with error bars) are shown together with total fit (blue solid lines), combinatorial background (magenta long-dashed lines), signal (black short-dashed lines), hadronic background (green dash-dotted lines), and the sum of cross-feed and peaking background (red dotted lines).

Figure 12

Lepton-flavor ratios ${\mathcal{R}}_{K^{(*)}}$ for the $K{\ell }^{+}{\ell }^{-}$ (red solid triangles) and $K^{*}{\ell }^{+}{\ell }^{-}$ modes (red open circles) as a function of $s$. The vertical yellow shaded bands show the vetoed $s$ regions around the $J/\psi$ and $\psi (2S)$.

Figure 13

The $m_{\mathrm{ES}}$ and $m_{K\pi }$ fit projections for the (a),(b) $K^{*+}{\ell }^{+}{\ell }^{-}$ and (c),(d) $K^{*0}{\ell }^{+}{\ell }^{-}$ modes in bin $s_2$. Data (points with error bars) are shown together with total fit (blue solid lines), combinatorial background (magenta long-dashed lines), signal (black short-dashed lines), hadronic background (green dash-dotted lines), and the sum of cross-feed and peaking background (red dotted lines).

Figure 14

Isospin asymmetry ${\mathcal{A}}_I$ for the (a) $K{\ell }^{+}{\ell }^{-}$ and (b) $K^{*}{\ell }^{+}{\ell }^{-}$ modes as a function of $s$ (red triangles), in comparison to results from Belle [27] (open squares). The vertical yellow shaded bands show the vetoed $s$ regions around the $J/\psi$ and $\psi (2S)$.