Measurements of branching fractions, rate asymmetries, and angular distributions in the rare decays $B\to K{\ell }^{+}{\ell }^{-}$ and $B\to K^{*}{\ell }^{+}{\ell }^{-}$

We present measurements of the flavor-changing neutral current decays $B\to K{\ell }^{+}{\ell }^{-}$ and $B\to K^{*}{\ell }^{+}{\ell }^{-}$, where ${\ell }^{+}{\ell }^{-}$ is either an $e^{+}{e}^{-}$ or ${\mu }^{+}{\mu }^{-}$ pair. The data sample comprises $229\times {10}^6{\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ storage ring. Flavor-changing neutral current decays are highly suppressed in the standard model and their predicted properties could be significantly modified by new physics at the electroweak scale. We measure the branching fractions $\mathcal{B}(B\to K{\ell }^{+}{\ell }^{-})=(0.34\pm 0.07\pm 0.02)\times {10}^{-6}$, $\mathcal{B}(B\to K^{*}{\ell }^{+}{\ell }^{-})=({0.78}_{-0.17}^{+0.19}\pm 0.11)\times {10}^{-6}$, the direct $CP$ asymmetries of these decays, and the relative abundances of decays to electrons and muons. For two regions in ${\ell }^{+}{\ell }^{-}$ mass, above and below $m_{J/\psi }$, we measure partial branching fractions and the forward-backward angular asymmetry of the lepton pair. In these same regions we also measure the $K^{*}$ longitudinal polarization in $B\to K^{*}{\ell }^{+}{\ell }^{-}$ decays. Upper limits are obtained for the lepton-flavor-violating decays $B\to Ke\mu$ and $B\to K^{*}e\mu$. All measurements are consistent with standard model expectations.

Figure 1

Examples of standard model Feynman diagrams for the decays $B\to K^{(*)}{\ell }^{+}{\ell }^{-}$. For the photon or $Z$ penguin diagrams on the left, boson emission can occur on any of the $b$, $t$, $c$, $u$, $s$, or $W$ lines.

Figure 2

Simulated distribution of (a) $A_{\mathrm{FB}}$ and (b) $F_L$ for the decay $B\to K^{*}{\ell }^{+}{\ell }^{-}$. The points represent the distributions assuming the SM (solid lines), $C_7^{\mathrm{eff}}=-C_7(\mathrm{SM})$ (dotted lines), $C_9^{\mathrm{eff}}{C}_{10}^{\mathrm{eff}}=-C_9{C}_{10}(\mathrm{SM})$ (dashed lines), and $C_7^{\mathrm{eff}}$, $C_9^{\mathrm{eff}}{C}_{10}^{\mathrm{eff}}=-C_7(\mathrm{SM})$, $-C_9{C}_{10}(\mathrm{SM})$(dot-dashed lines) generated using the form factor model of [27]. In the case of $F_L$, the two solutions with $C_9^{\mathrm{eff}}{C}_{10}^{\mathrm{eff}}=-C_9{C}_{10}(\mathrm{SM})$ are not displayed; they are nearly identical to the two shown.

Figure 3

Predicted distributions of (a) $A_{\mathrm{FB}}(q^2)$ and (b) $F_L(q^2)$ in $B\to K^{*}{\ell }^{+}{\ell }^{-}$ for the two regions of $q^2$ considered. The lines represent the predictions of the SM (solid lines), $C_7^{\mathrm{eff}}=-C_7(\mathrm{SM})$ (dotted lines), $C_9^{\mathrm{eff}}{C}_{10}^{\mathrm{eff}}=-C_9{C}_{10}(\mathrm{SM})$ (dashed lines), and $C_7^{\mathrm{eff}}$, $C_9^{\mathrm{eff}}{C}_{10}^{\mathrm{eff}}=-C_7(\mathrm{SM})$, $-C_9{C}_{10}(\mathrm{SM})$ (dot-dashed lines) with the form factor model of Ref. [27]. In the case of $F_L$, the two solutions with $C_9^{\mathrm{eff}}{C}_{10}^{\mathrm{eff}}=-C_9{C}_{10}(\mathrm{SM})$ are not displayed; they are nearly identical to the two shown.

Figure 4

Charmonium veto regions (a) in the $B^{+}\to K^{+}{e}^{+}{e}^{-}$ channel. The points are simulated $J/\psi$ and $\psi (2S)$ events, with abundance equal to the mean number expected in $208{\mathrm{fb}}^{-1}$. The projections onto (b) $m_{{\ell }^{+}{\ell }^{-}}$ and (c) $\Delta E$ are shown at right, indicating the high density of points at $(m_{{\ell }^{+}{\ell }^{-}},\Delta E)=(m_{\psi },0.0)$. The vertical band corresponds to events where the $J/\psi$ ($\psi (2S)$) and $K^{+}$ come from different $B$ decays. For $\Delta E<0$ it also includes events with misreconstructed $B\to J/\psi K^{*}$, $B\to \psi (2S)K^{*}$, and nonresonant charmonium decays. The slanted band corresponds to events with mismeasured lepton track momentum.

Figure 5

Distribution of (a) the Fisher discriminant and (b) the $B\overline{B}$ likelihood ratio for $B^{+}\to K^{+}{e}^{+}{e}^{-}$ events in the $J/\psi$ veto sample. The points are data; the gray bands are simulated events, with a simulation uncertainty given by the band height. The dark gray portion represents the uncertainty due to simulation statistics, while the additional uncertainty due to the $B\to J/\psi K^{+}$ branching fraction is represented by the light gray band height. Events to the right of the vertical line are selected.

Figure 6

Distributions of the fit variables in $K{\ell }^{+}{\ell }^{-}$ data (points), compared with projections of the combined fit (curves): (a) $m_{\mathrm{ES}}$ distribution after requiring $-0.11<\Delta E<0.05\mathrm{GeV}$ and (b) $\Delta E$ distribution after requiring $|m_{\mathrm{ES}}-m_B|<6.6\mathrm{MeV}/c^2$. The solid curve is the sum of all fit components, including signal; the dashed curve is the sum of all background components.

Figure 7

Distributions of the fit variables in $K^{*}{\ell }^{+}{\ell }^{-}$ data (points), compared with projections of the combined fit (curves): (a) $m_{\mathrm{ES}}$ after requiring $-0.11<\Delta E<0.05\mathrm{GeV}$ and $0.817<m_{K\pi }<0.967\mathrm{GeV}/c^2$, (b) $\Delta E$ after requiring $|m_{\mathrm{ES}}-m_B|<6.6\mathrm{MeV}/c^2$, $0.817<m_{K\pi }<0.967\mathrm{GeV}/c^2$, and (c) $m_{K\pi }$ after requiring $|m_{\mathrm{ES}}-m_B|<6.6\mathrm{MeV}/c^2$ and $-0.11<\Delta E<0.05\mathrm{GeV}$. The solid curve is the sum of all fit components, including signal; the dashed curve is the sum of all background components.

Figure 8

Partial branching fractions in bins of $q^2$ for (a) $B\to K{\ell }^{+}{\ell }^{-}$ and (b) $B\to K^{*}{\ell }^{+}{\ell }^{-}$, normalized to the total measured branching fraction. The points with error bars are data, the lines represent the central values of standard model predictions based on the form factor models of Refs. [26, 27] (solid lines), [10] (dashed lines), and [7, 8] (dot-dashed lines).

Figure 9

(a) $F_L(q^2)$ and (b) $A_{\mathrm{FB}}(q^2)$ in $B\to K^{*}{\ell }^{+}{\ell }^{-}$. The points with error bars are data, with the arrow at low $q^2$ in $A_{\mathrm{FB}}$ indicating the 95% CL allowed region. The lines represent the predictions of the SM (solid lines), $C_7^{\mathrm{eff}}=-C_7(\mathrm{SM})$ (dotted lines), $C_9^{\mathrm{eff}}{C}_{10}^{\mathrm{eff}}=-C_9{C}_{10}(\mathrm{SM})$ (dashed lines), and $C_7^{\mathrm{eff}}$, $C_9^{\mathrm{eff}}{C}_{10}^{\mathrm{eff}}=-C_7(\mathrm{SM})$, $-C_9{C}_{10}(\mathrm{SM})$ (dot-dashed lines) with the form factor model of Ref. [27]. In the case of $F_L$, the two solutions with $C_9^{\mathrm{eff}}{C}_{10}^{\mathrm{eff}}=-C_9{C}_{10}(\mathrm{SM})$ are not displayed; they are nearly identical to the two shown.

Figure 10

Distributions of the fit variables in $Ke\mu$ data (points), compared with projections of the combined fit (curves): (a) $m_{\mathrm{ES}}$ distribution after requiring $-0.11<\Delta E<0.05\mathrm{GeV}$ and (b) $\Delta E$ distribution after requiring $|m_{\mathrm{ES}}-m_B|<6.6\mathrm{MeV}/c^2$. The solid curve is the sum of all fit components, including signal; the dashed curve is the sum of all background components.

Figure 11

Distributions of the fit variables in $K^{*}e\mu$ data (points), compared with projections of the combined fit (curves): (a) $m_{\mathrm{ES}}$ after requiring $-0.11<\Delta E<0.05\mathrm{GeV}$ and $0.817<m_{K\pi }<0.967\mathrm{GeV}/c^2$, (b) $\Delta E$ after requiring $|m_{\mathrm{ES}}-m_B|<6.6\mathrm{MeV}/c^2$, $0.817<m_{K\pi }<0.967\mathrm{GeV}/c^2$, and (c) $m_{K\pi }$ after requiring $|m_{\mathrm{ES}}-m_B|<6.6\mathrm{MeV}/c^2$ and $-0.11<\Delta E<0.05\mathrm{GeV}$. The solid curve is the sum of all fit components, including signal; the dashed curve is the sum of all background components.

Figure 12

Distributions of the fit variable $\cos {\theta }_K$ in $B\to K^{*}{\ell }^{+}{\ell }^{-}$ data (points), compared with projections of the combined fit (curves) after requiring $-0.11<\Delta E<0.05\mathrm{GeV}$, $|m_{\mathrm{ES}}-m_B|<6.6\mathrm{MeV}/c^2$, and $0.817<m_{K\pi }<0.967\mathrm{GeV}/c^2$. The solid curve is the sum of all fit components, the dashed curve is the sum of all background components, and the dot-dashed curve is the signal component. The $q^2$ regions (a) $0.1<q^2<8.41{\mathrm{GeV}}^2/c^4$, (b) $q^2>10.24{\mathrm{GeV}}^2/c^4$, and (c) $q^2>0.1{\mathrm{GeV}}^2/c^4$ are shown.

Figure 13

Distributions of the fit variable $\cos {\theta }^{*}$ in $B^{+}\to K^{+}{\ell }^{+}{\ell }^{-}$ data (points), compared with projections of the combined fit (curves) after requiring $-0.11<\Delta E<0.05\mathrm{GeV}$ and $|m_{\mathrm{ES}}-m_B|<6.6\mathrm{MeV}/c^2$. The solid curve is the sum of all fit components, the dashed curve is the sum of all background components, and the dot-dashed curve is the signal component. The $q^2$ regions (a) $0.1<q^2<8.41{\mathrm{GeV}}^2/c^4$, (b) $q^2>10.24{\mathrm{GeV}}^2/c^4$, and (c) $q^2>0.1{\mathrm{GeV}}^2/c^4$ are shown. The combined fits shown for (a) and (b) are performed by fixing $F_S$ to zero.

Figure 14

Distributions of the fit variable $\cos {\theta }^{*}$ in $B\to K^{*}{\ell }^{+}{\ell }^{-}$ data (points), compared with projections of the combined fit (curves) after requiring $-0.11<\Delta E<0.05\mathrm{GeV}$, $|m_{\mathrm{ES}}-m_B|<6.6\mathrm{MeV}/c^2$, and $0.817<m_{K\pi }<0.967\mathrm{GeV}/c^2$. The solid curve is the sum of all fit components, the dashed curve is the sum of all background components, and the dot-dashed curve is the signal component. The $q^2$ regions (a) $0.1<q^2<8.41{\mathrm{GeV}}^2/c^4$, (b) $q^2>10.24{\mathrm{GeV}}^2/c^4$, and (c) $q^2>0.1{\mathrm{GeV}}^2/c^4$ are shown. The combined fits shown for (a) and (c) are performed by fixing $A_{\mathrm{FB}}$ to its maximal physical value.