Measurement of the lepton forward-backward asymmetry in $B\to X_s{\ell }^{+}{\ell }^{-}$ decays with a sum of exclusive modes

We report the first measurement of the lepton forward-backward asymmetry ${\mathcal{A}}_{\mathrm{FB}}$ as a function of the squared four-momentum of the dilepton system, $q^2$, for the electroweak penguin process $B\to X_s{\ell }^{+}{\ell }^{-}$ with a sum of exclusive final states, where $\ell$ is an electron or a muon and $X_s$ is a hadronic recoil system with an $s$ quark. The results are based on a data sample containing $772\times {10}^6$ $B\overline{B}$ pairs recorded at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. ${\mathcal{A}}_{\mathrm{FB}}$ for the inclusive $B\to X_s{\ell }^{+}{\ell }^{-}$ is extrapolated from the sum of 10 exclusive $X_s$ states whose invariant mass is less than $2\mathrm{GeV}/c^2$. For $q^2>10.2{\mathrm{GeV}}^2/c^2$, ${\mathcal{A}}_{\mathrm{FB}}<0$ is excluded at the $2.3\sigma$ level, where $\sigma$ is the standard deviation. For $q^2<4.3{\mathrm{GeV}}^2/c^2$, the result is within $1.8\sigma$ of the standard model theoretical expectation.

Figure 1

Reconstruction efficiency on a plane of $q^2$ and $\cos \theta$ for (a) the electron and (b) the muon channels. The $J/\psi$ and $\psi (2S)$ veto regions are shown as hatched regions.

Figure 2

$M_{\mathrm{bc}}$ distributions in 1st $q^2$ bin for (a) $B\to X_s{e}^{+}{e}^{-}$ candidates with $\cos \theta >0$, (b) $B\to X_s{e}^{+}{e}^{-}$ candidates with $\cos \theta <0$, (c) $B\to X_s{\mu }^{+}{\mu }^{-}$ candidates with $\cos \theta >0$, and (d) $B\to X_s{\mu }^{+}{\mu }^{-}$ candidates with $\cos \theta <0$. The thicker dashed curve (red) shows the sum of the signal and the self cross-feed components. The thinner dashed curve (green) shows the combinatorial background component. The filled histogram (gray) shows the peaking background component. The sums of all components are shown by the solid curve (blue).

Figure 3

$M_{\mathrm{bc}}$ distributions in 2nd $q^2$ bin for (a) $B\to X_s{e}^{+}{e}^{-}$ candidates with $\cos \theta >0$, (b) $B\to X_s{e}^{+}{e}^{-}$ candidates with $\cos \theta <0$, (c) $B\to X_s{\mu }^{+}{\mu }^{-}$ candidates with $\cos \theta >0$, and (d) $B\to X_s{\mu }^{+}{\mu }^{-}$ candidates with $\cos \theta <0$. The thicker dashed curve (red) shows the sum of the signal and the self cross-feed components. The thinner dashed curve (green) shows the combinatorial background component. The filled histogram (gray) shows the peaking background component. The sums of all components are shown by the solid curve (blue).

Figure 4

$M_{\mathrm{bc}}$ distributions in 3rd $q^2$ bin for (a) $B\to X_s{e}^{+}{e}^{-}$ candidates with $\cos \theta >0$, (b) $B\to X_s{e}^{+}{e}^{-}$ candidates with $\cos \theta <0$, (c) $B\to X_s{\mu }^{+}{\mu }^{-}$ candidates with $\cos \theta >0$, and (d) $B\to X_s{\mu }^{+}{\mu }^{-}$ candidates with $\cos \theta <0$. The thicker dashed curve (red) shows the sum of the signal and the self cross-feed components. The thinner dashed curve (green) shows the combinatorial background component. The filled histogram (gray) shows the peaking background component. The sums of all components are shown by the solid curve (blue).

Figure 5

$M_{\mathrm{bc}}$ distributions in 4th $q^2$ bin for (a) $B\to X_s{e}^{+}{e}^{-}$ candidates with $\cos \theta >0$, (b) $B\to X_s{e}^{+}{e}^{-}$ candidates with $\cos \theta <0$, (c) $B\to X_s{\mu }^{+}{\mu }^{-}$ candidates with $\cos \theta >0$, and (d) $B\to X_s{\mu }^{+}{\mu }^{-}$ candidates with $\cos \theta <0$. The thicker dashed curve (red) shows the sum of the signal and the self cross-feed components. The thinner dashed curve (green) shows the combinatorial background component. The filled histogram (gray) shows the peaking background component. The sums of all components are shown by the solid curve (blue).

Figure 6

$M_{\mathrm{bc}}$ distributions in the low-$q^2$ region, $1<q^2<6{\mathrm{GeV}}^2$ for (a) $B\to X_s{e}^{+}{e}^{-}$ candidates with $\cos \theta >0$, (b) $B\to X_s{e}^{+}{e}^{-}$ candidates with $\cos \theta <0$, (c) $B\to X_s{\mu }^{+}{\mu }^{-}$ candidates with $\cos \theta >0$, and (d) $B\to X_s{\mu }^{+}{\mu }^{-}$ candidates with $\cos \theta <0$. The thicker dashed curve (red) shows the sum of the signal and the self cross-feed components. The thinner dashed curve (green) shows the combinatorial background component. The filled histogram (gray) shows the peaking background component. The sums of all components are shown by the solid curve (blue).

Figure 7

Measured ${\mathcal{A}}_{\mathrm{FB}}$ as a function of $q^2$. The curve (black) with the band (red) and dashed boxes (black) represent the SM prediction while filled circles with error bars show the fit results. The $J/\psi$ and $\psi (2\mathrm{S})$ veto regions are shown as teal hatched regions. For the electron channel, the pink shaded regions are added to the veto regions due to the large bremsstrahlung effect. The uncertainty on the SM prediction is estimated by varying the $b$-quark mass ($4.80\pm 0.15\mathrm{GeV}/c^2$), the $s$-quark mass ($0.20\pm 0.10\mathrm{GeV}/c^2$), and the renormalization scale ($\mu =2.5$ and 5 GeV) [4, 7]. The lower edge of the uncertainty is set to zero in the $q^2$ region larger than maximum possible value, which is determined by the masses of the bottom and strange quarks.