Measurement of $\mathcal{B}$ ($B\to X_s\gamma$), the $B\to X_s\gamma$ photon energy spectrum, and the direct $CP$ asymmetry in $B\to X_{s\mathbf{+}d}\gamma$ decays

The photon spectrum in $B\to X_s\gamma$ decay, where $X_s$ is any strange hadronic state, is studied using a data sample of $(382.8\pm 4.2)\times {10}^6$ $e^{+}{e}^{-}\to {\rm Y}(4S)\to B\overline{B}$ events collected by the BABAR experiment at the PEP-II collider. The spectrum is used to measure the branching fraction $\mathcal{B}(B\to X_s\gamma )=(3.21\pm 0.15\pm 0.29\pm 0.08)\times {10}^{-4}$ and the first, second, and third moments $⟨E_{\gamma }⟩=2.267\pm 0.019\pm 0.032\pm 0.003\mathrm{GeV}$, $⟨(E_{\gamma }-⟨E_{\gamma }⟩{)}^2⟩=0.0484\pm 0.0053\pm 0.0077\pm 0.0005{\mathrm{GeV}}^2$, and $⟨(E_{\gamma }-⟨E_{\gamma }⟩{)}^3⟩=-0.0048\pm 0.0011\pm 0.0011\pm 0.0004{\mathrm{GeV}}^3$, for the range $E_{\gamma }>1.8\mathrm{GeV}$, where $E_{\gamma }$ is the photon energy in the $B$-meson rest frame. Results are also presented for narrower $E_{\gamma }$ ranges. In addition, the direct $CP$ asymmetry $A_{CP}(B\to X_{s+d}\gamma )$ is measured to be $0.057\pm 0.063$. The spectrum itself is also unfolded to the $B$-meson rest frame; that is the frame in which theoretical predictions for its shape are made.

Figure 1

The leading order Feynman diagram for the electromagnetic radiative decay of the $b$ quark in the SM.

Figure 2

Estimated signal and background yields vs photon energy in the CM frame based on MC simulation, at two stages of the event selection: (a) after requiring an unvetoed high-energy photon (logarithmic scale); (b) after all selection requirements (linear scale). The three contributions are shown cumulatively. The signal distribution is for a KN model with $m_b=4.65\mathrm{GeV}/c^2$, while the continuum distribution has been scaled as described in Sec. 3.

Figure 3

Lepton distributions from MC simulation, after the photon selection requirements but before applying lepton-tag and NN criteria. Plots (a) and (b) are for electron tags, plots (c) and (d) for muon tags. Plots (a) and (c) show the CM-frame momentum distributions, with vertical lines indicating the minimum selection requirements. Plots (b) and (d) show the cosine of the CM angle between the lepton and the high-energy photon, after applying the momentum criteria; the vertical lines show the minimum requirement on this quantity. The signal (black dots) is from a KN model with $m_b=4.65\mathrm{GeV}/c^2$. The $B\overline{B}$ background (solid blue histogram) and continuum background (dashed red) are from the MC simulations. Each distribution is separately normalized to best illustrate its behavior.

Figure 4

The distribution of the NN output, from MC simulation after the photon selection and lepton-tag requirements, for (a) electron-tagged events and (b) muon-tagged events. The vertical lines show the minimum requirement on this quantity. The signal is from a KN model with $m_b=4.65\mathrm{GeV}/c^2$. The continuum is from the MC simulation. Normalizations are arbitrary.

Figure 5

Combined acceptance and event-selection efficiency vs measured $E_{\gamma }^{*}$ for a KN model with $m_b=4.65\mathrm{GeV}/c^2$. Uncertainties are from MC statistics. Corresponding efficiencies for a kinetic scheme model with parameters set to HFAG world average values are within 1% (relative) of the values plotted.

Figure 6

Fits to spectra of $\gamma \gamma$ combinations per interval of $\gamma \gamma$ mass for ${\pi }^0$ on-resonance data, in bins of $E_{{\pi }^0}^{*}$: (a) 1.4–1.6 GeV, (b) 1.6–1.8 GeV, (c) 1.8–2.0 GeV, (d) 2.0–2.2 GeV, (e) 2.2–2.4 GeV, and (f) 2.4–3.0 GeV. For each bin, the top plot shows the data (points), the total fit (upper curve), and the signal component of the fit (lower curve); the bottom plot shows the residuals, defined as $(\mathrm{\text{data}}-\mathrm{fit})/(\mathrm{\text{data uncertainty}})$. For the first few bins the signal shape does not precisely reproduce the center of the peak; an effect also seen in fits to MC ${\pi }^0$ signal only, but this does not affect the integrated signal yield.

Figure 7

Fits to spectra of $\gamma \gamma$ combinations per interval of $\gamma \gamma$ mass for $\eta$ on-resonance data, in bins of $E_{\eta }^{*}$: (a) 1.5–1.7 GeV, (b) 1.7–1.9 GeV, (c) 1.9–2.2 GeV, and (d) 2.2–2.6 GeV. For each bin, the top plot shows the data (points), the total fit (upper curve), and the signal component of the fit (lower curve); the bottom plot shows the residuals, defined as $(\mathrm{\text{data}}-\mathrm{fit})/(\mathrm{\text{data uncertainty}})$.

Figure 8

Invariant $e^{+}{e}^{-}$ mass distributions for $J/\psi \to e^{+}{e}^{-}$ electron-inefficiency studies. Plots (a) and (b) are for MC samples; plots (c) and (d) are for data samples. Plots (a) and (c) includes all (eClus, eTrk) and (eTrk, eTrk) pairs, while plots (b) and (d) include only the (eClus, eTrk) pairs. Dotted, dashed, and solid curves show, respectively, the $J/\psi$ signal and background components of each fit, and their sum. The numbers of fitted $J/\psi$ signal events are $156327\pm 550$, $313\pm 27$, $35825\pm 281$, and $109\pm 18$ for plots (a), (b), (c), and (d), respectively.

Figure 9

Data/MC correction factors for $\overline{p}$’s in three illustrative intervals of laboratory momentum, vs $x_{\mathrm{EMC}}$ [see Eq. (8)], from $\overline{\Lambda }$ control samples, including the same maximum lateral moment criterion used for $B\to X_s\gamma$ analysis.

Figure 10

$B$-meson semileptonic partial branching fraction vs CM-frame lepton momentum, averaged over $B$ charge states. Top: BABAR measurement [57] (filled black circles) and values in the $B\overline{B}$ MC simulation (open circles). Bottom: data/MC ratios, and results of a second-order polynomial fit from 1.0 to 2.2 GeV. The dashed curves show the $1\sigma$ error band.

Figure 11

The photon spectrum in $347.1{\mathrm{fb}}^{-1}$ of data after background subtraction. The inner error bars are statistical only, while the outer include both statistical and systematic errors in quadrature.

Figure 12

Comparison of data spectrum in reconstructed $E_{\gamma }^{*}$ to the predictions of three models, each normalized for best agreement with the data above 1.8 GeV, based on ${\chi }^2$ (including bin-to-bin correlations). The solid histogram is for a shape function scheme model with $m_b=4.51\mathrm{GeV}$ and ${\mu }_{\pi }^2=0.46{\mathrm{GeV}}^2$, which resembles the data in this range. The dot-dash histogram is for a kinetic scheme model with parameters $m_b=4.60\mathrm{GeV}$ and ${\mu }_{\pi }^2=0.45{\mathrm{GeV}}^2$, close to the HFAG world average. The dotted histogram is for a shape function scheme model with $m_b=4.40\mathrm{GeV}$ and ${\mu }_{\pi }^2=0.52{\mathrm{GeV}}^2$. The minimum values of ${\chi }^2$ are 6.7, 13.4, and 19.6, respectively.

Figure 13

The background-subtracted photon spectrum of Fig. 11 separated into yields for positive (filled circles) and negative (open circles) tagging lepton charges. Errors are statistical only. The dashed vertical lines show the range utilized for the $A_{CP}$ measurement.

Figure 14

The photon spectrum after unfolding the effects of calorimeter resolution and correcting for the selection efficiency and detector acceptance. The inner error is statistical only, the outer includes statistical, systematic, and model-dependence errors added in quadrature. The vertical line shows the boundary between the lower control region and the signal region.

Figure 15

The photon spectrum after unfolding resolution and Doppler smearing, shown as a partial branching fraction ($\Delta \mathcal{B}$, see Table 14 caption). The inner error is statistical only, the outer includes statistical, systematic, and model-dependence errors added in quadrature. Section 11d explains why results above 2.4 GeV are shown in wider bins. The vertical line shows the boundary between the lower control region and the signal region. The curve shows the spectrum in a kinetic scheme model (see text), normalized to the data from 1.8 to 2.8 GeV.

Figure 16

Measurements of $A_{CP}$ ($B\to X_{s+d}\gamma$), with statistical and systematic errors. The three published results, top to bottom, are from Refs. [42], [43], and [32], respectively. The uppermost result is based on a subset of the data used in the current analysis.

Figure 17

The measured branching fraction for this analysis (solid circles) compared to previous measurements for different $E_{\gamma }$ ranges (minimum energies $E_{\gamma }^B$ given on the left axis). The previous measurements are from CLEO (asterisks) [33], Belle (open triangles) [40], and BABAR using the semi-inclusive technique (open squares) [41]. Error bars show total uncertainties.

Figure 18

The shaded area shows the excluded region (at the 95% confidence level) in charged Higgs mass vs $\tan \beta$ for a type-II two-Higgs-doublet model, using the measured value of $\mathcal{B}(B\to X_s\gamma )=(3.31\pm 0.16\pm 0.30\pm 0.10)\times {10}^{-4}$ ($E_{\gamma }^B>1.6\mathrm{GeV}$) from this analysis. This plot is based on predictions in Refs. [15, 63].

Figure 19

The measured first (top) and second (bottom) moments from this analysis (solid circles) compared with the previous measurement for different $E_{\gamma }$ ranges (minimum energies given on the left axis). These previous measurements are CLEO (asterisks) [33], BABAR semi-inclusive (open squares) [41], and Belle (open triangles) [40]. Error bars show total uncertainties.