First observation of radiative $B^0\to \varphi K^0\gamma$ decays and measurements of their time-dependent $CP$ violation

We report the first observation of the radiative decay $B^0\to \varphi K^0\gamma$ using a data sample of $772\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We observe a signal of $37\pm 8$ events with a significance of 5.4 standard deviations including systematic uncertainties. The measured branching fraction is $\mathcal{B}(B^0\to \varphi K^0\gamma )=(2.74\pm 0.60\pm 0.32)\times {10}^{-6}$, where the uncertainties are statistical and systematic, respectively. We also report the first measurements of time-dependent $CP$-violation parameters: ${\mathcal{S}}_{\varphi K_S^0\gamma }=+{0.74}_{-1.05}^{+0.72}(\mathrm{stat}{)}_{-0.24}^{+0.10}(\mathrm{syst})$ and ${\mathcal{A}}_{\varphi K_S^0\gamma }=+0.35\pm 0.58(\mathrm{stat}{)}_{-0.10}^{+0.23}(\mathrm{syst})$. Furthermore, we measure $\mathcal{B}(B^{+}\to \varphi K^{+}\gamma )=(2.48\pm 0.30\pm 0.24)\times {10}^{-6}$, ${\mathcal{A}}_{CP}=-0.03\pm 0.11\pm 0.08$, and find that the signal is concentrated in the $M_{\varphi K}$ mass region near threshold.

Figure 1

$\Delta E$ and $M_{\mathrm{bc}}$ projections for $B^{+}\to \varphi K^{+}\gamma$ (upper row) and $B^0\to \varphi K_S^0\gamma$ (lower row). The $\Delta E$ projections include the requirement $M_{\mathrm{bc}}\in [5.27,5.29]\mathrm{GeV}/c^2$, while the $M_{\mathrm{bc}}$ projections require $\Delta E\in [-0.08,0.05]\mathrm{GeV}$. The points with error bars are the data. The curves show the total fit function (solid [red]), total background function (long-dashed black), continuum component (dotted [blue]), the $b\to c$ component (dash-dotted [green]) and the nonresonant component as well as other charmless backgrounds (filled [magenta] histogram).

Figure 2

Background-subtracted and efficiency-corrected $\varphi K$ mass distributions for the charged (left) and neutral (right) modes. The points with error bars represent the data. The yield in each bin is obtained by the fitting procedure described in the text. A three-body phase-space model from MC simulation is shown by the [blue] points without error bars and normalized to the total data signal yield.

Figure 3

$\Delta t$ distributions for $q=+1$ (open circles with error bars) and $q=-1$ (filled circles with error bars) (left) and the raw asymmetry (right) for well-tagged events. The dotted ($q=+1$) and dash-dotted ($q=-1$) curves in the $\Delta t$ plot (left) are the sum of backgrounds while the dashed ($q=+1$) and solid ($q=-1$) curves are the sum of signal and backgrounds. The solid curve in the asymmetry plot (right) shows the result of the UML fit.