Observation of $b\to d\gamma$ and Determination of $|V_{td}/V_{ts}|$

We report the observation of the flavor-changing neutral current process $b\to d\gamma$ using a sample of $386\times {10}^6$ $B$ meson pairs accumulated by the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. We measure branching fractions for the exclusive modes $B^{-}\to {\rho }^{-}\gamma$, ${\overline{B}}^0\to {\rho }^0\gamma$, and ${\overline{B}}^0\to \omega \gamma$. Assuming that these three modes are related by isospin, we find $\mathcal{B}\mathbf{(}\overline{B}\to (\rho ,\omega )\gamma \mathbf{)}=\mathbf{(}{1.32}_{-0.31}^{+0.34}(\mathrm{stat}{)}_{-0.09}^{+0.10}(\mathrm{syst})\mathbf{)}\times {10}^{-6}$ with a significance of $5.1\sigma$. This result is used to determine the ratio of Cabibbo-Kobayashi-Maskawa matrix elements $|V_{td}/V_{ts}|$ to be ${0.199}_{-0.025}^{+0.026}(\exp {)}_{-0.015}^{+0.018}(\mathrm{theor})$.

Figure 1

(a) Loop diagram for $b\to d\gamma$ and (b) annihilation diagram, which contributes only to $B^{-}\to {\rho }^{-}\gamma$.

Figure 2

Projections of the fit results to $M_{\mathrm{bc}}$ (in the region $-0.10\mathrm{GeV}<\Delta E<0.08\mathrm{GeV}$) and $\Delta E$ (in the region $5.273\mathrm{GeV}/c^2<M_{\mathrm{bc}}<5.285\mathrm{GeV}/c^2$) for the individual and simultaneous fits. Curves show the signal (dashed line), continuum (dotted line), $\overline{B}\to {\overline{K}}^{*}\gamma$ (dot-dashed line), other $B$ decay background (dot-dot-dashed line) components, and the total fit result (solid line).