Inclusive and exclusive measurements of $B$ decays to ${\chi }_{c1}$ and ${\chi }_{c2}$ at Belle

We report inclusive and exclusive measurements for ${\chi }_{c1}$ and ${\chi }_{c2}$ production in $B$ decays. We measure $\mathcal{B}(B\to {\chi }_{c1}X)=(3.03\pm 0.05(\mathrm{stat})\pm 0.24(\mathrm{syst}))\times {10}^{-3}$ and $\mathcal{B}(B\to {\chi }_{c2}X)=(0.70\pm 0.06(\mathrm{stat})\pm 0.10(\mathrm{syst}))\times {10}^{-3}$. For the first time, ${\chi }_{c2}$ production in exclusive $B$ decays in the modes $B^0\to {\chi }_{c2}{\pi }^{-}{K}^{+}$ and $B^{+}\to {\chi }_{c2}{\pi }^{+}{\pi }^{-}{K}^{+}$ has been observed, along with first evidence for the $B^{+}\to {\chi }_{c2}{\pi }^{+}{K}_S^0$ decay mode. For ${\chi }_{c1}$ production, we report the first observation in the $B^{+}\to {\chi }_{c1}{\pi }^{+}{\pi }^{-}{K}^{+}$, $B^0\to {\chi }_{c1}{\pi }^{+}{\pi }^{-}{K}_S^0$ and $B^0\to {\chi }_{c1}{\pi }^0{\pi }^{-}{K}^{+}$ decay modes. Using these decay modes, we observe a difference in the production mechanism of ${\chi }_{c2}$ in comparison to ${\chi }_{c1}$ in $B$ decays. In addition, we report searches for $X(3872)$ and ${\chi }_{c1}(2P)$ in the $B^{+}\to ({\chi }_{c1}{\pi }^{+}{\pi }^{-})K^{+}$ decay mode. The reported results use $772\times {10}^6$ $B\overline{B}$ events collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider.

Figure 1

$M_{J/\psi \gamma }$ distribution of the $B\to {\chi }_{cJ}(\to J/\psi (\to {\ell }^{+}{\ell }^{-})\gamma )X$ decays in data. The curves show the signal (cyan dash dotted for ${\chi }_{c1}$ and red dashed for ${\chi }_{c2}$) and the background component (green dash double dotted for combinatorial) as well as the overall fit (blue solid). The lower plot shows the pull of the residuals with respect to the fit.

Figure 2

Differential branching fractions $D\mathcal{B}(B\to {\chi }_{c1}X)$ with cyan circles (•) and $D\mathcal{B}(B\to {\chi }_{c2}X)$ with red triangles ($▾$) in each bin of $p_{{\chi }_{c\mathrm{J}}}^{*}$ extracted from the maximum likelihood fits performed with the $\mathrm{\Delta }M$ distribution of the data sample for $B\to {\chi }_{cJ}(\to J/\psi \gamma )X$ after continuum suppression but without feed down subtraction. The ${\psi }^{\prime }$ feed down component (estimated from the MC simulation using ${\psi }^{\prime }$ momentum distribution presented in Ref. [3]) is shown by the blue dash-dotted (magenta dotted) line for ${\chi }_{c1}$ (${\chi }_{c2}$). The uncertainties in these plots are statistical only.

Figure 3

$\mathrm{\Delta }E$ distribution for the (a) $B^0\to {\chi }_{c1}{\pi }^{-}{K}^{+}$, (b) $B^0\to {\chi }_{c2}{\pi }^{-}{K}^{+}$, (c) $B^{+}\to {\chi }_{c1}{\pi }^{+}{K}_S^0$, (d) $B^{+}\to {\chi }_{c2}{\pi }^{+}{K}_S^0$, (e) $B^{+}\to {\chi }_{c1}{\pi }^0{K}^{+}$, and (f) $B^{+}\to {\chi }_{c2}{\pi }^0{K}^{+}$ decay modes. The curves show the signal (red dashed), the peaking background (magenta dash dotted) and the background component (green dotted for combinatorial) as well as the overall fit (blue solid).

Figure 4

Background subtracted efficiency corrected ${}_S\mathcal{P}lot$ $M_{K\pi }$ and $M_{{\chi }_{cJ}\pi }$ distributions for the (a–b) $B^0\to {\chi }_{c1}{\pi }^{-}{K}^{+}$, (c–d) $B^0\to {\chi }_{c2}{\pi }^{-}{K}^{+}$, (e–f) $B^{+}\to {\chi }_{c1}{\pi }^{+}{K}_S^0$, (g–h) $B^{+}\to {\chi }_{c2}{\pi }^{+}{K}_S^0$ and (i–j) $B^{+}\to {\chi }_{c1}{\pi }^0{K}^{+}$ decay modes.

Figure 5

$\mathrm{\Delta }E$ distributions for the (a) $B^{+}\to {\chi }_{c1}{\pi }^{+}{\pi }^{-}{K}^{+}$, (b) $B^{+}\to {\chi }_{c2}{\pi }^{+}{\pi }^{-}{K}^{+}$, (c) $B^0\to {\chi }_{c1}{\pi }^{+}{\pi }^{-}{K}_S^0$, (d) $B^0\to {\chi }_{c2}{\pi }^{+}{\pi }^{-}{K}_S^0$, (e) $B^0\to {\chi }_{c1}{\pi }^0{\pi }^{-}{K}^{+}$ and (f) $B^0\to {\chi }_{c2}{\pi }^0{\pi }^{-}{K}^{+}$ decay modes. The curves show the signal (red dashed), peaking background (magenta dash dotted) and background component (green dotted for combinatorial) as well as the overall fit (blue solid).

Figure 6

Background subtracted efficiency corrected ${}_S\mathcal{P}lot$ (a) $M_{{\chi }_{c1}{\pi }^{+}{\pi }^{-}}$, (b) $M_{{\chi }_{c1}{\pi }^{\pm }}$, (c) $M_{{\chi }_{c2}{\pi }^{+}{\pi }^{-}}$ and (d) $M_{{\chi }_{c2}{\pi }^{\pm }}$ distributions for the $B^{+}\to {\chi }_{cJ}{\pi }^{+}{\pi }^{-}{K}^{+}$ decay modes.

Figure 7

Background subtracted efficiency corrected ${}_S\mathcal{P}lot$ (a and d) $M_{K^{+}{\pi }^{+}{\pi }^{-}}$, (b and e) $M_{K^{+}{\pi }^{-}}$ and (c and f) $M_{{\pi }^{+}{\pi }^{-}}$ distributions for $B^{+}\to {\chi }_{c1}{\pi }^{+}{\pi }^{-}{K}^{+}$ decay (upper) and $B^{+}\to {\chi }_{c2}{\pi }^{+}{\pi }^{-}{K}^{+}$ decay (lower), respectively.

Figure 8

The ${\chi }_{c1}{\pi }^{+}{\pi }^{-}$ invariant mass spectrum for $B^{+}\to {\chi }_{c1}{\pi }^{+}{\pi }^{-}{K}^{+}$ candidates. Two vertical red lines show the $\pm 3\sigma$ window to search for $X(3872)\to {\chi }_{c1}{\pi }^{+}{\pi }^{-}$. The curves show the ${\chi }_{c1}(2P)$ signal (red dashed) and the background (green dotted) and the overall fit (blue solid).