Study of the lineshape of $X(3872)$ using $B$ decays to $D^0\overline{D}{}^{\ast 0}K$

Abstract

We present a study of the $X(3872)$ lineshape in the decay $B\to X(3872)K\to D^0\overline{D}{}^{\ast 0}K$ using a data sample of $772\times 10^6$ $B\overline{B}$ pairs collected at the $\hat{I}\yen (4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The peak near the threshold in the $D^0\overline{D}{}^{\ast 0}$ invariant mass spectrum is fitted using a relativistic Breit-Wigner lineshape. We determine the mass and width parameters to be $m=3873.71_{-0.50}^{+0.56}(\mathrm{stat})\pm 0.13(\mathrm{syst})\mathrm{MeV}/c^2$ and $\hat{I}{“}_0=5.2_{-1.5}^{+2.2}(\mathrm{stat})\pm 0.4(\mathrm{syst})\mathrm{MeV}$, respectively. The branching fraction is found to be $\mathcal{B}(B^{+}\to X(3872)K^{+})\times \mathcal{B}(X(3872)\to D^0\overline{D}{}^{\ast 0})=(0.97_{-0.18}^{+0.21}(\mathrm{stat})\pm 0.10(\mathrm{syst}))\times 10^{-4}$. The signal from $B^0$ decays is observed for the first time with $5.2\ddot{I}ƒ$ significance, and the ratio of branching fractions between charged and neutral $B$ decays is measured to be $\mathcal{B}(B^0\to X(3872)K^0)/\mathcal{B}(B^{+}\to X(3872)K^{+})=1.34_{-0.40}^{+0.47}(\mathrm{stat}{)}_{-0.12}^{+0.10}(\mathrm{syst})$. The peak is also studied using a Flatté lineshape. We determine the lower limit on the $D\overline{D}{}^{\ast }$ coupling constant $g$ to be $0.075$ at 95% credibility in the parameter region where the ratio of $g$ to the mass difference from the $D^0\overline{D}{}^{\ast 0}$ threshold is equal to $-15.11{\mathrm{GeV}}^{-1}$, as measured by LHCb.

submitted to Phys. Rev D