Study of the lineshape of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math> decays to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mrow><mml:mo>*</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mi>K</mml:mi></mml:math>
H. Hirata, T. Iijima, Y. Kato, K. Tanida, I. Adachi, J. K. Ahn, H. Aihara, S. Al Said, D. M. Asner, H. Atmacan, T. Aushev, R. Ayad, V. Babu, Sw. Banerjee, P. K. Behera, K. Belous, J. V. Bennett, M. Bessner, V. Bhardwaj, B. Bhuyan, T. Bilka, D. Biswas, A. Bobrov, D. Bodrov, J. Borah, A. Bożek, M. Bračko, P. Branchini, T. E. Browder, A. Budano, M. Campajola, D. Červenkov, M.-C. Chang, P. Chang, B. G. Cheon, K. Chilikin, H.-E. Cho, K. Cho, S.-J. Cho, S.-K. Choi, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, S. Das, G. de Marino, G. De Nardo, G. De Pietro, R. Dhamija, F. Di Capua, J. Dingfelder, Z. Doležal, T. V. Dong, D. Epifanov, T. Ferber, D. Ferlewicz, B. G. Fulsom, V. Gaur, A. Garmash, A. Giri, P. Goldenzweig, E. Graziani, K. Gudkova, C. Hadjivasiliou, S. Halder, T. Hara, K. Hayasaka, H. Hayashii, M. T. Hedges, D. Herrmann, W.-S. Hou, C.-L. Hsu, K. Inami, N. Ipsita, A. Ishikawa, R. Itoh, M. Iwasaki, W. W. Jacobs, E.-J. Jang, S. Jia, Y. Jin, D. Kalita, C. Kiesling, C. H. Kim, D. Y. Kim, K.-H. Kim, Y.-K. Kim, K. Kinoshita, P. Kodyš, T. Konno, A. Korobov, S. Korpar, E. Kovalenko, P. Križan, P. Krokovny, T. Kuhr, R. Kumar, K. Kumara, A. Kuzmin, Y.-J. Kwon
Abstract
We present a study of the $X(3872)$ lineshape in the decay $B\ensuremath{\rightarrow}X(3872)K\ensuremath{\rightarrow}{D}^{0}{\overline{D}}^{*0}K$ using a data sample of $772\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }B\overline{B}$ pairs collected at the $\mathrm{\ensuremath{\Upsilon}}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider. The peak near the threshold in the ${D}^{0}{\overline{D}}^{*0}$ invariant mass spectrum is fitted using a relativistic Breit-Wigner lineshape. We determine the mass and width parameters to be ${m}_{\mathrm{BW}}=3873.7{1}_{\ensuremath{-}0.50}^{+0.56}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.13(\mathrm{syst})\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ and ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{BW}}={5.2}_{\ensuremath{-}1.5}^{+2.2}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.4(\mathrm{syst})\text{ }\text{ }\mathrm{MeV}$, respectively. The branching fraction is found to be $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}X(3872){K}^{+})\ifmmode\times\else\texttimes\fi{}\mathcal{B}(X(3872)\ensuremath{\rightarrow}{D}^{0}{\overline{D}}^{*0})=\phantom{\rule{0ex}{0ex}}(0.9{7}_{\ensuremath{-}0.18}^{+0.21}(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.10(\mathrm{syst}))\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. The signal from ${B}^{0}$ decays is observed for the first time with $5.2\ensuremath{\sigma}$ significance, and the ratio of branching fractions between charged and neutral $B$ decays is measured to be $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}X(3872){K}^{0})/\mathcal{B}({B}^{+}\ensuremath{\rightarrow}X(3872){K}^{+})={1.34}_{\ensuremath{-}0.40}^{+0.47}(\mathrm{stat}{)}_{\ensuremath{-}0.12}^{+0.10}(\mathrm{syst})$. The peak is also studied using a Flatt\'e lineshape. We determine the lower limit on the $D{\overline{D}}^{*}$ 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 ${D}^{0}{\overline{D}}^{*0}$ threshold is equal to $\ensuremath{-}15.11\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}1}$, as measured by LHCb.