Study of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> meson via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ψ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>S</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msub><mml:mi>h</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> decays at BESIII
M. Ablikim, М. Н. Ачасов, P. Adlarson, S. Ahmed, M. Albrecht, R. Aliberti, A. Amoroso, M. R. An, Q. An, X. H. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, V. Batozskaya, D. Becker, K. Begzsuren, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, J. Bloms, A. Bortone, I. Boyko, R. A. Briere, A. Brueggemann, H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Çetin, J. F. Chang, W. L. Chang, G. Chelkov, Chao Chen, G. Chen, H. S. Chen, M. L. Chen, S. J. Chen, T. Chen, X. R. Chen, X. T. Chen, Y. B. Chen, Z. J. Chen, W. S. Cheng, G. Cibinetto, F. Cossio, J. J. Cui, H. L. Dai, J. P. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, Y. Ding, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, S. X. Du, P. Egorov, Y. L. Fan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, K. Fischer, M. Fritsch, C. D. Fu, Yang Gao, Yang Gao, I. Garzia, P. T. Ge, C. Geng, E. Gersabeck, A. Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, M. H. Gu, C. Y. Guan, A. Q. Guo, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo, A. Guskov
Abstract
Using 448 million $\ensuremath{\psi}(2S)$ events, the spin-singlet $P$-wave charmonium state ${h}_{c}(1^{1}{P}_{1})$ is studied via the $\ensuremath{\psi}(2S)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{h}_{c}$ decay followed by the ${h}_{c}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{c}$ transition. The branching fractions are measured to be ${\mathcal{B}}_{\text{Inc}}(\ensuremath{\psi}(2S)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{h}_{c})\ifmmode\times\else\texttimes\fi{}{\mathcal{B}}_{\text{Tag}}({h}_{c}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{c})=(4.2{2}_{\ensuremath{-}0.26}^{+0.27}\ifmmode\pm\else\textpm\fi{}0.19)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, ${\mathcal{B}}_{\text{Inc}}(\ensuremath{\psi}(2S)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{h}_{c})=(7.32\ifmmode\pm\else\textpm\fi{}0.34\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.41)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, and ${\mathcal{B}}_{\text{Tag}}({h}_{c}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{c})=(57.6{6}_{\ensuremath{-}3.50}^{+3.62}\ifmmode\pm\else\textpm\fi{}0.58)%$, where the uncertainties are statistical and systematic, respectively. The ${h}_{c}(1^{1}{P}_{1})$ mass and width are determined to be $M=(3525.32\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.15)\text{ }\text{ }\mathrm{MeV}/{\mathrm{c}}^{2}$ and $\mathrm{\ensuremath{\Gamma}}=(0.7{8}_{\ensuremath{-}0.24}^{+0.27}\ifmmode\pm\else\textpm\fi{}0.12)\text{ }\text{ }\mathrm{MeV}$. Using the center of gravity mass of the three ${\ensuremath{\chi}}_{cJ}({1}^{3}{P}_{J})$ mesons [$M(\mathrm{c}.\mathrm{o}.\mathrm{g}.)$], the $1P$ hyperfine mass splitting is estimated to be ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{hyp}}=M({h}_{c})\ensuremath{-}M(\mathrm{c}.\mathrm{o}.\mathrm{g}.)=\phantom{\rule{0ex}{0ex}}(0.03\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.15)\text{ }\text{ }\mathrm{MeV}/{\mathrm{c}}^{2}$, which is consistent with the expectation that the $1P$ hyperfine splitting is zero at the lowest order.