Study of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi><mml:mi>γ</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>γ</mml:mi><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:math> at Belle
X. L. Wang, B. S. Gao, W. J. Zhu, I. Adachi, H. Aihara, S. Al Said, D. M. Asner, H. Atmacan, V. Aulchenko, T. Aushev, R. Ayad, V. Babu, S. Bahinipati, P. K. Behera, V. Bhardwaj, B. Bhuyan, T. Bilka, J. P. Biswal, A. Bobrov, G. Bonvicini, A. Bożek, M. Bračko, M. Campajola, D. Červenkov, M.-C. Chang, V. Chekelian, A. Chen, B. G. Cheon, K. Chilikin, H. E. Cho, K. Cho, S.-K. Choi, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, S. Das, G. De Nardo, R. Dhamija, F. Di Capua, Z. Doležal, T. V. Dong, S. Eidelman, T. Ferber, D. Ferlewicz, A. Frey, B. G. Fulsom, R. B. Garg, V. Gaur, N. Gabyshev, A. Garmash, A. Giri, P. Goldenzweig, B. Golob, C. Hadjivasiliou, T. Hara, O. Hartbrich, K. Hayasaka, H. Hayashii, M. T. Hedges, W.-S. Hou, C.-L. Hsu, T. Iijima, K. Inami, A. Ishikawa, R. Itoh, M. Iwasaki, M. Iwasaki, W. W. Jacobs, S. Jia, Y. Jin, C. Joo, K. K. Joo, J. Kahn, K. H. Kang, T. Kawasaki, C. Kiesling, C. H. Kim, D. Y. Kim, S. H. Kim, Y.-K. Kim, P. Kodyš, T. Konno, A. Korobov, S. Korpar, E. Kovalenko, P. Križan, R. Kroeger, P. Krokovny, R. Kulasiri, M. Kumar, R. Kumar, K. Kumara, A. Kuzmin, Y.-J. Kwon, K. Lalwani, J. S. Lange, I. S. Lee, S. C. Lee, P. Lewis
Abstract
Using $980\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data at and around the $\mathrm{\ensuremath{\Upsilon}}(nS)$ ($n=1$, 2, 3, 4, 5) resonances collected with the Belle detector at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider, the two-photon process $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\psi}(2S)$ is studied from the threshold to 4.2 GeV for the first time. Two structures are seen in the invariant mass distribution of $\ensuremath{\gamma}\ensuremath{\psi}(2S)$: one at ${M}_{{R}_{1}}=3922.4\ifmmode\pm\else\textpm\fi{}6.5\ifmmode\pm\else\textpm\fi{}2.0\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ with a width of ${\mathrm{\ensuremath{\Gamma}}}_{{R}_{1}}=22\ifmmode\pm\else\textpm\fi{}17\ifmmode\pm\else\textpm\fi{}4\text{ }\text{ }\mathrm{MeV}$, and another at ${M}_{{R}_{2}}=4014.3\ifmmode\pm\else\textpm\fi{}4.0\ifmmode\pm\else\textpm\fi{}1.5\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ with a width of ${\mathrm{\ensuremath{\Gamma}}}_{{R}_{2}}=4\ifmmode\pm\else\textpm\fi{}11\ifmmode\pm\else\textpm\fi{}6\text{ }\text{ }\mathrm{MeV}$; the signals are parametrized with the incoherent sum of two Breit-Wigner functions. The first structure is consistent with the $X(3915)$ or the ${\ensuremath{\chi}}_{c2}(3930)$, and the local statistical significance is determined to be $3.1\ensuremath{\sigma}$ with the systematic uncertainties included. The second matches none of the known charmonium or charmoniumlike states, and its global significance is determined to be $2.8\ensuremath{\sigma}$ including the look-elsewhere effect. The production rates are ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}\ensuremath{\gamma}}\mathcal{B}({R}_{1}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\psi}(2S))=9.8\ifmmode\pm\else\textpm\fi{}3.6\ifmmode\pm\else\textpm\fi{}1.3\text{ }\text{ }\mathrm{eV}$ assuming $({J}^{PC},|\ensuremath{\lambda}|)=({0}^{++},0)$ or $2.0\ifmmode\pm\else\textpm\fi{}0.7\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{eV}$ with $({2}^{++},2)$ for the first structure and ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\gamma}\ensuremath{\gamma}}\mathcal{B}({R}_{2}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\psi}(2S))=6.2\ifmmode\pm\else\textpm\fi{}2.2\ifmmode\pm\else\textpm\fi{}0.8\text{ }\text{ }\mathrm{eV}$ with $({0}^{++},0)$ or $1.2\ifmmode\pm\else\textpm\fi{}0.4\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{eV}$ with $({2}^{++},2)$ for the second. Here, the first errors are statistical and the second systematic, and $\ensuremath{\lambda}$ is the helicity.