The study of ${\hat{I}}^3{\hat{I}}^3\to {\hat{I}}^3\ddot{I}ˆ(2S)$ at Belle

Abstract

Using $980\mathrm{f}{\mathrm{b}}^{-1}$ of data on and around the $\hat{I}\yen (nS)(n=1,2,3,4,5)$ resonances collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider, the two-photon process ${\hat{I}}^3{\hat{I}}^3\to {\hat{I}}^3\ddot{I}ˆ(2S)$ is studied from the threshold to $4.2\mathrm{GeV}$ for the first time. Two structures are seen in the invariant mass distribution of ${\hat{I}}^3\ddot{I}ˆ(2S)$: one at $M_{R_1}=3922.4\pm 6.5\pm 2.0\mathrm{MeV}/c^2$ with a width of $\hat{I}{“}_{R_1}=22\pm 17\pm 4\mathrm{MeV}$, and another at $M_{R_2}=4014.3\pm 4.0\pm 1.5\mathrm{MeV}/c^2$ with a width of $\hat{I}{“}_{R_2}=4\pm 11\pm 6\mathrm{MeV}$; the signals are parametrized with the incoherent sum of two Breit-Wigner functions. The first structure is consistent with the $X(3915)$ or the $\ddot{I}{‡}_{c2}(3930)$, and the local statistical significance is determined to be $3.1\ddot{I}ƒ$ with the systematic uncertainties included. The second matches none of the known charmonium or charmoniumlike states, and its global significance is determined to be $2.8\ddot{I}ƒ$ including the look-elsewhere effect. The production rates are $\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}\mathcal{B}(R_1\to {\hat{I}}^3\ddot{I}ˆ(2S))=9.8\pm 3.6\pm 1.2\mathrm{eV}$ assuming $(J^{PC},|\hat{I}»|)=(0^{++},0)$ or $2.0\pm 0.7\pm 0.2\mathrm{eV}$ with $(2^{++},2)$ for the first structure and $\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}\mathcal{B}(R_2\to {\hat{I}}^3\ddot{I}ˆ(2S))=6.2\pm 2.2\pm 0.8\mathrm{eV}$ with $(0^{++},0)$ or $1.2\pm 0.4\pm 0.2\mathrm{eV}$ with $(2^{++},2)$ for the second one. Here, the first errors are statistical and the second systematic, and $\hat{I}»$ is the helicity.