First measurement of the masses of the $\hat{I}{\yen }_1(1D)$ and $\hat{I}{\yen }_3(1D)$ states and the energy dependence of the cross sections for $e^{+}{e}^{-}\to \hat{I}{\yen }_J(1D)\hat{I}\cdot$ and $e^{+}{e}^{-}\to \hat{I}{\yen }_J(1D)\ddot{I}{€}^{+}\ddot{I}{€}^{-}$

Abstract

We study the processes $e^{+}{e}^{-}\to \hat{I}{\yen }_J(1D)\hat{I}\cdot$ and $e^{+}{e}^{-}\to \hat{I}{\yen }_J(1D)\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ at center-of-mass energies $\sqrt{s}$=(10.73 -- 11.02) GeV using a $142.5{\mathrm{fb}}^{-1}$ data sample, including 122~fb${}^{-1}$ near the $\hat{I}\yen$(10860) peak ($\sqrt{s}$ = 10.866 GeV), collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. From the peak sample, the products of Born cross section times branching fraction are obtained for $\ddot{I}{ƒ}_{\mathrm{Born}}(e^{+}{e}^{-}\to \hat{I}{\yen }_J(1D)\hat{I}\cdot )$ or $\ddot{I}{ƒ}_{\mathrm{Born}}(e^{+}{e}^{-}\to \hat{I}{\yen }_J(1D)\ddot{I}{€}^{+}\ddot{I}{€}^{-})$ and $\mathcal{B}(\hat{I}{\yen }_J(1D)\to \ddot{I}{‡}_{b1}{\hat{I}}^3)$ or $\mathcal{B}(\hat{I}{\yen }_J(1D)\to \ddot{I}{‡}_{b2}{\hat{I}}^3)$ for each $\hat{I}{\yen }_J(1D)$ state. The corresponding branching fractions for $\hat{I}\yen (10860)$ decays are also obtained. The significances of the $\hat{I}{\yen }_1(1D)$, $\hat{I}{\yen }_2(1D)$, and $\hat{I}{\yen }_3(1D)$ signals are 4.8$\ddot{I}ƒ$, $>10\ddot{I}ƒ$, and 3.0$\ddot{I}ƒ$, respectively, including systematic uncertainties. The mass for $\hat{I}{\yen }_2(1D)$ is measured to be $(10167.0\pm 1.0\pm 0.2)$ MeV/$c^2$, where the first and second uncertainties are statistical and systematic. The mass splittings $\hat{I}”m_{12}=m(\hat{I}{\yen }_2(1D))-m(\hat{I}{\yen }_1(1D))$ and $\hat{I}”m_{23}=m(\hat{I}{\yen }_3(1D))-m(\hat{I}{\yen }_2(1D))$ are $(11.8\pm 1.5\pm 0.4)$ MeV/$c^2$ and $(7.6\pm 2.4\pm 0.6)$ MeV/$c^2$, respectively.~We determine the energy dependence of the cross sections for $e^{+}{e}^{-}\to \hat{I}{\yen }_J(1D)\hat{I}\cdot$ and $e^{+}{e}^{-}\to \hat{I}{\yen }_J(1D)\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ for the $\hat{I}{\yen }_1(1D)$, $\hat{I}{\yen }_2(1D)$, and $\hat{I}{\yen }_3(1D)$ states, combined.

12 pages, 7 figures