arxiv: 2607.04369 · v1 · pith:4K2PX62Z · submitted 2026-07-05 · hep-ex · hep-ph
First measurement of the masses of the Upsilon₁(1D) and Upsilon₃(1D) states and the energy dependence of the cross sections for e^+e^-toUpsilon_J(1D)η and e^+e^-toUpsilon_J(1D)π^+π^-
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We study the processes $e^+e^-\to\Upsilon_J(1D)\eta$ and $e^+e^-\to\Upsilon_J(1D)\pi^+\pi^-$ 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 $\Upsilon$(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 $\sigma_{\rm Born}(e^+e^-\to\Upsilon_J(1D)\eta)$ or $\sigma_{\rm Born}(e^+e^-\to\Upsilon_J(1D)\pi^+\pi^-)$ and ${\cal B}(\Upsilon_J(1D)\to\chi_{b1}\gamma)$ or ${\cal B}(\Upsilon_J(1D)\to\chi_{b2}\gamma)$ for each $\Upsilon_J(1D)$ state. The corresponding branching fractions for $\Upsilon(10860)$ decays are also obtained. The significances of the $\Upsilon_1(1D)$, $\Upsilon_2(1D)$, and $\Upsilon_3(1D)$ signals are 4.8$\sigma$, ${>}10\sigma$, and 3.0$\sigma$, respectively, including systematic uncertainties. The mass for $\Upsilon_2(1D)$ 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 $\Delta m_{12}=m(\Upsilon_2(1D))-m(\Upsilon_1(1D))$ and $\Delta m_{23}=m(\Upsilon_3(1D))-m(\Upsilon_2(1D))$ are $(11.8\pm1.5\pm0.4)$ MeV/$c^2$ and $(7.6\pm2.4\pm0.6)$ MeV/$c^2$, respectively.~We determine the energy dependence of the cross sections for $e^+e^-\to\Upsilon_J(1D)\eta$ and $e^+e^-\to\Upsilon_J(1D)\pi^+\pi^-$ for the $\Upsilon_1(1D)$, $\Upsilon_2(1D)$, and $\Upsilon_3(1D)$ states, combined.
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