Measurements of the $\Upsilon(10860)$ and $\Upsilon(11020)$ resonances via $\sigma(e^+e^-\rightarrow\Upsilon(n{\rm S})\pi^+\pi^-)$
We report new measurements of the total cross sections for $e^+e^-\to \Upsilon(n{\rm S})\pi^+\pi^-$ ($n$ = 1, 2, 3) and $e^+e^-\to b\bar b$ from a high-luminosity fine scan of the region $\sqrt{s} = 10.63$-$11.05$ GeV with the Belle detector. We observe that the $\Upsilon(n{\rm S})\pi^+\pi^-$ spectra have little or no non-resonant component and extract from them the masses and widths of $\Upsilon(10860)$ and $\Upsilon(11020)$ and their relative phase. We find $M_{10860}=(10891.1\pm3.2^{+0.6}_{-1.7})$ MeV/$c^2$ and $\Gamma_{10860}=(53.7^{+7.1}_{-5.6}\,^{+1.3}_{-5.4})$ MeV and report first measurements $M_{11020}=(10987.5^{+6.4}_{-2.5}\,^{+9.0}_{-2.1})$ MeV/$c^2$, $\Gamma_{11020}=(61^{+9}_{-19}\,^{+2}_{-20})$ MeV, and $\phi_{\rm 11020}-\phi_{\rm 10860} = (-1.0\pm0.4\,^{+1.4}_{-0.1})$ rad.