Production of $\mathit{\Upsilon }\left(1\mathit{S}\right)$ Mesons from ${\chi }_b$ Decays in $\mathit{p}\overline{\mathit{p}}$ Collisions at $\sqrt{\mathit{s}}=1.8\mathrm{}\mathrm{TeV}$

We have reconstructed the radiative decays ${\chi }_b\left(1P\right)\to \Upsilon \left(1S\right)\gamma$ and ${\chi }_b\left(2P\right)\to \Upsilon \left(1S\right)\gamma$ in $p\overline{p}$ collisions at $\sqrt{s}=1.8\mathrm{}\mathrm{TeV}$, and measured the fraction of $\Upsilon \left(1S\right)$ mesons that originate from these decays. For $\Upsilon \left(1S\right)$ mesons with $p_T^{\Upsilon }>8.0\mathrm{}\mathrm{GeV}/c$, the fractions that come from ${\chi }_b\left(1P\right)$ and ${\chi }_b\left(2P\right)$ decays are $[27.1\pm 6.9(\mathrm{stat})\pm 4.4(\mathrm{syst}\left)\right]\%$ and $[10.5\pm 4.4(\mathrm{stat})\pm 1.4(\mathrm{syst}\left)\right]\%$, respectively. We have derived the fraction of directly produced $\Upsilon \left(1S\right)$ mesons to be $[50.9\pm 8.2(\mathrm{stat})\pm 9.0(\mathrm{syst}\left)\right]\%$.