Systematic study of the experimental measurements on ratios of different Υ states
The world data on yields and ratios of different $\ensuremath{\Upsilon}$ states created in hadron collisions at $\sqrt{s}=19\text{--}8000$ GeV are examined in a systematic way. We derive that the ratios of $\ensuremath{\Upsilon}(2S)/\ensuremath{\Upsilon}(1S)$ and $\ensuremath{\Upsilon}(3S)/\ensuremath{\Upsilon}(1S)$ are $0.290\ifmmode\pm\else\textpm\fi{}0.007(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}0.014(\mathrm{syst}.)$ and $0.131\ifmmode\pm\else\textpm\fi{}0.005(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}0.003(\mathrm{syst}.)$, respectively, for $p+p$ collisions at $\sqrt{s}=200$ GeV. A small energy dependence of these ratios is observed within the broad collision energies. In addition, the rapidity, transverse momentum, and transverse mass dependence of these ratios are also reported.