Measurement of the mass splittings between thebb¯χb,J(1P)states

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Abstract

We present new measurements of photon energies and branching fractions for the radiative transitions $\ensuremath{\Upsilon}(2S)\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\chi}}_{b(J=0,1,2)}(1P).$ The masses of the ${\ensuremath{\chi}}_{b}$ states are determined from the measured radiative photon energies. The ratio of mass splittings between the ${\ensuremath{\chi}}_{b}$ substates, $r\ensuremath{\equiv}{(M}_{J=2}\ensuremath{-}{M}_{J=1}{)/(M}_{J=1}\ensuremath{-}{M}_{J=0}),$ with $M$ the ${\ensuremath{\chi}}_{b}$ mass, provides information on the nature of the $b\overline{b}$ confining potential. We find $r(1P)=0.542\ifmmode\pm\else\textpm\fi{}0.022\ifmmode\pm\else\textpm\fi{}0.024.$ This value is somewhat lower than the previous world average, but more consistent with the theoretical expectation that $r(1P)<r(2P);$ i.e., that this mass splitting ratio is smaller for the ${\ensuremath{\chi}}_{b}(1P)$ states than for the ${\ensuremath{\chi}}_{b}(2P)$ states.

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