Measurement of the mass splittings between the $b\overline{b}{\chi }_{b,J}\mathrm{}\left(1P\right)\mathrm{}$ states

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