D-wave quarkonium levels of theΥfamily

Measurement of the χ b (3P) mass and of the relative rate of χ b1(1P) and χ b2(1P) production

“…The observation in LHCb data of the recently observed χ b (3P ) state [14,15] is also presented. The measurement of its mass and of the mass splitting between the χ bJ (1P ) states (J = 1 and J = 2) provide useful information for testing QCD models [16][17][18].…”

“…The converted photons are reconstructed using e + and e − tracks, allowing a separation of the χ b1 and χ b2 mass peaks, due to the improved energy resolution of converted photons with respect to that of photons identified with the calorimeter. Any contribution from the χ b0 mesons decays is neglected, as their radiative decay rate is expected to be suppressed by an order of magnitude compared to that of the χ b2 meson [17,19].…”

“…Theory predictions vary from 9 to 12 MeV/c 2 [16,17] for ∆m 12 and this parameter is fixed to 10.5 MeV/c 2 . The value of r 12 is fixed based on theoretical predictions [17] and our experimental measurement. It can be expressed as the product of the ratio of branching fractions to Υ γ and of the ratio of production cross-sections of the χ b2 (3P ) and χ b1 (3P ) states.…”

The heavy hadron spectrum

“…They depend on the functional form of the spindependent potentials and on the expectation value of the spin and orbital angular momentum operators of equation 26 for a particular state. To calculate these the following equations are useful (for the last relation see Kwong and Rosner (1988)):…”

“…Three sets of S states and two sets of P states have been seen below this threshold for bb and two sets of S states and one set of P states for cc. Another set of P and two sets of D states are expected for bb , Kwong and Rosner (1988)). The states below threshold are very narrow since the Zweig-allowed decay to heavy-light states (see Fig.…”