Quark-Antiquark states and their radiative transitions in terms of the spectral integral equation: Bottomonia

In the framework of the spectral integral equation, we consider the b b states and their radiative transitions. We reconstruct the b b interaction on the basis of data for the levels of the bottomonium states with J PC = 0−+, 1−−, 0++, 1++, 2++ as well as the data for the radiative transitions γ (3S) → γχbJ(2P) and γ(2S) → γχbJ(1P) with J = 0, 1, 2. We calculate bottomonium levels with the radial quantum numbers n ≤ 6, their wave functions, and corresponding radiative transitions. The ratios Br[χbJ(2P) → γγ(2S)]/Br[χbJ(2P) → γγ(1S)] for J = 0, 1, 2 are found to be in agreement with data. We determine the b b component of the photon wave function using the data for the e + e − annihilation, e + e − → γ(9460), γ(10 023), γ(10 036), γ(10 580), γ(10 865), γ(11 019), and predict partial widths of the two-photon decays ηb0 → γγ, χb0 → γγ, χb2 → γγ for the radial excitation states below the B B threshold (n ≤ 3).