Relativistic effects in heavy-quarkonium spectroscopy

Abstract

It is shown that the discrepancy between the measured rate for $'+Xoy and that predicted by nonrelativistic models can be accounted for by ( v / c )~ relativistic corrections. A Breit-Fermi Hamiltonian is used to predict the energy level structure and E 1 transition rates in the charmonium and Y systems. It is obtained from an instantaneous approximation to a Bethe-Salpeter equation whose kernel is composed of Coulomb-gauge gluon exchange and a scalar confining piece. The model accounts for the observed fine and hyperfine structure of the charmonium levels and for the E 1 transition rates. It is used to predict the level structure and E 1 rates in the Y system. It is shown that an extension of Siegert's theorem is valid in the relativistic regime. This result is useful in analyzing E 1 transition-matrix elements.

Strong decays of nonstrangeq3baryons

“…(In the rest frame of B, P z = 0 and the spurious term is automatically absent.) By making the replacement, p λ /m q → −ik 0 λ [16], and the mapping onto the algebraic operators, 2/3 λ m → βD λ,m /X D [4,5], we can write Eq. (10) aŝ…”

Quark model approach to the $\eta$ meson electroproduction on the proton

“…Given the Hamiltonian of the three-quark system described by only two-body interactions [19], the current conservation gives…”

Photon Transitions inΥ(2S)andΥ(3S)Decays

“…However, the rate to the spin zero states appears to be lower: 0.822 ± 0.020 ± 0.063 (0.758 ± 0.019 ± 0.071) for the (J = 0)/(J = 1) 1P (2P ) ratio and 0.814 ± 0.020 ± 0.112 (0.760 ± 0.021 ± 0.087) for the (J = 0)/(J = 2) 1P (2P ) ratio. Suppression of the J = 0 matrix element was predicted by theoretical calculations implementing relativistic corrections [13]- [14].…”