β Scribed by Levere C. Hostler; Wayne W. Repko
No coin nor oath required. For personal study only.
The Bethe-Salpeter equation in the form due to Cung ef al. (Ann. Phys. (N. Y.) 98 (1976), 516) is investigated for the special case of instantaneous harmonic oscillator exchange. An exact reduction to a pair of coupled ordinary differential equations for the radial excitations of the 3(J f lb modes is achieved. The equations in the mass zero case are brought to a form which is quite close to Whittaker's equation. This similarity to Whittaker's equation is exploited in a computer study of the level structure as a function of the quark mass. This study covers the region from a highly relativistic spectrum depending only upon J to the nonrelativistic regime where the spectrum depends only upon L. An expression for the leptonic width of a %S, state in terms of the Bethe-Salpeter wave function is derived and applied to the &family. The effect of relativistic corrections is to reduce the predicted value of the leptonic width compared to the value calculated by assuming nonrelativistic kinematics. It is also shown that the relativistic treatment allows a 3O, state to couple directly to a virtual photon.
π SIMILAR VOLUMES
We construct weak axial one-boson exchange currents for the Bethe-Salpeter equation, starting from chiral Lagrangians of the Nβ( 1236)ΟΟa 1 Ο system. The currents fulfill the Ward-Takahashi identities and the matrix element of the full current between the two-body solutions of the Bethe-Salpeter equ