Observations on the potential confinement of a light fermion

Abstract

We consider possible dynamical models for a light fermion confined by a potential field. With the Dirac equation only Lorentz scalar confinement yields normalizable wavefunctions, while with the "no pair" variant of the Dirac equation only Lorentz vector confinement has normal Regge behaviour. A systematic investigation of Regge properties and phenomenological properties is carried out, including calculations of the Isgur-Wise function. We point out that the Isgur-Wise function provides a sensitive test of confinement models.In particular, the slope of the IW function at zero recoil point is found to be ξ ′ (1) ≃ −0.90 for the Dirac equation with scalar confinement, and ξ ′ (1) ≃ −1.20 for the no pair equation with vector confinement. Using heavy-light data alone we argue against scalar confinement.

Quark confinement dynamics

“…We note that this is also the result given by the Dirac equation with scalar confinement [10] in a heavy-light meson and that time component vector confinement gives a Regge slope of…”

“…By (2.1) and (2.7) we then find for a low particle velocity 10) For g = 2, the above equation becomes 11) which is of the same magnitude but opposite sign from the pure Thomas term. Discussing QCD in an electrodynamic context is not unreasonable in this model of quark dynamics given the assumptions we make about the physical fields.…”

“…As demonstrated analytically in [10], scalar confinement with the Salpeter equation does not give the desired linear trajectories.…”

Regge trajectories for the mesons consisting of different quarks

“…For the potential models, the concavity of the Regge trajectories is of cardinal significance because it is related to the choice of the appropriate dynamic equation or the appropriate potential. If the confining potential is linear [102][103][104][105][106][107][108][109][110][111][112][113][114][115][116], the Schrödinger equation produces the convex Regge trajectories while the spinless Salpeter equation [13,117], the Dirac equation [118] and the Klein-Gordon equation [119][120][121][122][123] give the linear Regge trajectories. The QSSE [25,31,101] and the eigenvalue equation for the square mass operator lead to the concave Regge trajectories.…”

Regge trajectories for heavy quarkonia from the quadratic form of the spinless Salpeter-type equation

“…In Ref. [47], the authors show that the Regge trajectories become linear for the Dirac equation with the linear confinement for large orbital angular momenta. The Regge trajectories for the Klein-Gordon equation are considered in Refs.…”