On a systematic derivation of the quark-antiquark potential

Quark confinement dynamics

“…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.…”

“…If the confinement is pure time component vector we substitute (4.14) into (4.6) to obtain (4.15) In the case of scalar confinement we take (4.16) A similar reduction gives (4.17) Finally, the low quark velocity expansion of the Wilson minimal area law provides the effective Hamiltonian implied by QCD [11], (4.18) We observe that our model, scalar confinement, and low quark velocity expansion of the Wilson loop model [11] all have the pure Thomas spin-orbit interaction. The Darwin terms differ but are sensitive to the ordering prescription applied to symmetrize the operators.…”

Nonperturbative Determination of the QCD Potential atO(1/m)

“…[14,15], since the spectral representation of V d (r) consists of the same amplitudes and the energy gaps. We plan to present this result as well as the other velocity-dependent potentials at O(1/m 2 ) in a separate publication.…”

“…Further, by integrating out the scale mv, where v is quark velocity, one arrives at a framework called potential NRQCD (pN-RQCD) [7,8,9,10], where the static potential emerges as the leading-order contribution, followed by relativistic corrections in powers of 1/m. The potential at O(1/m 2 ) contains the leading order spin-dependent corrections [11,12,13] and the velocity-dependent potentials [14,15]. Perturbation theory may be applied to the determination of these potentials to some extent.…”

Running coupling constant and masses in QCD, the meson spectrum

“…[8], if full relativistic kinematics is kept, but the spin dependent terms are neglected, it becomes identical to the potential of the relativistic flux tube model [3].…”