Solutions to a gauge-invariant, equal-time two-body wave equation. Light-mass quark-antiquark system

Geffen, D. A.; Suura, H.

doi:10.1103/physrevd.16.3305

Cited by 32 publications

(23 citation statements)

References 15 publications

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“…The existence of that type of confining solutions with vectorlike potentials was already pointed out by Geffen and Suura [55]. In that work, the masslessness of the ground state is ensured by the presence of the short-distance Coulomb-like potential and the adjustment of the corresponding coupling constant.…”

Section: The Breit Approximationmentioning

confidence: 86%

Bound state equation in the Wilson loop approach with minimal surfaces

Jugeau

Sazdjian

2003

Nuclear Physics B

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The large-distance dynamics in quarkonium systems is investigated, in the large N c limit, through the saturation of Wilson loop averages by minimal surfaces. Using a representation for the quark propagator in the presence of the external gluon field based on the use of path-ordered phase factors, a covariant three-dimensional bound state equation of the Breit-Salpeter type is derived, in which the interaction potentials are provided by the energy-momentum vector of the straight segment joining the quark to the antiquark and carrying a constant linear energy density, equal to the string tension. The interaction potentials are confining and reduce to the linear vector potential in the static case and receive, for moving quarks, contributions from the moments of inertia of the straight segment. The self-energy parts of the quark propagators induce spontaneous breakdown of chiral symmetry with a mechanism identical to that of the exchange of one Coulombgluon. In the nonrelativistic limit, long range spin-spin potentials are absent; the moments of inertia of the straight segment provide negative contributions to the spin-orbit potentials going in the opposite direction to those of the pure timelike vector potential. In the ultrarelativistic limit, the mass spectrum displays linear Regge trajectories with slopes in agreement with their classical relationship with the string tension.

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Section: The Breit Approximationmentioning

confidence: 86%

Bound state equation in the Wilson loop approach with minimal surfaces

Jugeau

Sazdjian

2003

Nuclear Physics B

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“…The Conclusions will summarize the main results and describe their possible future applications. We refer to [11][12][13][14][15][16][17][18][19][20] for other important related work in the field.…”

Section: Introductionmentioning

confidence: 99%

Strong ellipticity and spectral properties of chiral bag boundary conditions

Beneventano

Gilkey

Kirsten

et al. 2003

J. Phys. A: Math. Gen.

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“…After a separation of the angular dependence in the rest frame (with m 1 = m 2 ) the radial components F i (r) of the wave function were found [5] to be potentially singular at r = 0 and at E − V (r) = 0. Requiring local normalizability at these points resulted in quantized energy levels and a reasonable spectrum, including linear Regge trajectories.…”

Section: Pos(eps-hep 2009)073mentioning

confidence: 99%

“…Our derivation is valid at leading order in the gauge coupling g, consequently the potential is purely linear. The properties of this equation (with k = 0 and m 1 = m 2 ) was studied phenomenologically [5] using a linear + Coulomb potential (see also [6] and references therein). It was previously seen to follow from stationary phase arguments assuming retarded boundary conditions [7].…”

Section: Pos(eps-hep 2009)073mentioning

confidence: 99%

The Quark Model via an hbar expansion of QCD

Hoyer¹

2010

Proceedings of European Physical Society Europhysics Conference on High Energy Physics — PoS(EPS-HEP 2009)

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I discuss the possibility that the quark model emerges as the lowest order of anh expansion of QCD bound states. In a hamiltonian approach the instantaneous A 0 potential is determined by the field equations separately for each Fock component. These equations allow also a linear potential as a homogeneous solution. Stationarity of the action sets the direction of the ensuing constant electric field to be along the fermion pair separation. States bound by this non-perturbative, linear A 0 potential are analogous to the Born term of standard perturbative expansions of scattering amplitudes, in that they represent the dominant contribution at lowest order inh (no loops) and at O (g) in the potential. The Dirac equation for relativistic fermions bound by an external A 0 potential is most easily derived using retarded boundary conditions. I demonstrate why this boundary condition does not affect the bound state energies at lowest order inh. Translated to physical Feynman boundary conditions the Dirac bound states are a superposition of Fock states with any number of fermionantifermion pairs. Applying this approach to relativistic quark-antiquark states in QCD results in a bound state equation which was previously proposed without derivation and shown to provide a reasonable description of the meson spectrum, including linear Regge trajectories. The equal-time wave functions have unique Lorentz transformation properties, which ensure the correct dependence of the bound state energy on the center-of-mass momentum. This indicates that the solution is exact at the Born level, i.e., at lowest order inh and at O (g) in the QCD interaction.

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Solutions to a gauge-invariant, equal-time two-body wave equation. Light-mass quark-antiquark system

Cited by 32 publications

References 15 publications

Bound state equation in the Wilson loop approach with minimal surfaces

Bound state equation in the Wilson loop approach with minimal surfaces

Strong ellipticity and spectral properties of chiral bag boundary conditions

The Quark Model via an hbar expansion of QCD

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