Comment on “Valence QCD: Connecting QCD to the quark model”

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 61, Issue 11, 2000, Pages

  Isgur, Nathan ^a  

^a THOMAS JEFFERSON NATIONAL ACCELERATOR FACILITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750659904     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.61.118501     Document Type: Article

References (15)

1. K. F. Liu, Phys. Rev. D 59, 112001 (1999).
2. It should be noted that the time-ordered graphs of VQCD are not the same as those of the normal Feynman propagator. Among other differences related to the projector (Formula presented), the VQCD dispersion relation is (Formula presented) versus the relativistic (Formula presented) or the nonrelativistic (Formula presented).
3. The one-gluon-exchange-perturbed quark potential model was introduced in A. De Rújula, H. Georgi, and S. L. Glashow, Phys. Rev. D 12, 147 (1975). It was extensively applied to baryons in Refs. 4.
4. For a general review of the Isgur-Karl model and references, see N. Isgur, in Modern Topics in Electron Scattering, edited by B. Frois and I. Sick (World Scientific, Singapore, 1991), p. 2.
5. The physical (Formula presented) splitting is about 300 MeV. The authors explain that most of the deviation of their QQCD results from 300 MeV comes from not being in the infinite volume and continuum limits. See, for example, F. Butler, H. Chen, J. Sexton, A. Vaccarino, and D. Weingarten, Phys. Rev. Lett. 70, 2849 (1993)
6. F. ButlerH. ChenJ. SextonA. VaccarinoD. WeingartenNucl. Phys. B430, 179 (1994). Of course some of the discrepancy may also be due to quenching. In any case, these relatively minor differences do not affect the issue being addressed here.
7. Reference 1 also gives results for the (Formula presented). The scalar sector is so controversial and so poorly understood experimentally that I have focused on the (Formula presented), but no conclusion I have drawn depends on this selection.
8. A poor spectrum does not always lead to a poor description of the ground state. For example, the ground state of the Coulomb-plus-linear potential problem can in certain circumstances be dominated by the Coulomb region so that its gross properties are independent of the string tension, leaving only short distance effects like the hyperfine interaction sensitive to the slope of the linear potential.
9. N. Isgur and M.B. Wise, Phys. Lett. B 232, 113 (1989)
10. Phys. Lett. BN. IsgurM.B. Wise237, 527 (1990).For an overview of heavy quark symmetry, see N. Isgur and M.B. Wise, in B Decays, edited by S. Stone (World Scientific, Singapore, 1991), p. 158; and in Heavy Flavors, edited by A.J. Buras and M. Lindner (World Scientific, Singapore, 1992), p. 234.
11. Sophisticated calculations in a variety of models now exist, but for an early example in the naive harmonic oscillator approximation where one obtains the simple result (Formula presented), see N. Isgur, in The New Aspects of Subnuclear Physics, edited by A. Zichichi (Plenum, New York, 1980), p. 107.
12. S. Okubo, Phys. Lett. 5, 165 (1963)
13. S. OkuboPhys. Rev. D 16, 2336 (1977);G. Zweig, CERN Report No. 8419 TH 412, 1964;reprinted in Developments in the Quark Theory of Hadrons, edited by D. B. Lichtenberg and S. P. Rosen (Hadronic, Massachusetts, 1980)
14. J. Iizuka, K. Okada, and O. Shito, Prog. Theor. Phys. 35, 1061 (1966)
15. J. Iizuka, Prog. Theor. Phys. Suppl. 37-38, 21 (1966).