Beyond the adiabatic approximation: The impact of thresholds on the hadronic spectrum

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 60, Issue 5, 1999, Pages

  Isgur, Nathan ^a  

^a THOMAS JEFFERSON NATIONAL ACCELERATOR FACILITY   (United States)

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Indexed keywords

EID: 17244374272     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.60.054013     Document Type: Article

References (40)

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7. Lowest order meson loop Feynman graphs can have two distinct topologies at the quark level: those with a closed (Formula presented) loop and those where only the (relativistically) propagating valence lines appear. Both types of graphs, when analyzed in a hadronic basis, have mesons “in the air.” In mesons, the latter class of graphs either correspond to (Formula presented) meson loops (and so are dual to Z graphs) or to direct “s-channel” (Formula presented)-mixing-type OZI violations 2. In baryons, such graphs correspond to a variety of meson loops, but all are dual to Z graphs. Given these dualities, one can imagine that non-closed-(Formula presented)-loop diagrams are subsumed into the valence quark model. We focus here on the pure (Formula presented) loop processes which are not otherwise taken into account in the quark model.
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12. For a review of the adiabatic approximation in the context of the flux tube model [based on N. Isgur and J. Paton, Phys. Rev. D 31, 2910 (1985) and Refs. 12 ]
13. see N. Isgur, in Proceedings of Few Body Problems in Physics, Williamsburg, VA, 1994, AIP Conf. Proc. No. 334 edited by F. Gross, (AIP, New York, 1995), p. 3. For some early discussions of incorporating the nonperturbative effects of (Formula presented) loops (which were all in the context of (Formula presented) spectroscopy and decays)
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16. Phys. Rev. Lett.and E. C. Poggio and H. J. Schnitzer, 41, 1344 (1978). These discussions are all different, and each introduces essential elements of the adiabatic approximation adopted here.
17. The considerations of this paper are trivially extended to mesons (Formula presented) with arbitrary masses (Formula presented) and (Formula presented).
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35. One could instead expand Eq. (14) in (Formula presented) This would lead to a Yukawa-like nonlocality in (Formula presented) which, using a local approximation to this nonlocality and an analogue to Eq. (31), would give an alternative definition of (Formula presented). This version of (Formula presented) would not contain the adiabatic limit as (Formula presented), and so probably converges more slowly than Eq. (35).
36. If the pair creation occurs by creating a gap of classical length (Formula presented) in the flux tube, then (Formula presented). In other models the pair creation might be intrinsically nonlocal (for an example, see Ref. 1); in such cases the definition of (Formula presented) requires that one make a local approximation of the form of Eq. (31) to the model’s actual matrix element (Formula presented).
37. The explicit considerations given here for mesons are trivially extended to baryons and to both meson and baryon hybrids. There is no reason to expect exact equality of the “improved” string tensions in these diverse systems. Indeed, S. Capstick and N. Isgur, Phys. Rev. D 34, 2809 (1986) note that the baryon string tension seems to differ by about 20% from the meson string tension.
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40. For an initial study of the relative importance of threshold and valence effects on spectroscopy, see N. Isgur, Phys. Rev. D 57, 4041 (1998) where the influence of low-lying S-wave thresholds on the (Formula presented) and (Formula presented) heavy quark mesons is considered.