Abstract
We prove that the large angular momentum behaviour of the leading Regge trajectory of a meson (q \(\bar q\)) or a baryon (qqq) can be obtained by minimizing the classical energy of the system for given angular momentum. A two-body quark-antiquark linear potential plus relativistic kinematics produces asymptotically linear Regge trajectories for mesons. For baryons we take either a sum of two-body potentials with half strength or a string of minimum length connecting the quarks, and find in both cases that the favoured configuration is a quark-diquark system and that the baryon and meson trajectories have the same slope. Short-distance singularities of the potential are shown to be unimportant.
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W. Bartel, A.N. Diddens: CERN internal report NP/73-4 (1973); M. Ambrosio et al.: Phys. Lett.115B, 495 (1982); N. Amos et al.: Phys. Lett.128B, 343 (1983)
G.F. Chew, S. Frautschi: Phys. Rev. Lett.7, 394 (1961);8, 41 (1962)
T. Regge: Nuovo Cimento14, 951 (1959);18, 947 (1960)
A. Ahmadzadeh, P.G. Burke, C. Tate: Phys. Rev.131, 1315 (1963); Ya. I. Azimov, A.A. Ansel'm, V.M. Shekter: Soviet Phys. JETP17, 464, 726 (1963)
A. Martin: In: Prespectives in partiles and fields. eds. M. Lévy, J.L. Basdevant, D. Speiser, J. Weyers, M. Jacob, R. Gastmans, p. 559. New York; Plenum, 1985
S. Ono, F. Schöberl: Phys. Lett.188B, 419 (1982)
D.P. Stanley, D. Robson: Phys. Rev.D21, 3180 (1980)
J.S. Kang, H. Schnitzer: Phys. Rev.D12, 841 (1975); J. Dias de Deus, J. Pulido: Z. Phys. C — Particles and Fields9, 255 (1981)
J.L. Basdevant, S. Boukraa: Z. Phys. C — Particles and Fields28, 413 (1985); See also S. Godfrey: Phys. Rev.D31, 2375 (1985). Related, unpublished work, has been done by H. Baacke.
N. Isgur, G. Karl: Phys. Lett.72B, 109 (1977); Phys. Rev.D18, 4187 (1978)
J.M. Richard, P. Taxil: Phys. Lett.128B, 453 (1983); Ann. Phys.150, 267 (1983)
D.P. Stanley, D. Robson: Phys. Rev. Lett.45, 235 (1980)
P. Hasenfratz, R.R. Horgan, J. Kuti, J.M. Richard: Phys. Lett.94B, 401 (1980)
H.G. Dosch, V.F. Müller: Nucl. Phys.B116, 470 (1976)
D.B. Lichtenberg, E. Predazzi, D.H. Weingarten, J.G. Wills: Phys. Rev.D18, 2569 (1978); D.B. Lichtenberg, W. Namgung, E. Predazzi, J.G. Wills: Phys. Rev. Lett.48, 1653 (1982); I.A. Schmidt, R. Blankenbecler: Phys. Rev.D16, 1318 (1977); G.R. Goldstein, J. Maharana: Nuovo Cimento59A, 393 (1980); P. Kaus, private communication (Aspen, 1980)
B. Baumgartner, H. Grosse, A. Martin: Nucl. Phys.B254, 528 (1985). In this article, a factor (24)−1 is missing in the third term of the asymptotic expansion, but this is irrelevant here
I. Herbst: Commun. Math. Phys.53, 285 (1977)
P. Cea, et al.: Phys. Rev.D26, 1157 (1982)
J.M. Richard: Phys. Lett.100B, 515 (1981)
D. Pedoe: Circles. London: Pergamon Press, 1957
S. Golden: Phys. Rev137B, 1127 (1965);K. Symanzik: J. Math. Phys.6, 1155 (1965)
K. Szegö: Phys. Lett.68B, 239 (1977)
I.S. Gradshteyn, I.M. Ryzhik: Tables of integrals, series and products. New York: Academic Press 1965
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Martin, A. Regge trajectories in the quark model. Z. Phys. C - Particles and Fields 32, 359–367 (1986). https://doi.org/10.1007/BF01551832
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DOI: https://doi.org/10.1007/BF01551832