Two-gluon model of hadronic transitions between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> states in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>c</mi><mrow><mrow><mover><mrow><mi>c</mi></mrow><mrow><mi>¯</mi></mrow></mover></mrow></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi><mrow><mrow><mover><mrow><mi>b</mi></mrow><mrow><mi>¯</mi></mrow></mover></mrow></mrow></math> systems

M. Chemtob; H. Navelet

doi:10.1103/PhysRevD.41.2187

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Two-gluon model of hadronic transitions between $S$ , $D$ , and $P$ states in $c \bar{c}$ and $b \bar{b}$ systems

M. Chemtob and H. Navelet

Service de Physique Théorique CEN-Saclay 91191 Gif-sur-Yvette CEDEX, France

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Phys. Rev. D 41, 2187 – Published 1 April, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.2187

Abstract

The hadronic transitions between the narrow excited states of orbital angular momentum $S$ , $D$ , and $P$ in the charmonium and bottomonium systems are described as two-gluon emission processes and their probability amplitudes evaluated in the semiperturbative approach based on Feynman diagrams. The hadronization amplitudes of gluons into the light hadrons are introduced by projecting onto the states of zero intrinsic angular momentum of the two gluons. The transition rates into the two space-parity channels $0^{\pm}$ are considered. Detailed predictions are presented for the rates and mass distributions in the $π π$ and $η$ , $π^{0}$ channels. The matching of theory with data necessitates the incorporation of a large enhancement factor in the $0^{-}$ channel relative to the $0^{+}$ channel, for which one possible interpretation is that the color coupling constant for magnetic gluons exceeds significantly that for electric gluons. We compare our results to those of the QCD multipole-expansion approach.

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[c1] G. Abrams et al., Phys. Rev. Lett. 34, 1181 (1975)

[c2] T. Bowcock et al., Phys. Rev. Lett. 58, 307 (1987) I. C. Brock, in Hadrons, Quarks and Gluons, proceedings of the 22nd Rencontre de Moriond, Les Arcs, France, 1987, edited by J. Tran Than Van (Editions Frontières, Gif-sur-Yvette, France, 1987)

[c3] L. S. Brown and R. Cahn, Phys. Rev. Lett. 35, 1 (1975) M. Voloshin, Pis'ma Zh. Eksp. Teor. Fiz. 21, 733 (1975) [JETP Lett. 21, 347 (1975)] R. Cahn, Phys. Rev. D 12, 3559 (1975)

[c4] H. Goldberg, Phys. Rev. Lett. 35, 605 (1975)

[c5] A. Billoire, R. Lacaze, A. Morel, and H. Navelet, Nucl. Phys. B155, 493 (1979)

[c6] K. Gottfried, Phys. Rev. Lett. 40, 598 (1978) M. B. Voloshin, Nucl. Phys. B154, 365 (1979)

[c7] M. E. Peskin, in Dynamics and Spectroscopy at High Energy, proceedings of the Eleventh SLAC Summer Institute on Particle Physics, Stanford, California, 1983, edited by P. M. McDonough (SLAC, Report No. 267, Stanford, 1984)

[c8] T. M. Yan, Phys. Rev. D 22, 1652 (1980)

[c9] M. B. Voloshin and V. Zakharov, Phys. Rev. Lett. 45, 688 (1980)

[c10] V. A. Novikov and M. A. Shifman, Z. Phys. C 8, 43 (1981)

[c11] M. B. Voloshin, Yad. Fiz. 43, 1571 (1986) [Sov. J. Nucl. Phys. 43, 1011 (1986)]

[c12] P. Moxhay, Phys. Rev. D 37, 2557 (1988)

[c13] Y. P. Kuang and T. M. Yan, Phys. Rev. D 24, 2874 (1981)

[c14] Y. P. Kuang, S. F. Tuan, and T. M. Yan, in Hadron 1987, proceedings of the 2nd International Conference on hadron Spectroscopy, Tsukuba, Japan 1987, edited by Y. Oyanagi, K. Takamatsu, and T. Tsuru (KEK Report No. 87-7, Tsukuba, 1987) Phys. Rev. D 37, 1210 (1988)

[c15] G. Belanger, T. DeGrand, and P. Moxhay, Phys. Rev. D 39, 257 (1989) M. B. Voloshin, Pis'ma Zh. Eksp. Teor. Fiz. 37, 58 (1983) [JETP Lett. 37, 69 (1983)]

[c16] H. J. Lipkin and S. F. Tuan, Phys. Lett. B 206, 349 (1988) Phys. Rev. Lett. 62, 2910 (1989)

[c17] R. Blankenbecler and L. F. Cook, Jr., Phys. Rev. 119, 1745 (1960) R. G. Arnold, C. E. Carlson, and F. Gross, Phys. Rev. C 21, 1426 (1980)

[c18] R. Blankenbecler and R. Sugar, Phys. Rev. 142, 1051 (1966)

[c19] R. Barbieri and E. Remiddi, Nucl. Phys. B141, 413 (1978)

[c20] G. C. Wick, Ann. Phys. (N.Y.) 18, 65 (1962) M. I. Shirokov, Zh. Eksp. Teor. Fiz. 40, 1387 (1961) [Sov. Phys. JETP 13, 975 (1961)]

[c21] Particle Data Group, G. P. Yost et al., Phys. Lett. B 204, 1 (1988)

[c22] D. Gross, S. Treiman, and F. Wilczek, Phys. Rev. D 19, 2188 (1979)

[c23] V. A. Novikov, L. B. Okun, M. A. Shifman, A. I. Vainshtein, M. B. Voloshin, and V. I. Zakharov, Phys. Rep. 41, 1 (1978)

[c24] E. Eichten, K. Gottfried, T. Kinoshita, K. Lane, and T. M. Yan, Phys. Rev. D 21, 203 (1980)

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Two-gluon model of hadronic transitions between $S$ , $D$ , and $P$ states in $c \bar{c}$ and $b \bar{b}$ systems

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Two-gluon model of hadronic transitions between S, D, and P states in cc¯ and bb¯ systems

Abstract

References (24)

Two-gluon model of hadronic transitions between $S$ , $D$ , and $P$ states in $c \bar{c}$ and $b \bar{b}$ systems