Prog. Theor. Phys. Vol. 78 No. 5 (1987) pp. 1132-1141
Can ι(1440) Be a Pseudoscalar Glueball Which Appreciably Mixes with η′(958)?
Department of Applied Physics, Chubu University, Kasugai 487
*Center for Theoretical Physics, Department of Physics and Astronomy,
University of Maryland, College Park, Maryland 20742
Research Institute for Fundamental Physics, Kyoto University, Kyoto 606
(Received July 16, 1987)
We have studied the η- η′- ι mixing by using the Gell-Mann-Oakes-Renner type approach to the chiral U(3) ×U(3) and also U(4) ×U(4) algebras involving anomaly and found that η′- ι mixing could be appreciable. The model also predicted (by using PCAC and also sometimes a simple quark counting argument) that while the rate of ι→γγ is relatively small, Γ(ι→ργ) will be rather large ≃1 MeV. The η- η′-ι mixing has also been studied by us using the method of “asymptotic flavor SU(3) symmetry plus the constraint algebras involving the generators of underlying symmetry groups of QCD”. Essentially the same conclusion as derived in the first approach has been obtained for the structures of η- η′-ι mixing. In this paper, we study the ι→γγ and ι→ργ decays in the second approach without using quark counting argument. We find a result which is compatible (at least in flavor SU(3) symmetry studied) with that of the first approach. We conclude that a part of the present experimental situation can be understood with the presence of pseudoscalar glueball ι(1440) which mixes rather appreciably with the η′. Critical experiments for the model are also discussed.
DOI : 10.1143/PTP.78.1132
- D. L. Scharre et al., Phys. Lett. 97B (1980), 329.
C. Edwards et al., Phys. Rev. Lett. 49 (1982), 259[APS].
- M. S. Chanowitz, Invited Talk at the VIV'th International Symposium on Multiparticle Dynamics at High Energies, Lake Tahoe, 1983.
- The Mark III Collaboration, in AIP Conference Proceedings No. 132, Hadron Spectroscopy-1985 ed. S. Oneda, AIP, 1985, p. 14.
D. Hitlin, in Proceedings of the 1983 International Symposium on Lepton and Photon Interactions at High Energies, ed. D. G. Cassel and D. L. Kreinick, Cornell University, Aug. 4-9, 1983, p. 746.
- H. Kolanoski, in Proceedings of the 1985 International Symposium on Lepton and Photon Interactions at High Energies, ed. M. Konuma and K. Takahashi, Kyoto, August 19-24, 1985, Kyoto, p. 90.
H. Aihara et al., Phys. Rev. Lett. 57 (1986), 51[APS].
- See D. Hitlin's talk in Ref. 3) and J. D. Richman, in Proceedings of the Twentieth Recontre de Moriond, ed. J. Tran Thanh Van (Editions Frontieres, Gif-sur-Yvette, France, 1985), p. 471.
- S. Protopopescu, Invited Talk at The International Conference on Hadron Spectroscopy (Hadron '87), at KEK, April 16-18, 1987.
- C. Rosenzweig et al., Nucl. Phys. B206 (1982), 12; ibid. B207 (1982), 546 (E).
W. F. Palmer and S. S. Pinzky, Phys. Rev. D27 (1983), 2219[APS].
- N. N. Achasov et al., Phys. Lett. 96B (1980), 168.
M. Frank et al., Phys. Rev. D32 (1985), 2971[APS].
- T. A. Armstrong et al., Phys. Lett. 146B (1984), 273.
T. A. Armstrong et al., in Proceedings of the International Europhysics Conference on High-Energy Physics, ed. L. Nitti and G. Preparate, Bari Italy, July 18-24, 1985, p. 314.
S. U. Chung et al., Phys. Rev. Lett. 55 (1985), 779[APS].
A. Ando et al., Phys. Rev. Lett. 57 (1986), 1296[APS].
- P. Baillon et al., Nuovo Cim. 50A (1967), 393.
- L. Kopke (the Mark III Collaboration), in Proceedings of the XXIII International Conference on High Energy Physics, ed. S. C. Loken, Berkeley, July 16-23, 1986, p. 692.
- M. S. Chanowitz, Phys. Lett. 164B (1985), 379.
S. Iwao, Lett. Nuovo Cim. 35 (1982), 209.
- C. E. Carlson and T. H. Hansson, Nucl. Phys. B199 (1982), 441.
- T. Teshima and S. Oneda, Phys. Lett. 123B (1983), 455.
T. Teshima and S. Oneda, Phys. Rev. D29 (1984), 2067[APS].
- The Gell-Mann-Oakes-Renner method used in Refs. 18) and 19) corresponds to p = 0 (instead of p →∞ sum rules. There we took a great pain in estimating the effect of symmetry breaking and the method can be applicable only to the PS-mesons. For the method used in this paper, asymptotic symmetry provides us with an unambiguous recipe for computing symmetry breaking effect and the method is applicable to any meson.
K. Milton, Phys. Rev. Lett. 57 (1986), 1530[APS].
T. Teshima and S. Oneda, Phys. Rev. D27 (1983), 1551[APS].
- As discussed in Ref. 24), we take a non-collinear limit p →∞ and k →∞ in such a way as (p - k)2 →0. Actually exactly the same sum rule Eq. (2 ·7) can also be derived by using the commutator [JµEM(x), VK0] = 0 with µ= x and y and a collinear limit as discussed in Ref. 26).
- S. Oneda and K. Terasaki, Prog. Theor. Phys. Suppl. No. 82 (1985).
S. Matsuda and S. Oneda, Phys. Rev. 187 (1969), 2107[APS].
S. Oneda, T. Tanuma, T. Toiya and M. D. Slaughter, Phys. Rev. D23 (1981), 789[APS].
- Particle Data Group, Phys. Lett. 170B (1986).
- This is being studied by M. D. Slaughter.
Citing Article(s) :
Progress of Theoretical Physics Vol. 97 No. 2 (1997) pp. 351-355
Revisit of Glueball and Neutral Pseudoscalar Meson Admixture