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Prog. Theor. Phys. Vol. 56 No. 6 (1976) pp. 1902-1909

An Improved Mass Formula for 0^--Mesons in Broken SU(4)-Model for New Particles

Ziro Maki, Tadayuki Teshima^* and Isao Umemura^**

Research Institute for Fundamental Physics, Kyoto University, Kyoto 606
^*Department of Applied Physics, Chubu Institute of Technology, Kasugai 487
^**Department of Nuclear Engineering, Kyoto University, Kyoto 606

(Received June 23, 1976)

Abstract:

A possible generalization of the Gell-Mann-Oakes-Renner type mass formula for the 16-plet 0^--mesons is proposed by introducing the violation of SU(4) symmetry of the vacuum and the corrections to the decay constants f's of corresponding mesons. The results obtained include, for example, a new sum rule for squared masses of charmed mesons, m_F² - m_D² = λ(m_K² - m_π²) with a parameter λ representing the effects of corrections considered. This sum rule would provide a direct measure for the effects of violation of SU(4) symmetry once the masses of D- and F-mesons are determined precisely.
Also discussed are the more involved relations among the masses of D-, F- and η_c-mesons based on the proposed new mass formula. By identifying recently communicated (K^±π^\mp)-state at 1.87 GeV with the D⁰-meson, the expected mass values of F⁺-mesons are estimated under various assumptions on the patterns of symmetry breakings.

URL : http://ptp.ipap.jp/link?PTP/56/1902/
DOI : 10.1143/PTP.56.1902

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References:

1. Early works as well as a historical sketch of the quartet model were given in Z. Maki, T. Maskawa and I.Umemura, Prog. Theor. Phys. 47 (1972), 1682[PTP].
   See also the references cited in Ref. 3).
2. K. Niu, E. Mikumo and Y. Maeda, Prog. Theor. Phys. 46 (1971), 1644[PTP].
   T. Hayashi, T. Kawai, M. Matsuda, S. Ogawa and S. Shige-Eda, Prog. Theor. Phys. 47 (1972), 280[PTP].
   J. J. Aubert et al., Phys. Rev. Lett. 33 (1974), 1404[APS].
   J.-E. Augustin et al., Prog. Theor. Phys. 53 (1975), 1541[PTP].
3. See Ref. 1) and
   Z. Maki, K. Ohnishi, T. Teshima and I. Umemura, Prog. Theor. Phys. 54 (1975), 823[PTP]; ibid. 55 (1976), 267[PTP].
4. R. Simard and M. Suzuki, Phys. Rev. D 12 (1975), 2002[APS].
   T. Hayashi, T. Karino, M. Matsuda and S. Ogawa, Prog. Theor. Phys. 54 (1975), 286[PTP].
   S. Sawada, Prog. Theor. Phys. 55 (1976), 818[PTP].
5. See Ref. 3).
6. B. H. Wiik, in Proceedings of the 1975 International Symposium on Lepton and Photon Interactions at High Energies, edited by W. T. Kirk, p. 69.
7. M. Gell-Mann, R. J. Oakes and B. Renner, Phys. Rev. 175 (1968), 2195[APS].
8. P. Dittner and S. Eliezer, Phys. Rev. D 8 (1973), 1929[APS].
9. For example, Talk at the RIFP-Seminar by Tran Thanh Van (Orsay), June 1, 1976, Kyoto.
10. N. H. Fuchs and T. K. Kuo, Nuovo Cim. A 64 (1969), 382.
    See also, S. Okubo and V. S. Mathur, Phys. Rev. D 1 (1970), 2046[APS]; ibid. 1 (1970), 2051[APS]; ibid. 1 (1970), 3468[APS].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 58 No. 3 (1977) pp. 907-920 :

   Broken Chiral SU(4) ⊗SU(4) Based on SU(4) \supsetSU(2) ⊗SU(2)

   Masao Inose

2. Progress of Theoretical Physics Vol. 58 No. 3 (1977) pp. 921-930 :

   On the Masses of Charmed Mesons and Charmoniums

   Kazuyoshi Izawa

3. Progress of Theoretical Physics Vol. 58 No. 3 (1977) pp. 1049-1051 :

   A Study of SU(4) ⊗SU(4) Symmetry Breaking Parameter

   V. P. Gautam and Bijan Bagchi

4. Progress of Theoretical Physics Vol. 59 No. 2 (1978) pp. 507-514 :

   Masses and Decay Constants of Charmed Mesons

   Ziro Maki and Isao Umemura

5. Progress of Theoretical Physics Vol. 59 No. 3 (1978) pp. 927-939 :

   “χ” Particles and Their Radiative Interactions

   Nobuyuki Aizawa, Tadayuki Teshima and Isao Umemura

6. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1613-1624 :

   Broken Chiral SU(4)×SU(4)

   Takashi Fukuda

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