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Sum rules for the coupling constants of three boson octets in brokenSU 3

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Il Nuovo Cimento A (1965-1970)

Summary

Sum rules for the coupling constants of three bosons octets are given. They are applied to K** (1430) and A2 (1320) resonances. It is concluded that they belong to aJ P=2+ octet rather than a 27-plet.

Riassunto

Si danno le regole di somma per le costanti di accoppiamento di tre ottetti di bosoni e si applicano alle risonanze K** (1430) e A2 (1320). Si conclude che esse appartengono a un ottettoJ P=2+ piuttosto che a un 27-pletto.

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References

  1. V. Gupta andV. Singh:Phys.; Rev.,139, B 782 (1964). We follow the techniques and notation of this paper.

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  2. S. L. Glashow andR. H. Socolow:Decay Modes of Spin-Two Mesons, preprint (1965). This refers to other work on the 2+ octet.

  3. M. Gell-Mann:Phys. Rev. Lett.,12, 155 (1964). ℰ-charge conjugation parity of the eighth component.

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  4. Recall that if an octetM has ℰ(M)=±1, then theG-parity ofM(1, 0)=∓1 and ofM (0. 0)=∓1. Also, the symmetry breaking spurion octet “S” has ℰ(S)=+1.

  5. The sum rules for this case, in terms of coupling constants, have already been noted byS. L. Glashow andM. Muraskin:Phys. Rev.,132, 482 (1963).

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  6. Our information on the f’ stems from ref. (2) above.S. L. Glashow andR. H. Socolow:Decay Modes of Spin-Two Mesons, preprint (1965). This refers to other work on the 2+ octet.

  7. G. Goldhaber: UCRL-11971 (1965).

  8. Note that A2, K**, f’ satisfy the Gell-Mann-Okubo mass formula to within 10%. But the same mass sum rule is valid if they all belong to a 27-plet. Thus the satisfaction of only the mass formula by them cannot decide whether they are in an8 or27.

  9. The sum rules for this case can be obtained by feeding in the equalities (6.43) and (6.44), of ref. (1),, in the eqs. (6.25) to (6.24).

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Author notes

  1. V. Gupta

    Present address: Tata Institute of Fundamental Research, 5, Bombay, India

Authors and Affiliations

  1. California Institute of Technology, Pasadena, Cal.

    V. Gupta

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  1. V. Gupta
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Additional information

Work supported in part by the U. S. Atomic Energy Commission. Prepared under Contract AT(11-1)-68 for the San Francisco Operations Office, U. S. Atomic Energy Commission.

Traduzione a cura della Redazione.

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Gupta, V. Sum rules for the coupling constants of three boson octets in brokenSU 3 . Nuovo Cimento A (1965-1970) 42, 737–742 (1966). https://doi.org/10.1007/BF02720552

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