Fundamental Quartets and Chiral $U(4) \otimes U(4)$

A New Approach to η → 2γ Decay and Models of Elementary Particles

“…(3 · 3), (2 ·15) and (2 · 7a, b) for the case of quartet models. It is worthwhile to remark that our decay amplitudes for pa~2r have the form proportional to fr in contrast with that of modified PCAC treatment by Adler/ 6 l in the latter of which the amplitudes are linear in fr- 1 At present, however, there is no definite experimental information with regard to the above processes except for r;,:;2r< (240 ± 120) ke V. Accumulating reliable data would be highly desirable for checking our model and method of approach. § 4.…”

Quartet Scheme of Hadrons in Chiral $U(4) \otimes U(4)$

“…Starting with a most general scheme compatible with the principle of lepton-baryon symmetry ( § 2), we put our scheme into the framework of approximate chiral U(4)Q9U(4) symmetry. Although our arguments in this note were concentrated on the properties of o--mesons, the results obtained here seem to be helpful to test our model by future experimental in-Quartet Scheme of Hadrons zn Chiral U(4)@U (4) formation.…”

“…As far as the strong interactions are concerned there are no distinctions between Models I and II, since the latter case can be reduced to the former by an identification *> Op=On=O corresponds to the identity transformation. **> A formula equivalent to (2,4) was first proposed in Ref. 9) on the leptonic basis in order to explain the weak angle by means of the lepton masses.…”

“…We have not presented the discussion of the properties of other hadrons such as vector mesons or baryons, for, in these cases, the generalization of the broken SU (3) arguments to the case of broken SU (4) seems to be rather straightforward in that it would not be necessary to pay a special attention to the complications as in the case of N.G.-bosons. For example, it is easily verified for vector mesons that only by a simple breaking pattern !J{' in Eq.…”

“…A rough sketch of our new approach was given in a previous note. 4 ) That is, we pointed out that, following the analysis made by Ogawa and his col-laboraters5) on the new decay event of a charged heavy particle xch reported recently by Niu et al, 6 ) the approximate symmetry of strong interaction could be lated only in a weak interaction process; this implies, in turn, that the models with lepton-baryon symmetry are preferable over the other type of quartet models since the stability of the new quantum number is automatically ensured. *> If we follow the Nagoya-model picture 8 > of lepton-baryon symmetry, we impose naturally the U( 4) symmetry, rather than SU( 4), among four fundamental fields as a basic structure of strong interactions even if its violation were quite large.…”