# Weak-interaction mixing in the six-quark ambidextrous model of quantum flavourdynamics

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## References

- (1).S. Weinberg:
*The problem of mass*, Harvard preprint (1977);F. Wilczek andA. Zee:*Phys. Lett.*,**70**B, 418 (1977);S. Pakvasa andH. Sugawara:*Phys. Lett.*,**73**B, 61 (1978);R. N. Mohapatra andG. Senjanovic:*Phys. Lett.*,**73**B, 176 (1978);T. Hagiwara, T. Kitazoe, G. B. Mainland andK. Tanaka:*Cabibbo current and CP violation in a six-quark gauge model*, Ohio preprint (1977);C. G. Braco:*Discrete symmetries, Cabibbo universality, and flavour-mixing angles*, Bonn preprint (1977); see alsoF. Gürsey andM. Serdaroglu:*Lett. Nuovo Cimento*,**21**, 28 (1978);R. Barbieri, R. Gatto andF. Strocchi:*Phys. Lett.*,**74**B, 344 (1978).Google Scholar - (2).
- (3).
- (4).A. Ebrahim:
*Phys. Lett.*,**72**B, 457 (1978);**73**B, 181 (1978);*Quark masses and flavour-mixing angles in a six-quark model of quantum flavourdynamics*, to be published in*Phys. Lett.*, B.ADSCrossRefGoogle Scholar - (5).The quark mass parameters used in this note are the current quark masses (or ultraviolet quark masses) that are related to the pseudoscalar-meson masses and decay constants via the PCAC relation, and not the constituent quark masses (or infra-red quark masses) that are related to hadronic masses via
*SU*_{6}-type mass formulae. The ratio of masses of consecutive quarks obtained using these two definitions ranges from about\(\sqrt {\cot g \theta _C } \gtrsim 2\) for the constituent quark masses of about cotg^{2}φ_{C}⋍ 20 for the current quark masses. In spite or this vast difference in the two types of quark mass parameters, characterized by different choice of the renormalization point, the distinction between them has not been consistently maintained in the literature. For a discussion, seeA. Ebrahim: ref. (4,6); ;H. Fritzsch andP. Minkowski:*Ann. Phys.*,**93**, 193 (1975);H. Fritzsch:*The world of flavour and colour*, CERN-TH-2359 (1977);*Chromodynamic theory of hadrons*, CERN-TH-2483 (1978);M. Gellmann:*Aust. Journ. Phys.*,**29**, 473 (1976);*Present trends in the theory of hadrons*, CERN-ISR Workshop/2-6 (1977).ADSCrossRefGoogle Scholar - (6).R. Gatto, G. Sartori andM. Tonin:
*Phys. Lett.*,**28**B, 128 (1968);N. Cabibbo andL. Maiani:*Phys. Lett.*,**29**B, 131 (1968);R. J. Oakes:*Phys. Lett.*,**29**B, 683 (1969);A. Ebrahim andM. Serdaroblu:*Phys. Lett.*,**48**B, 338 (1974);**50**B, 258 (1974);A. Ebrahim:*Lett. Nuovo Cimento*,**13**, 297 (1975).ADSCrossRefGoogle Scholar - (7).J. Ellis, M. K. Gaillard andD. V. Nanopoulos:
*Nucl. Phys.*,**109**B, 213 (1976);J. Ellis, M. K. Gaillard, N. V. Nanopoulous andS. Rudaz:*Nucl. Phys.*,**131**B, 285 (1977).ADSCrossRefGoogle Scholar - (8).Similarly, the simplest possible generalization of the procedure that generates the form of the chiral symmetry breaking Hamiltonian density of the strong interaction at the three-quark level appears to be consistent with experiment when additional quark flavours are incorporated. SeeA. Ebrahim:
*Phys. Lett.*,**70**B, 421 (1977);*Pattern of quark masses*, preprint (1978);*Discrete scale symmetry and the quark mass spectrum*, preprint (1978).ADSCrossRefGoogle Scholar - (9).See for example,M. S. Chanowitz, J. Ellis andM. K. Gaillard:
*Nucl. Phys.*,**128**B, 506 (1977).ADSCrossRefGoogle Scholar - (10).For a critical discussion concerning the Higgs system in quantum flavordynamics, seeM. A. B. Beg:
*Quantum flavordynamics: a status report*, Rockefeller preprint (1978).Google Scholar - (11).See, for example,R. N. Mohapatra:
*Weak interaction models with spontaneously broken left-right symmetry*, CCNY-HEP-78/1 (1978).Google Scholar - (12).We note that the scheme for relating quark masses and flavour-mixing angles given here will not work if the quark doublets are chosen differently from eq. (11), as is often done in six-quark vectorlike models of quantum flavour dynamics.Google Scholar
- (13).The form of the Higgs potential that will given this pattern of vacuum expectation values has been discussed in ref. (2)..ADSCrossRefGoogle Scholar
- (14).
- (15).We note that the diagonalization of the quark mass matrices automatically imply that the left-handed and right-handed flavour-mixing angles are equal. We also note that the quark mass matrices can be made real by a suitable choice of phases for the quark fields, and hence for the form of the quark mass matrices chosen in this note, the
*CP*-violating phase vanishes identically.Google Scholar - (16).We note that the quark mass ratios given in eq. (8) are the only ones that can arise through weak-interaction mixing. This gives a certain amount of uniqueness to the relations between quark masses and flavour-mixing angles suggested in this note.Google Scholar

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