HIERARCHY OF QUARK MASSES, CABIBBO ANGLES AND CP VIOLATION

HIERARCHY OF QUARK MASSES, CABIBBO ANGLES AND CP VIOLATION

28 June 1978 | C. D. Froggatt and H.B. Nielsen
The paper explores the hierarchy of quark masses, Cabibbo angles, and CP violation. It proposes that large quark mass ratios arise from differences in quantum numbers between left- and right-handed quark components. These differences determine the order of magnitude of quark masses, and the generalized Cabibbo angle is predicted to be the square root of the corresponding mass ratio. However, the mechanism for CP conservation remains unclear. The paper discusses the quark mass matrix and its decomposition into weak eigenstates, leading to estimates of generalized Cabibbo angles and CP violation. It also considers the role of approximate selection rules and quantum numbers in generating large mass ratios. The paper suggests that the quark mass matrix can be expressed in terms of a parameter ε, which is related to the symmetry breaking parameter. This leads to large quark mass ratios, with the order of magnitude determined by the difference in quantum numbers between left- and right-handed quarks. The paper also examines the implications of the weak coupling matrix and its relation to the generalized Cabibbo angles. It shows that the weak coupling matrix can be expressed in terms of these angles and that the CP violation parameter is expected to be random. However, the observed CP conservation is a puzzle for the model, and the paper suggests that a small CP violation parameter may be introduced to resolve this issue. The paper concludes that the model provides a natural explanation for the large quark mass ratios and the order of magnitude of the weak coupling matrix. However, the observed CP conservation remains a challenge, and the model may need to be modified to account for this. The paper suggests that introducing additional quantum numbers or quark substructure could help resolve the issue of CP violation.The paper explores the hierarchy of quark masses, Cabibbo angles, and CP violation. It proposes that large quark mass ratios arise from differences in quantum numbers between left- and right-handed quark components. These differences determine the order of magnitude of quark masses, and the generalized Cabibbo angle is predicted to be the square root of the corresponding mass ratio. However, the mechanism for CP conservation remains unclear. The paper discusses the quark mass matrix and its decomposition into weak eigenstates, leading to estimates of generalized Cabibbo angles and CP violation. It also considers the role of approximate selection rules and quantum numbers in generating large mass ratios. The paper suggests that the quark mass matrix can be expressed in terms of a parameter ε, which is related to the symmetry breaking parameter. This leads to large quark mass ratios, with the order of magnitude determined by the difference in quantum numbers between left- and right-handed quarks. The paper also examines the implications of the weak coupling matrix and its relation to the generalized Cabibbo angles. It shows that the weak coupling matrix can be expressed in terms of these angles and that the CP violation parameter is expected to be random. However, the observed CP conservation is a puzzle for the model, and the paper suggests that a small CP violation parameter may be introduced to resolve this issue. The paper concludes that the model provides a natural explanation for the large quark mass ratios and the order of magnitude of the weak coupling matrix. However, the observed CP conservation remains a challenge, and the model may need to be modified to account for this. The paper suggests that introducing additional quantum numbers or quark substructure could help resolve the issue of CP violation.
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[slides and audio] Hierarchy of Quark Masses%2C Cabibbo Angles and CP Violation