A SPECULATION ON THE POSSIBLE DYNAMICAL ORIGIN OF CABIBBO ANGLE *

A major problem in weak interaction theory was solved in 1957, when Marshak and Sudarshan,’ and, subsequently, Feynman and Ge l l -Mad and Sakurai,’ suggested that the weak current that participates in leptonic and semileptonic decays is of the V-A type. Although this suggestion clarified the Lorentz structure of the weak Hamiltonian, its internal symmetry property remained a mystery. Particularly puzzling was the paradox as to why strangeness-changing decays are systematically suppressed compared to the strangeness-conserving ones. This paradox was a problem 20 years ago and still remains one, even though the general status of V-A theory has undergone tremendous advancement with the recent progress in gauge theories4 and the discovery of charm particles.5 The origin of the Cabibbo angle6 may well be the subject that receives the most intensive scrutiny by weak interaction theorists in the coming decade. In this paper, we will limit ourselves with this problem. We do not present any solution but, rather, a possible line of attack. Our suggestion involves the so called pseudo-Goldstone phenomenon within the framework of gauge theories and the presence of certain “angles” in these theories that could be determined dynamically. We propose that theories with fermions be constructed with a view to identifying the above “angles” with the Cabibbo angle. The pseudo-Goldstone phenomenon was first discovered by Weinberg’ for gauge theories, for which the global symmetry group of the Higgs potential is larger than the local gauge group of the entire Lagrangian. There are two aspects of this phenomenon. First, it leads to physical zero-mass particles in the tree approximation (i.e., such particles cannot be absorbed as longitudinal modes of the gauge fields) that acquire mass as a result of the loop corrections. Weinberg conjectured that these particles may be identified with light-mass bosom, such as K, K, and 9. This conjecture would, then, provide an insight into the dynamics of approximate symmetries of strong interactions. Second, this phenomenon implies that vacuum expectation values (VEV) of certain Higgs fields remain arbitrary in the tree approximation and are fixed only when loop effects are taken into account. We suggest that the latter aspects of pseudo-Goldstone phenomena may have many interesting physical applications. One such application was made by Georgi and Pais,* who exploited this second feature to realize the c o n j e c t ~ r e ~ * ’ ~ that CP violation may arise as a quantum effect. As indicated earlier in this paper, we are investigating the possibility that the Cabibbo angle may also be connected with this feature of pseudo-Goldstone phenomena. In support of our conjecture, we present a toy model without any fermions. The model is based on the gauge group SU(3), where, in the tree approximation, the VEV of the Higgs multiplet that corresponds to minimum energy