@article{cbd09ba168514525a1ac70c086edcb4b,
title = "Discrete flavor symmetries and a formula for the cabibbo angle",
abstract = "A discrete flavor symmetry is proposed which leads to the relation tan2θc = md ms. The symmetry may be implemented in weak interaction models where the breakdown of parity is spontaneous.",
author = "Frank Wilczek and Z. Zee",
note = "Funding Information: One obstacle to further progress in the gauge theory of weak and electromagnetic interactions is the proliferation of undetermined parameters. The gauge symmetry fixes in an elegant fashion the interaction of gauge bosons with each other and with matter, but unfortunately says little about the other sectors in the Lagrangian. It is especially important to control the couplings of Higgs particles to Fermions, since these generate quark and lepton masses and mixing angles like the Cabibbo angle, which are directly relevant to experiment. Various types of symmetries may be imposed on the couplings of the Fermions to the Higgs particles. Continuous global symmetries lead to massless Nambu-Goldstone bosons when the Higgs scalars acquire vacuum expectation values, which presumably are excluded. If the global symmetries are gauged so that the would-be massless scalars are absorbed into massive vectors, one typically gets gauge particles mediating bizarre interactions (e.g. As = 2 processes, strangeness or lepton number changing neutral currents, etc.). These particles must be made very heavy, and this program becomes complicated and possibly inconsistent \[1\ ]. Another approach, explored by many people but in an especially systematic way by Georgi and Pais \[2\], is to reduce the number of independent couplings by imposing discrete symmetries. Of course, this approach is not inconsistent with the one previously mentioned. Unfortunately, the number of possible discrete symmetries is very large (unlike the case of continuous groups, where there are only a few groups and representations * Supported in part by ERDA under Contract No. E(11-1)3072 and the National Science Foundation, Grant No. MPS75-22514. A.P. Sloan Fellows.",
year = "1977",
month = oct,
day = "24",
doi = "10.1016/0370-2693(77)90403-8",
language = "English (US)",
volume = "70",
pages = "418--420",
journal = "Physics Letters B",
issn = "0370-2693",
publisher = "Elsevier",
number = "4",
}