The generation problem and the symplectic group

• Published in: Nuclear physics. B Vol. 250; no. 1; pp. 641 - 665
• Main Authors: Kuo, T.K., Nakagawa, N.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 1985; Elsevier
• Subjects: Classical and quantum physics: mechanics and fields; Exact sciences and technology; Physics; Theory of quantized fields; Quantum field theory; Symplectic group
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(85)90498-5

The generation structure of quarks and leptons is studied in a series of extended electroweak models. They are gauge models constructed from subgroups of left-right symmetric SU(4) × S P L(6) × S P R(6). In particular, SU C (3) × S P L(6) × U Y (1), as well as SU C (3) × SU L(3) × SU R(3) × U X (1), are investigated in greater detail. It is shown that models based on such subgroups yield massless first generation fermions at the tree level. They acquire masses from those of the third generation via two-loop radiative corrections. Moreover, since such corrections are induced by charged scalar fields, it is found that there is a natural correlation between the two apparently conflicting inequalities m u < m d and m t > m b.