Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2010-06-03
Phys.Rev.D83:015009,2011
Physics
High Energy Physics
High Energy Physics - Phenomenology
17 pages, 2 tables; LaTeX; typos corrected, references added or replaced, argument in Secs. 2 and 3 revised, results unchanged
Scientific paper
10.1103/PhysRevD.83.015009
In the Standard Model the hypercharges of quarks and leptons are not determined by the gauge group $SU(3)_{\rm c} \times SU(2)_{\rm L} \times U(1)_{\rm Y}$ alone. We show that, if we choose the semidirect product group $[SU(3)_{\rm c} \times SU(2)_{\rm L}] \rtimes U(1)_{\rm Y}$ as its gauge group, the hyperchages are settled to be $n/6 \mod {\mathbb{Z}}\;(n = 0,1,3,4) $. In addition, the conditions for gauge-anomaly cancellation give strong constraints. As a result, the ratios of the hypercharges are uniquely determined and the gravitational anomaly is automatically canceled. The standard charge assignment to quarks and leptons can be properly reproduced. For exotic matter fields their hypercharges are also discussed.
Hattori Chuichiro
Matsunaga Mamoru
Matsuoka Takeo
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