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Chiral Scalar Fields, Custodial Symmetry in Electroweak SU(2)L X U(1) and the Quantization of the Electric Charge
I study the scalar representations of the electroweak group of the Standard
Model, which is a subgroup of the chiral group U(N)L x U(N)R with N flavours,
for N even, with a special emphasis on their chiral properties and on their
behaviour by the discrete symmetries P and CP. They exhaust the scalar
and pseudoscalar degrees of freedom of the chiral group, for which a SU(2)L x
U(1) renormalizable, anomaly-free gauge theory naturally springs out. It is
shown to have a global diagonal SU(2)V symmetry independently of the value of
the hypercharge coupling, which becomes local at the limit when the latter
vanishes. When acting in the 4-dimensional space of states spanned by the
special representations under scrutiny in this paper, the electric charge is
one of the three generators of this ``custodial'' symmetry; that the latter
stays an unbroken symmetry is thus correlated with the quantization of the
electric charge.Comment: 15 pages Latex. Minor corrections and addenda. Version to be
published in Phys. Lett.
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