Symmetry breaking and naturalness of parity conservation in weak neutral currents in left- right—symmetric gauge theories

We discuss the symmetry-breaking patterns and the naturalness of parity conservation in weak neutral-current interactions in the left-right—symmetric $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\otimes \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R\otimes \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ gauge theories. Two Higgs systems are discussed which enable us to achieve the desired breaking of the gauge symmetry. We show by a detailed analysis of the Higgs potential that the more economical of the two Higgs systems, that involving left and right Higgs scalar doublets, fails to meet the criteria of naturalness of parity conservation in neutral-current interactions. We find that with the second Higgs system neutral currents conserve parity naturally regardless of the structure of the physical charged-current weak interactions. Implications of this for the computability of induced parity violation in higher orders and the search for parity nonconservation in atoms are also discussed.