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Perfect Chiral Symmetry and CP Violation

Playing the game of ignoring the Higgs field altogether, we ask how we could have CP violation. It means that we a priory have a flavour blind theory, having even an $U(3)$ symmetry for each type of Standard Model group representation, {\em i.e.} an $\big[U(3)\big]^5$ global symmetry. This we can call Perfect Chiral Symmetry ($P\chi S$). In such a special, $P\chi S$ regime, at least four different fermion representations are needed in order to produce CP violation. Such CP violation is highly suppressed, first met by the dim = 12 term, and could hardly be relevant for the CP violation observed in the low energy particle physics. However, such mechanism, in which besides quarks also leptons participate simultaneously in the CP-violation (and also in B-violation and L-violation) game, might be interesting for explaining the observed baryon asymmetry of the universe.

CP violation; chiral symmetry; flavour symmetry; irrelevant operators; lepton-number violation; baryon-number violation

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