δCP for leptons and a new take on CP physics with the FSM

Abstract

A bonus of the framed Standard Model (FSM), constructed initially to explain the mass and mixing patterns of quarks and leptons, is a solution (without axions) of the strong CP problem by cancelling the theta-angle term [Formula: see text] in colour a by a chiral transformation on a quark zero mode which is inherent in FSM, and produces thereby a CP-violating phase in the CKM matrix similar in size to what is observed.1 Extending here to flavour, one finds that there are two terms proportional to [Formula: see text]: (a) in the action from flavour instantons with unknown coefficient, say [Formula: see text], (b) induced by the above FSM solution to the strong CP-problem with therefore known coefficient [Formula: see text]. Both terms can be cancelled in the FSM by a chiral transformation on the lepton zero mode to give a Jarlskog invariant [Formula: see text] in the PMNS matrix for leptons of order [Formula: see text], as is hinted by the experiment. But if, as suggested in Ref. 2, the term [Formula: see text] is to be cancelled by a chiral transformation in the predicted hidden sector to solve the strong CP problem therein, leaving only the term [Formula: see text] to be cancelled by the chiral transformation on leptons, then the following prediction results: [Formula: see text] [Formula: see text] which is (i) of the right order, (ii) of the right sign and (iii) in the range favoured by the present experiment. Together with the earlier result for quarks, this offers an attractive unified treatment of all known CP physics. a We use [Formula: see text], [Formula: see text] and [Formula: see text] here to denote, respectively the [Formula: see text], flavour [Formula: see text] and colour [Formula: see text] gauge fields.