${\delta }_{CP}$ 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 asolution (without axions) of the strong CP problem by cancelling the theta-angle term ${\theta }_I$ $Tr(H^{\mu \nu }{H}_{\mu \nu }^{\ast })$ in colour 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. Extending here to flavour, one finds that there are two terms proportional to $Tr(G^{\mu \nu }{G}_{\mu \nu }^{\ast })$: (a) in the action from flavour instantons with unknown coefficient, say ${\theta }_I^{\prime }$, (b) induced by the above FSM solution to the strong CP-problem with therefore known coefficient ${\theta }_C^{\prime }$. Both terms can be cancelled in the FSM by a chiral transformation on the lepton zero mode to give a Jarlskog invariant $J^{\prime }$ in the PMNS matrix for leptons of order $10^{-2}$, as is hinted by experiment. But if the term ${\theta }_I^{\prime }$ is to be cancelled by a chiral transformation in the predicted hidden sector to solve the strong CP problem therein, leaving only the term ${\theta }_C^{\prime }$ to be cancelled by the chiral transformation on leptons, then the following prediction results: $J^{\prime }\sim -0.012$ (${\delta }_{CP}^{\prime }\sim (1.11)\pi$) which is (i) of the right order, (ii) of the right sign, (iii) in the range favoured by present experiment. Together with the earlier result for quarks, this offers an attractive unified treatment of all known CP physics.

Comments: 26 pages, 1 figure