Abstract
For all the success of the Standard Model (SM), it is on the verge of being surpassed. In this regard we argue, by showing a minimal flavor-structured model based on the non-Abelian discrete SL2(F3) symmetry, that U(1) mixed-gravitational anomaly cancellation could be of central importance in constraining the fermion contents of a new chiral gauge theory. Such anomaly-free condition together with the SM flavor structure demands a condition k1X1/2=k2X2 with Xi being a charge of U(1)Xi and ki being an integer, both of which are flavor dependent. We show that axionic domain-wall condition NDW with the anomaly free-condition depends on both U(1)X charged quark and lepton flavors; the seesaw scale congruent to the scale of Peccei–Quinn symmetry breakdown can be constrained through constraints coming from astrophysics and particle physics. Then the model extended by SL2(F3)×U(1)X symmetry can well be flavor-structured in a unique way that NDW=1 with the U(1)X mixed-gravitational anomaly-free condition demands additional Majorana fermion and the flavor puzzles of SM are well delineated by new expansion parameters expressed in terms of U(1)X charges and U(1)X-[SU(3)C]2 anomaly coefficients. And the model provides remarkable results on neutrino (hierarchical mass spectra and unmeasurable neutrinoless-double-beta decay rate together with the predictions on atmospheric mixing angle and leptonic Dirac CP phase favored by the recent long-baseline neutrino experiments), QCD axion, and flavored-axion.
Highlights
Symmetries play an important role in physics in general and in quantum field theory in particular
In this paper we present, by showing an extended flavored-PQ model which extend to a compact symmetry 2 GF for new physics beyond Standard Model (SM), that the U(1) mixed-gravitational anomaly cancellation is of central importance in constraining the fermion contents of a new chiral gauge theory, and the flavor structure of GF is 3 strongly correlated with physical observables
16 Here, in numerical calculation, we have only considered the mass matrices in Eq (21) since it is expected that the corrections to the vacuum expectation value (VEV) due to dimensional operators contributing to Eq (7) could be small enough below a few percent level, see Appendix B
Summary
Symmetries play an important role in physics in general and in quantum field theory in particular. The standard model (SM) as a low-energy effective theory has been very predictive and well tested, due to the symmetries satisfied by the theory - Lorentz invariance plus the SU(3)C × SU(2)L × U(1)Y gauge symmetry in addition to the discrete space-time symmetries like P and CP It leaves many open questions for theoretical and cosmological issues that have not been solved yet. In turn its results give an upper bound on QCD axion mass with different values of tan β in Eq (32) and gAee in Eq (58), since axion to leptons and quarks couplings depend on structure of the quark and lepton sector In this sense, if the astronomical constraint of star cooling [12] favored by the model in Ref. In appendix we consider possible next-to-leading order corrections
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