Abstract
We show how the scales responsible for Peccei-Quinn (PQ), seesaw, and Froggatt and Nielsen (FN) mechanisms can be fixed, by constructing a compact model for resolving rather recent, but fast-growing issues in astro-particle physics, including quark and leptonic mixings and CP violations, high-energy neutrinos, QCD axion, and axion cooling of stars. The model is motivated by the flavored PQ symmetry for unifying the flavor physics and string theory. The QCD axion decay constant congruent to the seesaw scale, through its connection to the astro-particle constraints of both the stellar evolution induced by the flavored-axion bremsstrahlung off electrons $e+Ze\rightarrow Ze+e+A_i$ and the rare flavor-changing decay process induced by the flavored-axion $K^+\rightarrow\pi^++A_i$, is shown to be fixed at $F_A=3.56^{+0.84}_{-0.84}\times10^{10}$ GeV (consequently, the QCD axion mass $m_a=1.54^{+0.48}_{-0.29}\times10^{-4}$ eV, Compton wavelength of its oscillation $\lambda_a=8.04^{+1.90}_{-1.90}\,{\rm mm}$, and axion to neutron coupling $g_{Ann}=2.14^{+0.66}_{-0.41}\times10^{-12}$, etc.). Subsequently, the scale associated to FN mechanism is dynamically fixed through its connection to the standard model fermion masses and mixings, $\Lambda=2.04^{\,+0.48}_{\,-0.48}\times10^{11}\,{\rm GeV}$, and such fundamental scale might give a hint where some string moduli are stabilized in type-IIB string vacua. In the near future, the NA62 experiment expected to reach the sensitivity of ${\rm Br}(K^+\rightarrow\pi^++A_i)<1.0\times10^{-12}$ will probe the flavored-axions or exclude the model, if the astrophysical constraint of star cooling is really responsible for the flavored-axion.
Highlights
Symmetries have always played an important role in physics in general and in quantum field theory in particular
Motivated by the flavored-PQ symmetry to unify flavor physics and string theory [1,7], we have constructed a compact model based on SL2ðF3Þ × Uð1ÞX symmetry for resolving rather recent, but fast-growing issues in astroparticle physics, including quark and leptonic mixings and CP violations, high-energy neutrinos, the QCD axion, and axion cooling of stars
Since astroparticle physics observations have increasingly placed tight constraints on parameters for flavored axions, we have shown how the scale responsible for the PQ mechanism could be fixed, and in turn the scale responsible for the FN mechanism through flavor physics
Summary
Symmetries have always played 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, namely, Lorentz invariance plus the SUð3ÞC × SUð2ÞL × Uð1ÞY gauge symmetry, in addition to the discrete spacetime symmetries like P and CP It leaves many open questions for theoretical and cosmological issues that have not been solved yet The flavor puzzle of the SM chargedfermion mass hierarchies could be solved by implementing the Froggatt-Nielsen (FN) mechanism [9] If these mechanisms are realized in nature at low energies, finding the scales responsible for the seesaw, PQ, and FN mechanisms could be an important step of resolving these fundamental issues of particle physics and cosmology. The spontaneous breaking of Uð1ÞX gives rise to the Nambu-Goldstone (NG) mode (called the axion) and provides an elegant solution to the strong CP problem
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