Tri-bimaximal neutrino mixing from A4 and θ13∼θC

It is a common believe that, if the tri-bimaximal mixing (TBM) pattern is explained by vacuum alignment in an $A_4$ model, only a very small reactor angle, say ${\theta }_{13}～O({\lambda }_C^2)$ being ${\lambda }_C\equiv {\theta }_C$ the Cabibbo angle, can be accommodated. This statement is based on the assumption that all the flavon fields acquire VEVs at a very similar scale and the departures from exact TBM arise at the same perturbation level. From the experimental point of view, however, a relatively large value ${\theta }_{13}～O({\lambda }_C)$ is not yet excluded by present data. In this paper, we propose a seesaw $A_4$ model in which the previous assumption can naturally be evaded. The aim is to describe a ${\theta }_{13}～O({\lambda }_C)$ without conflicting with the TBM prediction for ${\theta }_{12}$ which is rather close to the observed value (at ${\lambda }_C^2$ level). In our model the deviation of the atmospherical angle from maximal is subject to the sum-rule: ${\sin }^2{\theta }_{23}\approx 1/2+\sqrt{2}/2\cos \delta \sin {\theta }_{13}$ which is a next-to-leading order prediction of our model.     

Vacuum phase transition at nonzero baryon density

It is argued that the dominant contribution to the interaction of quark–gluon plasma at moderate T?Tc$T?T_c$ is given by the nonperturbative vacuum field correlators. Basing on that nonperturbative equation of state of quark–gluon plasma is computed and in the lowest approximation expressed in terms of absolute values of Polyakov lines for quarks and gluons Lfund(T),Ladj(T)=(Lfund)^9/4$L_{\mathrm{fund}}(T),L_{\mathrm{adj}}(T)={(L_{\mathrm{fund}})}^{9/4}$ known from lattice and analytic calculations. Phase transition at any μ   is described as a transition due to vanishing of one of correlators, DE(x)$D^E(x)$, which implies the change of gluonic condensate ΔG₂$\mathrm{\Delta }{G}_2$. Resulting transition temperature Tc(μ)$T_c(\mu )$ is calculated in terms of ΔG₂$\mathrm{\Delta }{G}_2$ and Lfund(Tc)$L_{\mathrm{fund}}(T_c)$. The phase curve Tc(μ)$T_c(\mu )$ is in a good agreement with lattice data. In particular Tc(0)=0.27$T_c(0)=0.27$; 0.19; 0.17 GeV$0.17\text{ GeV}$ for nf=0,2,3$n_f=0,2,3$ and fixed ΔG₂=0.0035 GeV⁴$\mathrm{\Delta }{G}_2=0.0035{\text{ GeV}}^4$.     

Primordial quantum chromodynamics: QCD of a Fermi-Bose couple of coloured preons

We consider QCD of a massive Fermi-Bose couple of two colour triplets δ and χ of spin 1/2 and 0, respectively, and of equal charge ? 1/3, interacting with a colour octet of gluons. We conjecture that leptons and quarks of the lowest generation are bound states ${\nu }_e=\delta \overline{\chi },e=\delta (\chi \chi )P$ and $u=\overline{\delta }\overline{\chi },d=\overline{\delta }(\chi \chi )P$.