The Dark Side of θ13\theta_{13}, δCP\delta_{CP}, Leptogenesis and Inflation in Type-I Seesaw

In the context of the type-I seesaw mechanism, it is known that $\theta_{13}$ is zero and leptogenesis can not be realized if there exists a residual flavor symmetry resulting in the Tri-Bimaximal neutrino mixing pattern. We propose a simple framework where additional particles, odd under a $Z_2$ symmetry, break the residual flavor symmetry and the lightest of the $Z_2$ odd particles is the dark matter candidate. As as result, nonzero $\theta_{13}$, $\delta_{CP}$, leptogenesis and the correct dark matter density can be accommodated. On the other hand, a $Z_2$ odd scalar can play the role of the inflaton with mass of $10^{13}$ GeV motivated by the recent BICEP2 results. Interestingly, the model can "generate" $\delta_{CP} \simeq -\pi/2$, preferred by the T2K experiment in the normal hierarchy neutrino mass spectrum.Comment: 23 pages, 8 Figures and 5 Tables. v3: a toy A4 flavor model provided, version accepted by JHE

Precise Rates in the Law of the Logarithm in the Hilbert Space

Complete Convergence, Tail Probabilities of Sums of i.i.d Random Variables, the Law of the Logarithm, Strong Approximation