Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRenormalisation Group Corrections to the Littlest Seesaw Model and Maximal Atmospheric Mixing
83
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The Littlest Seesaw (LS) model involves two right-handed neutrinos and a very constrained Dirac neutrino mass matrix, involving one texture zero and two independent Dirac masses, leading to a highly predictive scheme in which all neutrino masses and the entire PMNS matrix is successfully predicted in terms of just two real parameters. We calculate the renormalisation group (RG) corrections to the LS predictions, with and without supersymmetry, including also the threshold effects induced by the decoupling of heavy Majorana neutrinos both analytically and numerically. We find that the predictions for neutrino mixing angles and mass ratios are rather stable under RG corrections. For example we find that the LS model with RG corrections predicts close to maximal atmospheric mixing, $theta_{23}=45^circ pm 1^circ$, in most considered cases, in tension with the latest NOvA results. The techniques used here apply to other seesaw models with a strong normal mass hierarchy.
rate research
Read More
We propose the Littlest Seesaw (LS) model consisting of just two right-handed neutrinos, where one of them, dominantly responsible for the atmospheric neutrino mass, has couplings to $( u_e, u_{mu}, u_{tau})$ proportional to $(0,1,1)$, while the subdominant right-handed neutrino, mainly responsible for the solar neutrino mass, has couplings to $( u_e, u_{mu}, u_{tau})$ proportional to $(1,n,n-2)$. This constrained sequential dominance (CSD) model preserves the first column of the tri-bimaximal (TB) mixing matrix (TM1) and has a reactor angle $theta_{13} sim (n-1) frac{sqrt{2}}{3} frac{m_2}{m_3}$. This is a generalisation of CSD ($n=1$) which led to TB mixing and arises almost as easily if $ngeq 1$ is a real number. We derive exact analytic formulas for the neutrino masses, lepton mixing angles and CP phases in terms of the four input parameters and discuss exact sum rules. We show how CSD ($n=3$) may arise from vacuum alignment due to residual symmetries of $S_4$. We propose a benchmark model based on $S_4times Z_3times Z_3$, which fixes $n=3$ and the leptogenesis phase $eta = 2pi/3$, leaving only two inputs $m_a$ and $m_b=m_{ee}$ describing $Delta m^2_{31}$, $Delta m^2_{21}$ and $U_{PMNS}$. The LS model predicts a normal mass hierarchy with a massless neutrino $m_1=0$ and TM1 atmospheric sum rules. The benchmark LS model additionally predicts: solar angle $theta_{12}=34^circ$, reactor angle $theta_{13}=8.7^circ$, atmospheric angle $theta_{23}=46^circ$, and Dirac phase $delta_{CP}=-87^{circ}$.
Neutrino mass sum rules are an important class of predictions in flavour models relating the Majorana phases to the neutrino masses. This leads, for instance, to enormous restrictions on the effective mass as probed in experiments on neutrinoless double beta decay. While up to now these sum rules have in practically all cases been taken to hold exactly, we will go here beyond that. After a discussion of the types of corrections that could possibly appear and elucidating on the theory behind neutrino mass sum rules, we estimate and explicitly compute the impact of radiative corrections, as these appear in general and thus hold for whole groups of models. We discuss all neutrino mass sum rules currently present in the literature, which together have realisations in more than 50 explicit neutrino flavour models. We find that, while the effect of the renormalisation group running can be visible, the qualitative features do not change. This finding strongly backs up the solidity of the predictions derived in the literature, and it thus marks a very important step in deriving testable and reliable predictions from neutrino flavour models.
We propose a $mu-tau$ reflection symmetric Littlest Seesaw ($mutau$-LSS) model. In this model the two mass parameters of the LSS model are fixed to be in a special ratio by symmetry, so that the resulting neutrino mass matrix in the flavour basis (after the seesaw mechanism has been applied) satisfies $mu-tau$ reflection symmetry and has only one free adjustable parameter, namely an overall free mass scale. However the physical low energy predictions of the neutrino masses and lepton mixing angles and CP phases are subject to renormalisation group (RG) corrections, which introduces further parameters. Although the high energy model is rather complicated, involving $(S_4times U(1))^2$ and supersymmetry, with many flavons and driving fields, the low energy neutrino mass matrix has ultimate simplicity.
In this paper, we investigate the double covering of modular $Gamma^{}_5 simeq A^{}_5$ group and derive all the modular forms of weight one for the first time. The modular forms of higher weights are also explicitly given by decomposing the direct products of weight-one forms. For the double covering group $Gamma^prime_5 simeq A^prime_5$, there exist two inequivalent two-dimensional irreducible representations, into which we can assign two right-handed neutrino singlets in the minimal seesaw model. Two concrete models with such a salient feature have been constructed to successfully explain lepton mass spectra and flavor mixing pattern. The allowed parameter space for these two minimal scenarios has been numerically explored, and analytically studied with some reasonable assumptions.
After the successful determination of the reactor neutrino mixing angle theta_13 ~ 0.16 eq 0, a new feature suggested by the current neutrino oscillation data is a sizeable deviation of the atmospheric neutrino mixing angle theta_23 from pi/4. Using the fact that the neutrino mixing matrix U = U_e^dagger U_ u, where U_e and U_ u result from the diagonalisation of the charged lepton and neutrino mass matrices, and assuming that U_ u has a i) bimaximal (BM), ii) tri-bimaximal (TBM) form, or else iii) corresponds to the conservation of the lepton charge L = L_e - L_mu - L_tau (LC), we investigate quantitatively what are the minimal forms of U_e, in terms of angles and phases it contains, that can provide the requisite corrections to U_ u so that theta_13, theta_23 and the solar neutrino mixing angle theta_12 have values compatible with the current data. Two possible orderings of the 12 and the 23 rotations in U_e, standard and inverse, are considered. The results we obtain depend strongly on the type of ordering. In the case of standard ordering, in particular, the Dirac CP violation phase delta, present in U, is predicted to have a value in a narrow interval around i) delta ~ pi in the BM (or LC) case, ii) delta ~ 3pi/2 or pi/2 in the TBM case, the CP conserving values delta = 0, pi, 2pi being excluded in the TBM case at more than 4sigma. In the addendum we discuss the implications of the latest 2013 data.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
