Large leptonic Dirac CP phase from broken democracy with random perturbations

Abstract

A large value of the leptonic Dirac CP phase can arise from broken democracy, where the mass matrices are democratic up to small random perturbations. Such perturbations are a natural consequence of broken residual S3 symmetries that dictate the democratic mass matrices at leading order. With random perturbations, the leptonic Dirac CP phase has a higher probability to attain a value around ±π/2. Comparing with the anarchy model, broken democracy can benefit from residual S3 symmetries, and it can produce much better, realistic predictions for the mass hierarchy, mixing angles, and Dirac CP phase in both quark and lepton sectors. Our approach provides a general framework for a class of models in which a residual symmetry determines the general features at leading order, and where, in the absence of other fundamental principles, the symmetry breaking appears in the form of random perturbations. *

Broken democracy with intermediate S2×S2 residual symmetry and random perturbations

“…It is interesting to see that the addition of the S L 2 ×S R 2 term only perturbs the 2-3 mixing while keeping the 1-2 and 1-3 mixings unaffected. This leads to very unique features compared to those explored in our previous paper [17].…”

“…3 is not unique due to the two-fold degeneracy between m 1 and m 2 . A 2 × 2 mixing among the degenerate eigenstates modifies all the mixing angles and the Dirac CP phase, but leaves a unique correlation among them, as elaborated in Section 2 of [17]. The mixing pattern in Eq.…”

“…Starting with democratic mass matrices for the quarks and charged leptons, and a diagonal Majorana neutrino mass matrix, we have V CKM = I and V PMNS = V † . Upon introducing perturbative corrections, the observed fermion masses and mixing angles can then be explained [17,46]. As global symmetries are not protected against the quantum gravity effects, the perturbations are naturally anarchical.…”

Scalar and gauge sectors in the 3-Higgs Doublet Model under the $$S_3$$ symmetry

“…The small value of tan θ found in these two examples indicates a maximal mixing between the S 3 singlet and doublet (see Eqs. (44,45)). It is also consistent with a numerical study of the S3-4H model (basically the S3-3H with one extra inert Higgs doublet), where compliance with the experimental Higgs bounds was found for small values of tan θ , assuming certain conditions on the Yukawa couplings [75].…”

“…Since then, the S 3 symmetry has been extensively 0123456789(). : V,-vol studied in different contexts, both in the quark [37][38][39][40][41][42][43][44][45][46] and lepton sectors [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64], due to its simplicity and predictivity, as well as in the scalar sector [65][66][67][68][69][70][71][72] where more predictions arise. More recently, there have been also studies of dark matter candidates in models with S 3 symmetry [73][74][75][76][77][78].…”