Discrete Flavor Symmetries and Lepton Masses and Mixings

Abstract

We discuss neutrino mass and mixing models based on discrete flavor symmetries. These models can include a variety of new interactions and non-standard particles such as sterile neutrinos, scalar Higgs singlets and multiplets. We point at connections of the models with leptogenesis and dark matter and the ways to detect the corresponding non-standard particles at intensity and energy frontier experiments.

Common origin of θ13 and dark matter within the flavor symmetric scoto-seesaw framework

“…To obtain the flavor structure of the Yukawa couplings the flavons φ s , φ a , φ T , ξ are introduced. The inclusion of flavon fields (SM gauge singlets) is a characteristic feature of models with discrete flavor symmetries [19][20][21][22][23][24][25]. In a similar manner, we also incorporate additional Z N discrete symmetries which forbid the exchange of flavon fields eliminating unwanted terms [20][21][22][23][24][25][126][127][128].…”

“…The inclusion of flavon fields (SM gauge singlets) is a characteristic feature of models with discrete flavor symmetries [19][20][21][22][23][24][25]. In a similar manner, we also incorporate additional Z N discrete symmetries which forbid the exchange of flavon fields eliminating unwanted terms [20][21][22][23][24][25][126][127][128]. In what follows, we will call the whole framework the Flavor-Scoto-Seesaw (FSS) model where each element of the FSS model's construction is well motivated towards understanding a common origin of θ 13 and DM.…”

“…For this purpose discrete symmetry groups such as A 4 , S 4 , A 5 , ∆ (27) are often used [18]. For a general overview and implementation of discrete symmetries in neutrino physics see [19][20][21][22][23][24][25]. Such discrete flavor symmetries can explain various fixed mixing schemes such as bi-maximal (BM), golden ratio (GR) and hexagonal (HG) [26][27][28][29][30] mixings, with the most popular one being the tri-bimaximal (TBM) mixing [31,32].…”

Soft breaking of the µ ↔ τ symmetry by S4 ⊗ Z2

“…Another important point is that, conforming to the experimental data, the PMNS mixing matrix exhibits large values in its entries, in addition, the second and third rows satisfy the relation |U µi | = |U τ i | (i = 1, 2, 3) in good approximation for the normal and inverted hierarchy. The aforementioned facts might be understood by means of a symmetry in the effective neutrino mass matrix, then the concept of flavor symmetry turn out being crucial to explain the mixings, and a variety of discrete symmetries [7,8,[8][9][10][11][12][13][14] have been applied to the lepton sector. In particular, the neutrino data seem to obey an approximated µ ↔ τ symmetry (for a complete review see [15]), that consists in the exchange label µ ↔ τ in the effective neutrino mass matrix when the charged lepton mass one is diagonal.…”

“…Despite this, from the model building point of view, the well studied µ ↔ τ symmetry has been a guide to construct lepton models [16][17][18][19][20][21][22][23][24] and there is a possibility that a soft breaking [21][22][23][25][26][27][28][29] of this symmetry can accommodate the experimental results so that there is still strong motivation to study on the µ ↔ τ symmetry. Apart from this, elaborated flavored models have been proposed to face the lepton mixings and related issues as leptogenesis, dark matter, and so forth [14,30,31].…”