The current status of our knowledge of the 3-neutrino mixing parameters and of the CP violation in the lepton sector is summarised. The non-Abelian discrete symmetry approach to understanding the ...observed pattern of neutrino mixing and the related predictions for neutrino mixing angles and leptonic Dirac CP violation are reviewed. Possible tests of these predictions using the existing data on neutrino mixing angles as well as prospective data from current and future neutrino oscillation experiments (T2K, NO
ν
A, Daya Bay, T2HK, T2HKK, DUNE) are also discussed.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
A
bstract
The formalism of combined finite modular and generalised CP (gCP) sym-metries for theories of flavour is developed. The corresponding consistency conditions for the two symmetry ...transformations acting on the modulus
τ
and on the matter fields are derived. The implications of gCP symmetry in theories of flavour based on modular invariance described by finite modular groups are illustrated with the example of a modular
S
4
model of lepton flavour. Due to the addition of the gCP symmetry, viable modular models turn out to be more constrained, with the modulus
τ
being the only source of CP violation.
Using the fact that the neutrino mixing matrix U=Ue†Uν, where Ue and Uν result from the diagonalisation of the charged lepton and neutrino mass matrices, we consider a number of forms of Uν ...associated with a variety of discrete symmetries: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding iii) to the conservation of the lepton charge L′=Le−Lμ−Lτ (LC), iv) to golden ratio type A (GRA) mixing, v) to golden ratio type B (GRB) mixing, and vi) to hexagonal (HG) mixing. Employing the minimal form of Ue, in terms of angles and phases it contains, that can provide the requisite corrections to Uν so that reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 have values compatible with the current data, including a possible sizable deviation of θ23 from π/4, we discuss the possibility to obtain predictions for the CP violation phases in the neutrino mixing matrix. Considering the “standard ordering” of the 12 and the 23 rotations in Ue and following the approach developed in 1 we derive predictions for the Dirac phase δ and the rephasing invariant JCP in the cases of GRA, GRB and HG forms of Uν (results for the TBM and BM (LC) forms were obtained in 1). We show also that under rather general conditions within the scheme considered the values of the Majorana phases in the PMNS matrix can be predicted for each of the forms of Uν discussed. We give examples of these predictions and of their implications for neutrinoless double beta decay. In the GRA, GRB and HG cases, as in the TBM one, relatively large CP violation effects in neutrino oscillations are predicted (|JCP|∼(0.031–0.034)). Distinguishing between the TBM, BM (LC), GRA, GRB and HG forms of Uν requires a measurement of cosδ or a relatively high precision measurement of JCP.
We study models of lepton masses and mixing based on broken modular invariance. We consider invariance under the finite modular group Γ4≃S4 and focus on the minimal scenario where the expectation ...value of the modulus is the only source of symmetry breaking, such that no flavons need to be introduced. After constructing a basis for the lowest weight modular forms, we build two minimal models, one of which successfully accommodates charged lepton masses and neutrino oscillation data, while predicting the values of the Dirac and Majorana CPV phases.
The problem of normalisation of the modular forms in modular invariant lepton and quark flavour models is discussed. Modular invariant normalisations of the modular forms are proposed.
In the framework of the modular symmetry approach to lepton flavour, we consider a class of theories where matter superfields transform in representations of the finite modular group Γ5 ≃ A5. We ...explicitly construct a basis for the 11 modular forms of weight 2 and level 5. We show how these forms arrange themselves into two triplets and a quintet of A5. We also present multiplets of modular forms of higher weight. Finally, we provide an example of application of our results, constructing two models of neutrino masses and mixing based on the supersymmetric Weinberg operator.
We investigate models of charged lepton and neutrino masses and lepton mixing based on broken modular symmetry. The matter fields in these models are assumed to transform in irreducible ...representations of the finite modular group Γ4 ≃ S4. We analyse the minimal scenario in which the only source of symmetry breaking is the vacuum expectation value of the modulus field. In this scenario there is no need to introduce flavon fields. Using the basis for the lowest weight modular forms found earlier, we build minimal phenomenologically viable models in which the neutrino masses are generated via the type I seesaw mechanism. While successfully accommodating charged lepton masses, neutrino mixing angles and mass-squared differences, these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino mass scale), of the Dirac and Majorana CP violation (CPV) phases, as well as specific correlations between the values of the atmospheric neutrino mixing parameter sin2θ23 and i) the Dirac CPV phase δ, ii) the sum of the neutrino masses, and iii) the effective Majorana mass in neutrinoless double beta decay. We consider also the case of residual symmetries ℤ3ST and ℤ2S respectively in the charged lepton and neutrino sectors, corresponding to specific vacuum expectation values of the modulus.
A
bstract
In modular-invariant models of flavour, hierarchical fermion mass matrices may arise solely due to the proximity of the modulus
τ
to a point of residual symmetry. This mechanism does not ...require flavon fields, and modular weights are not analogous to Froggatt-Nielsen charges. Instead, we show that hierarchies depend on the decomposition of field representations under the residual symmetry group. We systematically go through the possible fermion field representation choices which may yield hierarchical structures in the vicinity of symmetric points, for the four smallest finite modular groups, isomorphic to
S
3
,
A
4
,
S
4
, and
A
5
, as well as for their double covers. We find a restricted set of pairs of representations for which the discussed mechanism may produce viable fermion (charged-lepton and quark) mass hierarchies. We present two lepton flavour models in which the charged-lepton mass hierarchies are naturally obtained, while lepton mixing is somewhat fine-tuned. After formulating the conditions for obtaining a viable lepton mixing matrix in the symmetric limit, we construct a model in which both the charged-lepton and neutrino sectors are free from fine-tuning.
A
bstract
We study the problem of modulus stabilisation in the framework of the modular symmetry approach to the flavour problem. By analysing simple UV-motivated CP-invariant potentials for the ...modulus
τ
we find that a class of these potentials has (non-fine-tuned) CP-breaking minima in the vicinity of the point of
ℤ
3
ST
residual symmetry,
τ
≃
e
2
πi
/3
. Stabilising the modulus at these novel minima breaks spontaneously the CP symmetry and can naturally explain the mass hierarchies of charged leptons and possibly of quarks.
A
bstract
We perform a detailed analysis of the one-loop corrections to the light neutrino mass matrix within low scale type I seesaw extensions of the Standard Model and their implications in ...experimental searches for neutrinoless double beta decay. We show that a sizable contribution to the effective Majorana neutrino mass from the exchange of heavy Majorana neutrinos is always possible, provided one requires a fine-tuned cancellation between the tree-level and one-loop contribution to the light neutrino masses. We quantify the level of fine-tuning as a function of the seesaw parameters and introduce a generalisation of the Casas-Ibarra parametrization of the neutrino Yukawa matrix, which easily allows to include the one-loop corrections to the light neutrino masses.
PDF
