Aspects of high scale leptogenesis with low-energy leptonic CP violation

Using the density matrix equations (DME) for high scale leptogenesis based on the type I seesaw mechanism, in which the CP violation (CPV) is provided by the low-energy Dirac or/and Majorana phases of the neutrino mixing (PMNS) matrix, we investigate the 1-to-2 and the 2-to-3 flavour regime transitions, where the 1, 2 and 3 leptogenesis flavour regimes in the generation of the baryon asymmetry of the Universe ηB are described by the Boltzmann equations. Concentrating on the 1-to-2 flavour transition we determine the general conditions under which ηB goes through zero and changes sign in the transition. Analysing in detail the behaviour of ηB in the transition in the case of two heavy Majorana neutrinos N1,2 with hierarchical masses, M1 ≪ M2, we find, in particular, that i) the Boltzmann equations in many cases fail to describe correctly the generation of ηB in the 1, 2 and 3 flavour regimes, ii) the 2-flavour regime can persist above (below) ∼ 1012 GeV (∼ 109 GeV), iii) the flavour effects in leptogenesis persist beyond the typically considered maximal for these effects leptogenesis scale of 1012 GeV. We further determine the minimal scale M1min at which we can have successful leptogenesis when the CPV is provided only by the Dirac or Majorana phases of the PMNS matrix as well as the ranges of scales and values of the phases for having successful leptogenesis. We show, in particular, that when the CPV is due to the Dirac phase δ, there is a direct relation between the sign of sin δ and the sign of ηB in the regions of viable leptogenesis in the case of normal hierarchical light neutrino mass spectrum; for the inverted hierarchical spectrum the same result holds for M1 ≲ 1013 GeV. The considered different scenarios of leptogenesis are testable and falsifiable in low-energy neutrino experiments.

Model independent analysis of Dirac CP violating phase for some well-known mixing scenarios

In this paper, we present a model independent analysis of Leptonic CP violation for some well-known mixing scenarios. In particular, we considered modified schemes for bimaximal (BM), democratic (DC), hexagonal (HG) and tribimaximal (TBM) mixing for our numerical investigation. These model independent corrections to mixing matrices are parametrized in terms of complex rotation matrices [Formula: see text] with related modified PMNS matrix of the forms [Formula: see text] where [Formula: see text] is a complex rotation in [Formula: see text] sector and [Formula: see text] is unperturbed mixing scheme. We present generic formulae for mixing angles, Dirac CP phase [Formula: see text] and Jarlskog invariant [Formula: see text] in terms of correction parameters. The parameter space of each modified mixing case is scanned for fitting neutrino mixing angles using [Formula: see text] approach and the corresponding predictions for Leptonic CP phase [Formula: see text] and Jarlskog invariant [Formula: see text] has been evaluated from allowed parameter space. The obtained ranges are reported for all viable cases.

Searching for non-unitary neutrino oscillations in the present T2K and NO$$\nu $$A data

The mixing of three active neutrino flavors is parameterized by the unitary PMNS matrix. If there are more than three neutrino flavors and if the extra generations are heavy iso-singlets, the effective $$3\times 3$$ 3 × 3 mixing matrix for the three active neutrinos will be non-unitary. We have analyzed the latest T2K and NO$$\nu $$ ν A data with the hypothesis of non-unitary mixing of the active neutrinos. We found that the 2019 NO$$\nu $$ ν A data slightly (at $$\sim 1\, \sigma $$ ∼ 1 σ CL) prefer the non-unitary mixing over unitary mixing. In fact, allowing the non-unitary mixing brings the NO$$\nu $$ ν A best-fit point in the $$\sin ^2{\theta _{23}}-\delta _{\mathrm {CP}}$$ sin 2 θ 23 - δ CP plane closer to the T2K best-fit point. The 2019 T2K data, on the other hand, cannot rule out any of the two mixing schemes. A combined analysis of the NO$$\nu $$ ν A and T2K 2019 data prefers the non-unitary mixing at $$1\, \sigma $$ 1 σ CL. We derive constraints on the non-unitary mixing parameters using the best-fit to the combined NO$$\nu $$ ν A and T2K data. These constraints are weaker than previously found. The latest 2020 data from both the experiments prefer non-unitarity over unitary mixing at $$1\, \sigma $$ 1 σ CL. The combined analysis prefers non-unitarity at $$2\, \sigma $$ 2 σ CL. The stronger tension, which exists between the latest 2020 data of the two experiments, also gets reduced with non-unitary analysis.

Renormalizable SO(10) GUT with Suppressed Dimension-5 Proton Decays

We study a renormalizable SUSY SO(10) GUT model where the Yukawa couplings of single 10, single $${\bf \overline{126}}$$ and single 120 fields, Y10, Y126, Y120, account for the quark and lepton Yukawa couplings and the neutrino mass. We pursue the possibility that Y10, Y126, Y120 reproduce the correct quark and lepton masses, CKM and PMNS matrices and neutrino mass differences, and at the same time suppress dimension-5 proton decays (proton decays via colored Higgsino exchange) through their texture, so that the soft SUSY breaking scale can be reduced as much as possible without conflicting the current experimental bound on proton decays. We perform a numerical search for such a texture, and investigate implications of that texture on unknown neutrino parameters, the Dirac CP phase of PMNS matrix, the lightest neutrino mass and the (1, 1)-component of the neutrino mass matrix in the charged lepton basis. Here we concentrate on the case when the active neutrino mass is generated mostly by the Type-2 seesaw mechanism, in which case we can obtain predictions for the neutrino parameters from the condition that dimension-5 proton decays be suppressed as much as possible.

Radiative decays of charged leptons as constraints of unitarity polygons for active-sterile neutrino mixing and CP violation

We calculate the rates of radiative $$\beta ^- \rightarrow \alpha ^- + \gamma $$ β - → α - + γ decays for $$(\alpha , \beta ) = (e, \mu )$$ ( α , β ) = ( e , μ ) , $$(e, \tau )$$ ( e , τ ) and $$(\mu , \tau )$$ ( μ , τ ) by taking the unitary gauge in the $$(3+n)$$ ( 3 + n ) active-sterile neutrino mixing scheme, and make it clear that constraints on the unitarity of the $$3\times 3$$ 3 × 3 Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix U extracted from $$\beta ^- \rightarrow \alpha ^- + \gamma $$ β - → α - + γ decays in the minimal unitarity violation scheme differ from those obtained in the canonical seesaw mechanism with n heavy Majorana neutrinos by a factor 5/3. In such a natural seesaw case we show that the rates of $$\beta ^- \rightarrow \alpha ^- + \gamma $$ β - → α - + γ can be used to cleanly and strongly constrain the effective apex of a unitarity polygon, and compare its geometry with the geometry of its three sub-triangles formed by two vectors $$U^{}_{\alpha i} U^*_{\beta i}$$ U α i U β i ∗ and $$U^{}_{\alpha j} U^*_{\beta j}$$ U α j U β j ∗ (for $$i \ne j$$ i ≠ j ) in the complex plane. We find that the areas of such sub-triangles can be described in terms of the Jarlskog-like invariants of CP violation $${{\mathcal {J}}}^{ij}_{\alpha \beta }$$ J α β ij , and their small differences signify slight unitarity violation of the PMNS matrix U.

Neutrino Masses and Mixings

This chapter discusses the search for and eventual discovery of the masses of neutrinos. It explains that observability of neutrino mass depends on neutrino flavor mixing. It introduces the PMNS matrix describing neutrino mixing and describes the experimental determination of the parameters of this matrix.

A systematic analysis of perturbations for hexagonal mixing matrix

We present a systematic analysis of perturbative Hexagonal (HG) mixing for describing recent global fit neutrino mixing data with normal and inverted hierarchy. The corrections to unperturbed mixing are parametrized in terms of small orthogonal rotations [Formula: see text] with modified PMNS matrix of the forms [Formula: see text]. Here, [Formula: see text] is rotation in [Formula: see text] sector and [Formula: see text] is unperturbed Hexagonal mixing matrix. The detailed numerical investigation of all possible cases is performed with scanning of parameter space using [Formula: see text] approach. We found that the perturbative schemes governed by single rotation are unable to fit the mixing angle data even at [Formula: see text] level. The mixing schemes which involve two rotation matrices only [Formula: see text] are successful in fitting all neutrino mixing angles within [Formula: see text] range for normal hierarchy (NH). However for inverted hierarchy (IH), only [Formula: see text] is most preferable as it can fit all mixing angles at [Formula: see text] level. The remaining perturbative cases are either excluded at [Formula: see text] level or successful in producing mixing angles only at [Formula: see text] level. To study the impact of phase parameter, we also looked into CP violating effects for single rotation case. The predicted value of [Formula: see text] lies in the range [Formula: see text] for [Formula: see text] and [Formula: see text] case with normal (inverted) hierarchy.