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.

Flavor invariants and renormalization-group equations in the leptonic sector with massive Majorana neutrinos

In the present paper, we carry out a systematic study of the flavor invariants and their renormalization-group equations (RGEs) in the leptonic sector with three generations of charged leptons and massive Majorana neutrinos. First, following the approach of the Hilbert series from the invariant theory, we show that there are 34 basic flavor invariants in the generating set, among which 19 invariants are CP-even and the others are CP-odd. Any flavor invariants can be expressed as the polynomials of those 34 basic invariants in the generating set. Second, we explicitly construct all the basic invariants and derive their RGEs, which form a closed system of differential equations as they should. The numerical solutions to the RGEs of the basic flavor invariants have also been found. Furthermore, we demonstrate how to extract physical observables from the basic invariants. Our study is helpful for understanding the algebraic structure of flavor invariants in the leptonic sector, and also provides a novel way to explore leptonic flavor structures.

Complete one-loop matching of the type-I seesaw model onto the Standard Model effective field theory

In this paper, we accomplish the complete one-loop matching of the type-I seesaw model onto the Standard Model Effective Field Theory (SMEFT), by integrating out three heavy Majorana neutrinos with the functional approach. It turns out that only 31 dimension-six operators (barring flavor structures and Hermitian conjugates) in the Warsaw basis of the SMEFT can be obtained, and most of them appear at the one-loop level. The Wilson coefficients of these 31 dimension-six operators are computed up to $$ \mathcal{O} $$ O (M−2) with M being the mass scale of heavy Majorana neutrinos. As the effects of heavy Majorana neutrinos are encoded in the Wilson coefficients of these higher-dimensional operators, a complete one-loop matching is useful to explore the low-energy phenomenological consequences of the type-I seesaw model. In addition, the threshold corrections to the couplings in the Standard Model and to the coefficient of the dimension-five operator are also discussed.

Unified emergence of energy scales and cosmic inflation

In the quest for unification of the Standard Model with gravity, classical scale invariance can be utilized to dynamically generate the Planck mass MPl. However, the relation of Planck scale physics to the scale of electroweak symmetry breaking μH requires further explanation. In this paper, we propose a model that uses the spontaneous breaking of scale invariance in the scalar sector as a unified origin for dynamical generation of both scales. Using the Gildener-Weinberg approximation, only one scalar acquires a vacuum expectation value of υS ∼ (1016−17) GeV, thus radiatively generating $$ {M}_{\mathrm{P}1}\approx {\beta}_S^{1/2}{\upsilon}_S $$ M P 1 ≈ β S 1 / 2 υ S and μH via the neutrino option with right handed neutrino masses mN = yMυS ∼ 107 GeV. Consequently, active SM neutrinos are given a mass with the inclusion of a type-I seesaw mechanism. Furthermore, we adopt an unbroken Z2 symmetry and a Z2-odd set of right-handed Majorana neutrinos χ that do not take part in the neutrino option and are able to produce the correct dark matter relic abundance (dominantly) via inflaton decay. The model also describes cosmic inflation and the inflationary CMB observables are predicted to interpolate between those of R2 and linear chaotic inflationary model and are thus well within the strongest experimental constraints.

Precise capture rates of cosmic neutrinos and their implications on cosmology

We explore the potential of measurements of cosmological effects, such as neutrino spectral distortions from the neutrino decoupling and neutrino clustering in our Galaxy, via cosmic neutrino capture on tritium. We compute the precise capture rates of each neutrino species including such cosmological effects to probe them. These precise estimates of capture rates are also important in that the would-be deviation of the estimated capture rate could suggest new neutrino physics and/or a non-standard evolution of the universe. In addition, we discuss the precise differences between the capture rates of Dirac and Majorana neutrinos for each species, the required energy resolutions to detect each neutrino species and the method of reconstruction of the spectrum of cosmic neutrinos via the spectrum of emitted electrons, with emphasis on the PTOLEMY experiment.

Dark matter and torsion

Superheavy right-handed Majorana neutrinos are proposed as a promising candidate for dark matter, with dynamical axial torsion as the mediating agent.