Low Energy CP Violation Research Articles

Minimal seesaw and leptogenesis with the smallest modular finite group

We propose a model for leptons based on the smallest modular finite group Γ2 ≅ S3 that, for the first time, accounts for both the hints of large low-energy CP-violation in the lepton sector and the matter-antimatter asymmetry of the Universe, generated by only two heavy right-handed neutrinos. These same states are also employed in a Minimal seesaw mechanism to generate light neutrino masses. Besides the heavy neutrinos, our particle content is the same as the Standard Model (SM), with the addition of one single modulus τ, whose vacuum expectation value is responsible for both the modular and CP-symmetry breakings. We show that this minimalistic SM extension is enough to get an excellent fit to low energy neutrino observables and to the required baryon asymmetry ηB. Predictions for the neutrino mass ordering, effective masses in neutrinoless double beta decay and tritium decay as well as for the Majorana phases are also provided.

Scalar-singlet assisted leptogenesis with CP violation from the vacuum

In the vanilla type-I seesaw leptogenesis scenario, CP violation required to generate the lepton asymmetries in the heavy Majorana neutrino decays stem from complex Dirac-type Yukawa couplings. In this paper we explore the case in which that CP violation originates from the vacuum expectation value of a complex scalar singlet at a very high scale. This non-trivial CP-violating phase can be successfully communicated to the low-energy neutrino sector via the heavy neutrino portal. The new scalar-singlet degrees of freedom generate new contributions to the CP asymmetries relevant for leptogenesis not only at the one-loop level but also through tree-level three-body decays. These are computed here for an arbitrary number of heavy neutrinos, Higgs doublets and scalar singlets. We also take into account the new decays and scattering processes that enter the unflavoured Boltzmann equations governing the heavy-neutrino particle densities and the (B – L)-asymmetry evolution. Having established the framework of interest, we present a simple model with two RH neutrinos, two Higgs doublets and a complex scalar singlet, supplemented with a Ƶ8 flavour symmetry. This symmetry minimises the number of free parameters without compromising the possibility of spontaneous CP violation and compatibility with neutrino data. In fact, the only viable Ƶ8 charge assignment shows a preference for a non-trivial spontaneous CP-violating phase, which in turn leads to a non-vanishing CP asymmetry due to the direct link between high- and low-energy CP violation. An interesting feature of this simple setup is that the usual wave and vertex type-I seesaw contributions to the CP asymmetry vanish due to the Ƶ8 symmetry. Thus, the observed baryon-to-photon ratio can be explained thanks to the new couplings among the heavy neutrinos and the new scalar degrees of freedom.

Connecting low-energy CP violation, resonant leptogenesis and neutrinoless double beta decay in a radiative seesaw model

We present a study of resonant leptogenesis in a radiative seesaw model. We consider the case where two quasi-degenerate right-handed neutrinos realize resonant leptogenesis, and the CP violation necessary to achieve leptogenesis occurs through the CP phases present in the neutrino mixing matrix. A numerical analysis is performed by taking the best-fit values from the current global data for three neutrino mixing angles and two mass-squared differences. We have shown how the predicted value of baryon asymmetry depends on the Dirac and Majorana CP phases. With the particular choice for the mass parameters, this model prefers a normal hierarchy of neutrino masses based on the value of baryon asymmetry predicted. Using the constrained CP phases, we evaluate the effective neutrino mass, which is relevant to the neutrinoless double beta decay.

Leptogenesis from low-energy CP violation in minimal left-right symmetric model

We perform a thermal unflavored leptogenesis analysis on minimal left-right symmetric models with discrete left-right symmetry identified as generalized parity or charge conjugation. When left-right symmetry is unbroken in the lepton Yukawa sector, the neutrino Dirac coupling matrix is completely determined by neutrino masses and mixing angles, allowing CP violation needed to generate leptogenesis totally resides in the low-energy sector. With two lepton asymmetry generation ways, both type I and mixed type I+II neutrino mass generation mechanisms are considered. After solving the Boltzmann equations numerically, we find that the low-energy CP phases in the lepton mixing matrix can successfully produce the observed baryon asymmetry, and in some cases, the Dirac CP phase can be the only source of CP violation. Finally, we discuss the interplay among low-energy CP phase measurements, leptogenesis, and neutrinoless double beta decay. We show that the viable models for successful leptogenesis can be probed in next-generation neutrinoless double-beta decay experiments.

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.

Leptogenesis and low-energy CP violation in a type-II-dominated left-right seesaw model

We consider leptogenesis in a left-right-symmetric seesaw scenario in which neutrino mass generation and leptogenesis are dominated by the type-II seesaw term. Motivated by grand unification, we assume that the neutrino Dirac mass matrix is dominated by a single entry of the order of the top-quark mass, which leaves the low-energy phases of the lepton mixing matrix as the only sources of CP violation. Working in a regime where the triplet scalar predominantly decays into leptons, this results in a predictive scenario based on a minimal number of parameters. We perform a detailed analysis of the flavored Boltzmann equations within a revised density matrix framework and demonstrate that the observed baryon asymmetry can be successfully generated in this simple model. We point out that the significance of flavor effects is limited, and we discuss the implications for low-energy observables such as the Dirac CP phase and neutrinoless double beta decay.

Low-energy CP violation and leptogenesis in a minimal seesaw model

We investigate whether CP phases in the neutrino mixing matrix can be the source of the CP violation necessary to achieve leptogenesis. In general, low-energy CP violation in the neutrino sector is not directly linked to leptogenesis, but we show that the low-energy leptonic CP violation can give rise to the CP asymmetry required for leptogenesis in a minimal seesaw model where the Dirac neutrino mass matrix contains one-zero texture. Performing numerical analyses based on the current results of the global fit to neutrino data and the measurement of baryon asymmetry, we study how the CP phases in the neutrino mixing matrix can be constrained and show how lepton asymmetry is sensitive to two heavy Majorana neutrino masses as well as CP phases. From the constraints on the neutrino parameters, the values of the effective neutrino mass contributing to the amplitude of neutrinoless double beta decay are predicted.

A direct link between unflavored leptogenesis and low-energy CP violation via the one-loop quantum corrections

In the type-I seesaw mechanism the Casas-Ibarra (CI) parametrization provides a convenient description of the Dirac neutrino mass matrix in terms of the light and heavy Majorana neutrino masses, the lepton flavor mixing matrix U and an unknown complex orthogonal matrix O. If O is assumed to be real, it will be impossible to generate unflavored thermal leptogenesis via the lepton-number-violating and CP-violating decays of the lightest heavy Majorana neutrino. We find that this observation can be invalidated after small but unavoidable quantum corrections to the CI parametrization are taken into account with the help of the one-loop renormalization-group equations (RGEs) between the seesaw and electroweak scales. We illustrate a novel and viable unflavored leptogenesis scenario of this kind based on the RGEs in the seesaw-extended standard model, and show its direct link to the CP-violating phases of U at low energies.

Bridging resonant leptogenesis and low-energy CP violation with an RGE-modified seesaw relation

We propose a special type-I seesaw scenario in which the Yukawa coupling matrix Yν can be fully reconstructed by using the light Majorana neutrino masses mi, the heavy Majorana neutrino masses Mi and the PMNS lepton flavor mixing matrix U. It is the RGE-induced correction to the seesaw relation that helps interpret the observed baryon-antibaryon asymmetry of the Universe via flavored resonant thermal leptogenesis with M1≃M2≪M3. We show that our idea works well in either the τ-flavored regime with equilibrium temperature T≃M1∈(109,1012] GeV or the (μ+τ)-flavored regime with T≃M1∈(105,109] GeV, provided the light neutrinos have a normal mass ordering. We find that the same idea is also viable for a minimal type-I seesaw model with two nearly degenerate heavy Majorana neutrinos.

Leptogenesis in the Neutrino Option

We examine the compatibility between the Neutrino Option, in which the electroweak scale is generated by PeV mass type I seesaw Majorana neutrinos, and leptogenesis. We find the Neutrino Option is consistent with resonant leptogenesis. Working within the minimal seesaw scenario with two heavy Majorana neutrinos N1, 2, which form a pseudo-Dirac pair, we explore the viable parameter space. We find that the Neutrino Option and successful leptogenesis are compatible in the cases of a neutrino mass spectrum with normal (inverted) ordering for 1.2 × 106 < M(GeV) < 8.8 × 106(2.4 × 106 < M(GeV) < 7.4 × 106), with M = (M1 + M2)/2 and M1, 2 the masses of N1, 2. Successful leptogenesis requires that ∆M/M ≡ (M2 − M1)/M ∼ 10−8. We further show that leptogenesis can produce the baryon asymmetry of the Universe within the Neutrino Option scenario when the requisite CP violation in leptogenesis is provided exclusively by the Dirac or Majorana low energy CP violation phases of the PMNS matrix.

Leptogenesis from low energy CP violation

We revisit the possibility of producing the observed baryon asymmetry of the Universe via thermal leptogenesis, where CP violation comes exclusively from the low-energy phases of the neutrino mixing matrix. We demonstrate the viability of thermal flavoured leptogenesis across seven orders of magnitude (106< T (GeV) < 1013), using modern numerical machinery, where the lower bound can be reached only if flavour effects are taken into account and its value depends on the allowed degree of cancellation between the tree-level and radiative contributions to the light neutrino masses. At very high scales (T ≫1012 GeV), we clarify that thermal leptogenesis is sensitive to the low-energy phases, in contradiction with what is usually claimed in the literature. In particular we demonstrate that Majorana-phase leptogenesis is in general viable while Dirac-phase leptogenesis requires some level of fine-tuning.

Combining texture zeros with a remnant CP symmetry in the minimal type-I seesaw

In the framework of the two right-handed neutrino seesaw model, we consider maximally-restrictive texture-zero patterns for the lepton Yukawa coupling and mass matrices, together with the existence of a remnant CP symmetry. Under this premise, we find that several textures are compatible with the most recent data coming from neutrino oscillation and neutrinoless double beta decay experiments. It is shown that, the maximum number of allowed texture zeros in the Dirac Yukawa coupling matrix is two, for an inverted neutrino mass spectrum. In contrast, for Yukawa coupling matrices with just one texture zero, both normal and inverted orderings of neutrino masses are compatible with data. In all cases, the predictions for the low-energy Dirac and Majorana CP-violating phases, and for the effective mass parameter relevant in neutrinoless double-beta decay experiments, are presented and discussed. We also comment on the impact of future experimental improvements in scrutinising texture-zero patterns with a remnant CP symmetry, within the minimal version of the seesaw mechanism considered here.

CP violation in the lepton sector and implications for leptogenesis

We review the current status of the data on neutrino masses and lepton mixing and the prospects for measuring the CP-violating phases in the lepton sector. The possible connection between low energy CP violation encoded in the Dirac and Majorana phases of the Pontecorvo–Maki–Nakagawa–Sakata mixing matrix and successful leptogenesis is emphasized in the context of seesaw extensions of the Standard Model with a flavor symmetry [Formula: see text] (and CP symmetry).

Nonzeroθ13andCPviolation in a model withA4flavor symmetry

Motivated by recent observations of non-zero $\theta_{13}$ from the Daya Bay and RENO experiments, we propose a renormalizable neutrino model with $A_4$ discrete symmetry accounting for deviations from the tri-bimaximal mixing pattern of neutrino mixing matrix indicated by neutrino oscillation data. In the model, the light neutrino masses can be generated by radiative corrections, and we show how the light neutrino mass matrix can be diagonalized by the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix whose entries are determined by the current neutrino data including the Daya Bay result. We show that the origin of the deviations from the TBM mixing is non-degeneracy of the neutrino Yukawa coupling constants, and unremovable CP phases in the neutrino Yukawa matrix give rise to both low energy CP violation measurable from neutrino oscillation and high energy CP violation.

Hybrid textures in minimal seesaw mass matrices

In the context of the minimal seesaw framework, we discuss the implications of Dirac and Majorana mass matrices in which two properties coexist, namely, equalities among matrix elements and texture zeros. Among the large number of general possibilities, only 12 patterns are found to be consistent with the global neutrino oscillation data at the level of the most minimal number of free parameters. The predictions of the allowed textures for mass hierarchy, θ 13 and effective mass governing neutrino-less double beta decay are discussed. We also explore the possibility of having non-zero CP violation for each allowed solution. We find that only one allowed solution can accommodate both low and high energy CP violation. We discuss the prediction of this solution for leptogenesis and explore the correlation, between leptogenesis and low energy CP violation.

Casas–Ibarra parametrization and leptogenesis

The Casas–Ibarra parametrization is a description of the Dirac neutrino mass matrix MD in terms of the neutrino mixing matrix V, an orthogonal matrix O and the diagonal mass matrices of light and heavy Majorana neutrinos in the type-I seesaw mechanism. Because MD†MD is apparently independent of V but dependent on O in this parametrization, a number of authors have claimed that unflavored leptogenesis has nothing to do with CP violation at low energies. Here we question this logic by clarifying the physical meaning of O. We establish a clear relationship between O and the observable quantities, and find that O does depend on V. We show that both unflavored leptogenesis and flavored leptogenesis have no direct connection with low-energy CP violation.

ON THE ROLE OF LOW-ENERGY CP VIOLATION IN LEPTOGENESIS

The link between low-energy CP violation and leptogenesis became more accessible with the understanding of flavor effects. However, a definite well-motivated model where such a link occurs was still lacking. Adjoint SU(5) is a simple grand unified theory where neutrino masses are generated through the Type I and Type III seesaw mechanisms, and the lepton asymmetry is generated by the fermionic triplet responsible for the Type III seesaw. We focus exclusively on the case of inverted hierarchy for neutrinos, and we show that successful flavored leptogenesis in this theory strongly points towards low-energy CP violation. Moreover, since the range of allowed masses for the triplet is very restricted, we find that the discovery at the LHC of new states present in the theory, together with proton decay and unification of gauge couplings, can conspire to provide a hint in favor of leptogenesis.

NonzeroUe3,CPviolation, and leptogenesis in a seesaw type softly brokenA4symmetric model

We have shown that nonzero U{sub e3} is generated in a seesaw type softly broken A{sub 4} symmetric model through a single parameter perturbation in m{sub D} in a single element. We have explored all possible 9 cases to study the neutrino mixing angles considering the best fitted values of {delta}m{sub {center_dot}}{sup 2} and {delta}m{sub atm}{sup 2} with all parameters real. We have extended our analysis for the complex case and demonstrated large low energy CP violation (J{sub CP}{approx_equal}10{sup -2}) and m{sub ee} in addition to mixing and mass pattern. We have also investigated leptogenesis and for a reasonable choice of model parameters compatible with low energy data, the Wilkinson Microwave Anisotropy Probe (WMAP) value of baryon asymmetry 6x10{sup -10} is obtained for right-handed neutrino mass scale M{sub 0}{approx_equal}10{sup 13} GeV. We have obtained a relation among the phases responsible for leptogenesis and have shown that those phases also have correlations with low energy CP violating phases.

Phenomenological consequences of four zero neutrino Yukawa textures

For type I seesaw and in the basis where the charged lepton and heavy right-handed neutrino mass matrices are real and diagonal, four has been shown to be the maximum number of zeros allowed in the neutrino Yukawa coupling matrix Y ν . These four zero textures have been classified into two distinct categories. We investigate certain phenomenological consequences of these textures within a supersymmetric framework. This is done by using conditions implied on elements of the neutrino Majorana mass matrix for textures of each category in Y ν . These conditions turn out to be stable under radiative corrections. Including the effective mass, which appears in neutrinoless double beta decay, along with the usual neutrino masses, mixing angles and phases, it is shown analytically and through scatter plots how restricted regions in the seesaw parameter space are selected by these conditions. We also make consequential statements on the yet unobserved radiative lepton flavor violating decays such as μ → e γ . All these decay amplitudes are proportional to the moduli of entries of the neutrino Majorana mass matrix. We also show under which conditions the low energy CP violation, showing up in neutrino oscillations, is directly linked to the CP violation required for producing successful flavor dependent and flavor independent lepton asymmetries during leptogenesis.

General CP violation in minimal left–right symmetric model and constraints on the right-handed scale

In minimal left–right symmetric theories, the requirement of parity invariance allows only one complex phase in the Higgs potential and one in the Yukawa couplings, leading to a two-phase theory with both spontaneous and explicit CP violations. We present a systematic way to solve the right-handed quark mixing matrix analytically in this model and find that the leading order solution has the same hierarchical structure as the left-handed CKM matrix with one more CP-violating phase coming from the complex Higgs vev. Armed with this explicit right-handed mixing matrix, we explore its implications for flavor changing and conserving processes in detail, low-energy CP-violating observables in particular. We report an improved lower bound on the W R mass of 2.5 TeV from Δ M K and Δ M B , and a somewhat higher bound (4 TeV) from kaon decay parameters ϵ, ϵ ′ , and neutron electric dipole moment. The new bound on the flavor-changing neutral Higgs mass is 25 TeV.