Isabel Cordero-Carrión, Martin Hirsch, Avelino Vicente
After showing that the neutrino mass matrix in all Majorana models can be described by a general master formula, we will present a master parametrization for the Yukawa matrices, also valid for all Majorana models, that automatically ensures agreement with neutrino oscillation data. The application of the master parametrization will be illustrated in an example model.
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After introducing a master formula for the Majorana neutrino mass matrix we present a master parametrization for the Yukawa matrices automatically in agreement with neutrino oscillation data. This parametrization can be used for any model that induces Majorana neutrino masses. The application of the master parametrization is also illustrated in an example model, with special focus on its lepton flavor violating phenomenology.
A generalized connection between the quantum mechanical Bargmann invariants and the geometric phases was established for the Dirac fermions. We extend that formalism for the Majorana fermions by defining proper quantum mechanical ray and Hilbert spaces. We then relate both the Dirac and Majorana type Bargmann invariants to the rephasing invariant measures of CP violation with the Majorana neutrinos, assuming that the neutrinos have lepton number violating Majorana masses. We then generalize the recursive parametrization for studying any unitary matrices to include the Majorana fermions, which …
Under the assumption that the neutrinos are Majorana particles we study how the lepton mass matrices can be transformed into the simple form which has the same physical quantities by removing redundant parameters. We propose the exact parametrization of the lepton mass matrices which reflects the small nu_e-nu_mu mixing and the large nu_mu-nu_tau mixing. The relations between the twelve parameters and the physical quantities are shown. Furthermore we calculate the MNS matrix by applying the assumptions used in the quark sector. Finally we also check the validity of these assumptions from the e…
On the orthogonal matrix in the Casas-Ibarra parametrization for the Yukawa interactions of Majorana neutrinos
本文推广了Majorana中微子的Casas-Ibarra参数化，考虑精确seesaw关系与PMNS矩阵非幺正性，推导出正交矩阵的解析表达式，揭示了其特定模式等价于对seesaw参数空间施加特殊条件。
We reconsider decays of pseudoscalar mesons (P) to neutrino pairs and possibly additional photons in presence of (light) Majorana neutrinos. For this purpose we derive a model-independent general parametrization of neutrino mass matrices with physically interpretable and irreducible set of parameters. The parametrization is valid for any number of neutrinos and interpolates smoothly between the heavy Majorana and the (pseudo)Dirac neutrino limits. We apply the new parametrization to the study of $P \rightarrow νν$ and $P \rightarrow ννγ$ decays within the SM extended by additional singlet ferm…
We study the exactly degenerate case for three lefthanded Majorana neutrinos building a general parametrization for the leptonic mixing matrix characterized by two angles and one CP violating phase and identify a weak-basis invariant relevant, in this case, for CP violation. After lifting the degeneracy, this parametrization accommodates the present data on atmospheric and solar neutrinos, as well as neutrinoless double beta decay. Some of the leptonic mixing ansätze suggested in the literature correspond to special cases of this parametrization.
Given the eventuality of neutrino and muon factories in the foreseeable future, all possible 2-to-2 processes involving two neutrinos, whether Dirac or Majorana ones, and two charged fermions are considered on the basis of the most general Lorentz invariant four-fermion effective interaction possible, in the limit of massless particles. Such a parametrization should enable the assessment of the sensitivity to physics beyond the Standard Model, including the eventual discrimination between the Dirac or Majorana character of neutrinos, of specific experimental beam and detector designs.
We discuss a general formula which allows to automatically reproduce experimental data for Majorana neutrino mass models, while keeping the complete set of the remaining model parameters free for general scans, as necessary in order to provide reliable predictions for observables outside the neutrino sector. We provide a proof of this master parametrization and show how to apply it for several well-known neutrino mass models from the literature. We also discuss a list of special cases, in which the Yukawa couplings have to fulfill some particular additional conditions.
We study mixing and CP violation of three left-handed Majorana neutrinos in the limit of exactly degenerate masses, identify the weak-basis invariant relevant for CP violation and show that the leptonic mixing matrix is parametrized only by two angles and one phase. After the lifting of the degeneracy, this parametrization accommodates the present data on atmospheric and solar neutrinos, as well as double beta decay. Some of the leptonic mixing ansatze suggested in the literature correspond to special cases of this parametrization.
We obtain a general parametrization for the neutrino Majorana mass matrix in which all possible deviations from tribimaximal mixing are given by three complex parameters, and the deviation from each tribimaximal mixing eigenvector is identified with precisely two of them. This parametrization provides a useful tool for classifying the corrections to exact tribimaximal mixing in flavor models.
Constrained Neutrino Mass Matrix and Majorana Phases
本研究从唯象学角度约束中微子质量矩阵，通过质量矩阵元的线性关系得到两类参数化下共53种不依赖模型的结构，可预言Majorana相位等振荡参数，并尝试用三类对称群实现这些结构。
In a novel parametrization of neutrino mixing and in the approximation of $τ$-lepton dominance, we show that the one-loop renormalization-group equations (RGEs) of Dirac neutrinos are different from those of Majorana neutrinos even if two Majorana CP-violating phases vanish. As the latter can keep vanishing from the electroweak scale to the typical seesaw scale, it makes sense to distinguish between the RGE running effects of neutrino mixing parameters in Dirac and Majorana cases. The differences are found to be quite large in the minimal supersymmetric standard model with sizable $\tanβ$, pro…
We reformulate the canonical seesaw mechanism in the case that the electroweak gauge symmetry is unbroken, and show that it can "formally" work and allow us to derive an exact seesaw formula for the light and heavy Majorana neutrinos. We elucidate the reason why there is a mismatch between the mass eigenstates of heavy Majorana neutrinos associated with thermal leptogenesis and those associated with the seesaw framework, and establish the exact and explicit relations between the "original" and "derivational" seesaw parameters by using an Euler-like parametrization of the $6\times 6$ active-ste…
Given the most general Lorentz invariant four-fermion effective interaction possible for two neutrinos and two charged fermions, whether quarks or leptons, all possible 2-to-2 processes involving two neutrinos, whether Dirac or Majorana ones, and two charged fermions are considered. Explicit and convenient expressions are given for the associated differential cross-sections. Such a parametrization should help assess the sensitivity to physics beyond the Standard Model of neutrino beam experiments which are in the design stage at neutrino factories.
We point out that the $τ$-lepton dominance in the one-loop renormalization-group (RG) equations of neutrino mixing quantities allows us to set a criterion to choose the most suitable parametrization of the lepton flavor mixing matrix $U$: its elements $U^{}_{3i}$ (for $i=1,2,3$) should be as simple as possible. Such a novel parametrization is quite different from the "standard" one used in the literature and can lead to greatly simplified RG equations for three mixing angles and the physical CP-violating phase(s) in the standard model or its minimal supersymmetric extension, no matter whether …
Advantages of the original symmetrical form of the parametrization of the lepton mixing matrix are discussed. It provides a conceptually more transparent description of neutrino oscillations and lepton number violating processes like neutrinoless double beta decay, clarifying the significance of Dirac and Majorana phases. It is also ideal for parametrizing scenarios with light sterile neutrinos.
The Casas-Ibarra parametrization is a description of the Dirac neutrino mass matrix M_D 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 M^\dagger_D M_D is apparently independent of V but dependent on O in this parametrization, a number of authors have taken it for grant that unflavored leptogenesis has nothing to do with CP violation at low energies. Here we question this observation by clarifying the physical meaning of O. We establish a clear relationship between O an…
Taking the standard parametrization of three-flavor neutrino mixing, we carefully examine the evolution of three CP-violating phases $(δ, α^{}_1, α^{}_2)$ with energy scales in the realistic limit $θ^{}_{13} \to 0$. If $m^{}_3$ vanishes, we find that the one-loop renormalization-group equation (RGE) of $δ$ does not diverge and its running has no quasi-fixed point. When $m^{}_3 \neq 0$ holds, we show that the continuity condition derived by Antusch {\it et al} is always valid, no matter whether the $τ$-dominance approximation is taken or not. The RGE running of $δ$ undergoes a quasi-fixed point…
We show that the $3\times 3$ lepton flavor mixing matrix $V$ can be expanded in powers of a Wolfenstein-like parameter $Λ\equiv |V_{μ3}| \sim 1/\sqrt{2}$, which measures the strength of flavor conversion in atmospheric neutrino oscillations. The term of ${\cal O}(Λ^2)$ is associated with the large mixing angle in solar neutrino oscillations. The Dirac phase of CP violation enters at or below ${\cal O}(Λ^8)$, and the Majorana phases of CP violation are not subject to the $Λ$-expansion. Terrestrial matter effects on this new parametrization in realistic long-baseline neutrino oscillation experim…
Minimal Majorana neutrino mass models
本研究扩展了适用于所有马约拉纳中微子质量模型的Casas-Ibarra参数化方法，可系统识别自由参数最少的最小模型，发现汤川矩阵组合$y^\dagger y$在特定场景下仅依赖一个实自由度，相关模型可通过重中微子与带电轻子味破坏衰变实验检验。
We study leptonic CP violation from a new perspective. For Majorana neutrinos, a new parametrization for leptonic mixing of the form $V=O_{23} O_{12} K_{a}^{i}\cdot O$ reveals interesting aspects that are less clear in the standard parametrization. We identify several important scenario-cases with mixing angles in agreement with experiment and leading to large leptonic CP violation. If neutrinos happen to be quasi-degenerate, this new parametrization might be very useful, e.g., in reducing the number of relevant parameters of models.
We present a new parametrization of the minimal seesaw model, expressing the heavy-singlet neutrino Dirac Yukawa couplings $(Y_ν)_{ij}$ and Majorana masses $M_{N_i}$ in terms of effective light-neutrino observables and an auxiliary Hermitian matrix $H.$ In the minimal supersymmetric version of the seesaw model, the latter can be related directly to other low-energy observables, including processes that violate charged lepton flavour and CP. This parametrization enables one to respect the stringent constraints on muon-number violation while studying the possible ranges for other observables by …
Searches for $ΔL=2$ decays are crucial to disentangle the Dirac vs Majorana nature of neutrinos. While neutrinoless nuclear double beta decays are the most promising tool to look for di-electron signals of $ΔL=2$, searches of di-lepton channels with other flavors are far less limited by statistics. We revisit the calculation of $ΔL=2$ decays of hyperons $B^-_i\to B^+_f\ell^-\ell'^-$. We compute the rates of these decays by including the hyperon form factors, which yields finite results in the one-loop model mechanism involving Majorana neutrinos (long-range contributions). In addition, we stud…
The recent recomputation of the neutrino fluxes from nuclear reactors relaxes the tension between the LSND and MiniBooNE anomalies and disappearance data when interpreted in terms of sterile neutrino oscillations. The simplest extension of the Standard Model with such fermion singlets is the addition of right-handed sterile neutrinos with small Majorana masses. Even when introducing three right-handed neutrinos, this scenario has less free parameters than the 3+2 scenarios studied in the literature. This begs the question whether the best fit regions obtained can be reproduced by this simplest…
In the framework of seesaw mechanism with three neutrino flavors, we propose tentatively an efficient parametrization for the spectra of Dirac and righthanded Majorana neutrino mass matrices in terms of three free parameters. Two of them are related to (and determined by) the corresponding parameters introduced previously for the mass spectra of charged leptons and up and down quarks. The third is determined from the experimental estimate of solar $Δm^2_{21}$. Then, the atmospheric $Δm^2_{32}$ is {\it predicted} close to its experimental estimation. With the use of these three parameters all l…
Enlightened by the idea of the 3 times 3 CKM angle matrix proposed recently by Harrison et al., we introduce the Dirac angle matrix Phi and the Majorana angle matrix Psi in the lepton sector for Dirac and Majorana neutrinos respectively. We show that in presence of the CP violation, the angle matrix Phi or Psi is entirely equivalent to the complex MNS matrix V itself, but has the advantage of being real, phase rephasing invariant, directly associated to the leptonic unitarity triangles (UTs) and do not depend on any particular parametrization of V. In this paper, we further analyzed how the an…
Experimental Constraints on Seesaw Parameters in the Wigner-like Parametrization
本文在三右手中微子规范跷跷板模型中采用类Wigner参数化和特殊对角拟设，精确计算轻子味破坏衰变与共振热轻子生成可观测量，并用最新实验限制约束模型参数。
Current experimental data guarantees the presence of physics beyond the Standard Model in the neutrino sector. The responsible physical description might show itself through virtual effects on low-energy observables. In particular, massive neutrinos are able to produce contributions to the triple gauge coupling $WWγ$. The present paper deals with the calculation, estimation and analysis of one-loop contributions from Majorana neutrinos to the Lorentz-covariant $WWγ$ parametrization. Our calculations show that CP-odd effects vanish exactly, whereas CP-even contributions, $Δκ$ and $ΔQ$, remain. …
In addition to three active neutrinos, one or more light sterile neutrinos have been conjectured to account for the LSND, MiniBooNE and reactor antineutrino anomalies (at the sub-eV mass scale) or for warm dark matter in the Universe (at the keV mass scale). Heavy Majorana neutrinos at or above the TeV scale have also been assumed in some seesaw models. Such hypothetical particles can weakly mix with active neutrinos, and thus their existence can be detected at low energies. In the (3+3) scenario with three sterile neutrinos we present a full parametrization of the 6 X 6 flavor mixing matrix i…
The evidence for neutrino oscillations implies that three neutrino flavors (ν_e, ν_μ, ν_τ) must have different mass states (ν_1, ν_2, ν_3). The most popular idea of generating tiny masses of ν_i is to introduce three heavy Majorana neutrinos N_i (for i = 1, 2, 3) into the standard model and implement the seesaw mechanism. In this approach the neutrino mixing matrix V appearing in the charged current interactions of ν_i is not unitary, and the strength of unitarity violation of V is associated with the matrix R which describes the strength of charged current interactions of N_i. We present an e…
We present a classification of possible parametrizations of the 3x3 lepton flavor mixing matrix in terms of the rotation and phase angles. A particular parametrization, which is most convenient to describe the observables of neutrino oscillations and that of the neutrinoless double beta decay, is studied in detail. The possibility to determine the Dirac- and Majorana-type CP-violating phases are also discussed.
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 …
The neutrino masses and flavor mixings, which are missing in the Standard Model (SM), can be naturally incorporated in the type-I seesaw extension of the SM with heavy Majorana neutrinos being singlet under the SM gauge group. If the heavy Majorana neutrinos are around the electroweak scale and their mixings with the SM neutrinos are sizable, they can be produced at high energy colliders, leaving characteristic signatures with lepton-number violations. Employing the general parametrization for the neutrino Dirac mass matrix in the minimal seesaw scenario, we perform a parameter scan and identi…
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 {\it 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 a…
We demonstrate that only two ansatz can produce the features of the neutrino mixing angles. The first ansatz comes from the quark-lepton grand unification; $ν_{Di} = V_{CKM} ν_α$ is satisfied for left-handed neutrinos, where $ν_{Di}$ are the Dirac mass eigenstates and $ν_α$ are the flavour eigenstates. The second ansatz comes from the assumption; $ν_{Di} = U_{bimaximal} ν_{i}$ is satisfied between the Dirac mass eigenstates $ν_{Di}$ and the light Majorana neutrino mass eigenstates $ν_{i}$, where $U_{bimaximal}$ is the bimaximal mixing matrix. By these two ansatz, the Maki-Nakagawa-Sakata matri…
We propose a flexible and model independent parametrization of the neutrino mixing matrix, which takes advantage of the fact that there are up to three small quantities in neutrino mixing phenomenology: (i) the deviation from maximal mixing of solar neutrinos, (ii) the mixing matrix element U_{e3} and (iii) the deviation from maximal mixing of atmospheric neutrinos. It is possible to quantify those three observations with a parameter λ\sim 0.2, which appears at least linearly in all elements of the mixing matrix. The limit λ-> 0 corresponds to exact bimaximal mixing. Present and future experim…
Rephasing invariants of CP violation for heavy and light Majorana neutrinos
该研究在标准跷跷板机制下推导了轻、重马约拉纳中微子相关矩阵的马约拉纳型与狄拉克型CP破坏重相位不变量，通过类欧拉块参数化显式计算并讨论其物理作用，指出这类不变量可在多种轻子破坏过程中显现。
We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs$\to 3$ partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to fully inclusive Higgs production and to the NLO corrections to Higgs production in association with a jet, in the full theory. The computation is performed using the differential equations method. Whenever possible, a basis of master integrals that are pure functions of uniform weight is used. The result is expressed in terms of one-fold integrals of polylogar…
Analytic formulation of Leptogenesis with neutrino oscillation data employing the general parametrization for neutrino mass matrix
本文推导了在一般参数化下CP不对称参数的解析表达式，研究了包含两代和三代RHN的热与非热轻子生成场景，指出最轻RHN质量在非热轻子生成中可为零或低至Sphaleron退耦温度。
The see-saw mechanism is a very attractive explanation for small neutrino masses, parametrized at the GUT scale by the right-handed Majorana mass matrix, ${\cal M}$, and the neutrino Yukawa matrix, ${\bf Y_ν}$. We show that in a SUSY model with universal soft terms, ${\cal M}$ and ${\bf Y_ν}$ can be calculated from the light neutrino masses, the MNS matrix, and ${\bf Y^{\dagger}_ν} {\bf Y_ν}$, which enters into the left-handed slepton radiative corrections. This suggests that in principle the GUT-scale inputs of the seesaw could be reconstructed from the neutrino and sneutrino mass matrices. W…
The possible existence of an eV-mass sterile neutrino, slightly mixing with ordinary active neutrinos, is not yet excluded by neutrino oscillation experiments. Assuming neutrinos to be Majorana particles, we explore the impact of such a sterile neutrino on the effective neutrino mass of neutrinoless double-beta decays $\langle m \rangle^\prime_{ee} \equiv m^{}_1 |V^{}_{e1}|^2 e^{{\rm i}ρ} + m^{}_2 |V^{}_{e2}|^2 + m^{}_3 |V^{}_{e3}|^2 e^{{\rm i}σ} + m^{}_4 |V^{}_{e4}|^2 e^{{\rm i}ω}$, where $m^{}_i$ and $V^{}_{ei}$ (for $i = 1, 2, 3, 4$) denote respectively the absolute masses and the first-row…
CP violation in light neutrino oscillations and heavy neutrino decays: a general and explicit seesaw-bridged correlation
本文在最小跷跷板框架下，通过分块参数化推导中微子振荡CP破坏的Jarlskog不变量显式表达式，并与重Majorana中微子衰变CP不对称性比较，揭示二者关联的直接或间接程度。
We give a comprehensive account of our proposed experimental method of using atoms or molecules in order to measure parameters of neutrinos still undetermined; the absolute mass scale, the mass hierarchy pattern (normal or inverted), the neutrino mass type (Majorana or Dirac), and the CP violating phases including Majorana phases. There are advantages of atomic targets, due to the closeness of available atomic energies to anticipated neutrino masses, over nuclear target experiments. Disadvantage of using atomic targets, the smallness of rates, is overcome by the macro-coherent amplification me…
If the neutrino mass spectrum turns out to be m^{}_3 < m^{}_1 < m^{}_2, one may choose to relabel it as m^{\prime}_1 < m^{\prime}_2 < m^{\prime}_3 such that all the masses of fundamental fermions with the same electrical charges are in order. In this case the columns of the 3\times 3 lepton flavor mixing matrix U should be reordered accordingly, and the resulting pattern U^\prime may involve one or two large mixing angles in the standard parametrization or its variations. Since the Majorana neutrino mass matrix keeps unchanged in such a mass relabeling, a possible μ-τreflection symmetry is res…
The origin of tiny neutrino masses and the baryon number asymmetry of the Universe are naturally interpreted by the canonical seesaw and leptogenesis mechanisms, in which there are the heavy Majorana neutrino mass matrix $M_{\rm R}$, the Dirac neutrino mass matrix $M_{\rm D}$, the charged-lepton mass matrix $M_\ell$ and the effective (light) neutrino mass matrix $M_ν$. We find that ${\rm Im}\left(\det\left[ M^\dagger_{\rm D} M_{\rm D}, M^\dagger_{\rm R} M_{\rm R} \right]\right)$, ${\rm Im}\left(\det\left[ M_\ell M^\dagger_\ell, M_νM^\dagger_ν\right]\right)$ and ${\rm Im}\left(\det\left[ M_\ell…
In the flavor basis where the mass eigenstates of three charged leptons are identified with their flavor eigenstates, one may diagonalize a 3 X 3 Majorana neutrino mass matrix M_nu by means of the standard parametrization of the 3 X 3 neutrino mixing matrix V. In this treatment the unphysical phases of M_nu have to be carefully factored out, unless a special phase convention for neutrino fields is chosen so as to simplify M_nu to M'_nu without any unphysical phases. We choose this special flavor basis and establish some exact analytical relations between the matrix elements of M'_nu M'_nu^dag …
Most of the free parameters in the Standard Model (SM) -- a quantum field theory which has successfully elucidated the behaviors of strong, weak and electromagnetic interactions of all the known fundamental particles, come from the lepton and quark flavors. The discovery of neutrino oscillations has proved that the SM is incomplete, at least in its lepton sector; and thus the door of opportunity is opened to exploring new physics beyond the SM and solving a number of flavor puzzles. In this review article we give an overview of important progress made in understanding the mass spectra, flavor …
Leptoquark-mediated Dirac neutrino mass and its impact on $B \to K ν\barν$ and $K \to πν\barν$ decays
该研究在标量轻子夸克模型中通过辐射机制生成狄拉克中微子质量，并发现右手中微子效应能显著增强B→Kνν̄和K→πνν̄衰变，同时预测R_D超出量在实验误差内。
Flavor Tomography of Long-Lived Neutrino-Mass Mediators: Probing the Neutrino Mass Ordering at the HL-LHC
该研究提出在HL-LHC通过长寿命带电粒子的延迟轻子信号，利用共享耦合条件确定的味比区分中微子质量序，约25个事例即可实现3σ区分，且不依赖CP相位δ_CP。
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