Time Evolution of Lepton Number Carried by Majorana Neutrinos
Apriadi Salim Adam, Nicholas J. Benoit, Yuta Kawamura, Yamato Matsuo, Takuya Morozumi, Yusuke Shimizu, Yuya Tokunaga, Naoya Toyota
备注：
20 pages, 7 figures. arXiv admin note: text overlap with arXiv:2004.07664. In v3,references are corrected. In v4, Fig.7 is added. In v6,the typos in Eq.(24),(29-33), and (90) are corrected. In v7,Eq.(20) and an author address are corrected
We revisit the time evolution of the lepton family number for a SU(2) doublet consisting of a neutrino and a charged lepton. The lepton family number is defined through the weak basis of the SU(2) doublet, where the charged lepton mass matrix is real and diagonal. The lepton family number carried by the neutrino is defined by the left-handed current of the neutrino family. For this work we assume the neutrinos have Majorana mass. This Majorana mass term is switched on at time $t=0$ and the lepton family number is evolved. Since the operator in the flavor eigenstate is continuously connected to that of the mass eigenstate, the creation and annihilation operators for the two eigenstates are related to each other. We compute the time evolution of all lepton family numbers by choosing a specific initial flavor eigenstate for a neutrino. The evolution is studied for relativistic and nonrelativistic neutrinos. The nonrelativistic region is of particular interest for the Cosmic Neutrino Background predicted from big bang models. In that region we find the lepton family numbers are sensitive to Majorana and Dirac phases, the absolute mass, and mass hierarchy of neutrinos.
We discuss the various incarnations of a gauged B-L symmetry: 1) unbroken, it features Dirac neutrinos, neutrinogenesis to create the baryon asymmetry of our Universe, and a potentially light Z' boson; 2) broken by two units, we obtain the standard case of Majorana neutrinos, seesaw and thermal leptogenesis; 3) broken by four units, we find Dirac neutrinos with lepton-number-violating interactions, which can give rise to a new Dirac leptogenesis mechanism. We review and discuss the signatures distinguishing the three scenarios.
Heavy Majorana neutrinos are predicted in addition to ordinary active neutrinos in the models with the seesaw mechanism. We investigate the lepton number violation (LNV) in $B$ decays induced by such a heavy neutrino $N$ with GeV-scale mass. Especially, we consider the decay channel $B^+ \to μ^+ \, N \to μ^+ μ^+ π^-$ and derive the sensitivity limits on the mixing angle $Θ_μ$ by the future search experiments at Belle II and in $e^+ e^-$ collisions at the Future Circular Collider (FCC-ee).
Given the best-fit results of six neutrino oscillation parameters, we plot the Dirac and Majorana unitarity triangles (UTs) of the 3\times 3 lepton flavor mixing matrix to show their real shapes for the first time. The connections of the Majorana UTs with neutrino-antineutrino oscillations and neutrino decays are explored, and the possibilities of right or isosceles UTs are discussed. In the neutrino mass limit of m_1 \to 0 or m_3 \to 0, which is allowed by current experimental data, we show how the six triangles formed by the effective Majorana neutrino masses \langle m\rangle_{αβ} (for α, β=…
Motivated by the recent investigation of neutrinoless $τ$-lepton decays by the CLEO collaboration, we perform a systematic analysis of such decays in a possible new-physics scenario with heavy Dirac/Majorana neutrinos, including heavy-neutrino nondecoupling effects, finite quark masses, and quark as well as meson mixings. We find that $τ$-lepton decays into an electron or muon and a pseudoscalar or vector meson can have branching ratios close to the experimental sensitivity. Numerical estimates show that the predominant decay modes of this kind are $τ^-\to e^-ϕ$, $τ^-\to e^-ρ^0$, and $τ^-\to e…
We discuss the potential to observe lepton number violation (LNV) in displaced vertex searches for heavy neutral leptons (HNLs) at future lepton colliders. Even though a direct detection of LNV is impossible for the dominant production channel because lepton number is carried away by an unobservable neutrino, there are several signatures of LNV that can be searched for. They include the angular distribution and spectrum of decay products as well as the HNL lifetime. We comment on the perspectives to observe LNV in realistic neutrino mass models and argue that the dichotomy of Dirac vs Majorana…
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Observation of lepton number ($L$) violation by two units at colliders would provide evidence for the Majorana nature of neutrinos. We study signals of $L$-violation in the context of two popular models of neutrino masses, the type-II seesaw model and the Zee model, wherein small neutrino masses arise at the tree-level and one-loop level, respectively. We focus on $L$-violation signals at the LHC arising through the process $pp \to \ell^{\pm}\ell^{\prime \pm}$ + jets within these frameworks. We obtain sensitivity to $L$-violation in the type-II seesaw model for triplet scalar masses up to 700 …
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In this talk, we have reviewed the recent development on the time evolution of lepton family number carried by Majorana neutrinos \cite{Adam:2021qiq}. This article focuses on the subtle points of the derivation of the lepton family numbers and their time evolution. We also show how the time evolution is sensitive to $m_{ee}$ and $m_{eμ}$ components of the effective Majorana mass matrix by applying the formula to the two family case. The dependence on the Majorana phase is clarified and the implication on CNB (cosmic neutrino background) is also discussed.
In the light of the recent measurement of the leptonic mixing angle $θ_{13}$, implications of the latest mixing data have been investigated for non-minimal textures of lepton mass matrices assuming the neutrinos to be Majorana like. Large number of possible texture specific lepton mass matrices have been examined for their compatibility with the lepton mixing data in the case of normal hierarchy, inverted hierarchy and degenerate scenario of neutrino masses. Specifically, apart from other phenomenological quantities the implications of the lepton mixing angle $θ_{13}$ have been investigated on…
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Heavy neutral leptons (HNLs) are hypothetical particles able to explain several puzzles of fundamental physics, first and foremost - neutrino oscillations. Being sterile with respect to Standard Model interactions, these particles admit Majorana masses, allowing for violation of the total lepton number. Lepton number violating (LNV) processes thus become a key signature of HNLs, pursued by many experiments. In this work, we demonstrate that if HNLs are the sole origin of neutrino masses, destructive interference between Majorana states suppresses the same-sign di-lepton signal. In the phenomen…
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Several beyond the Standard Model scenarios introduce new heavy neutrinos, whose Dirac or Majorana nature could be tested by comparing the rates of lepton number violating and lepton number conserving processes: a Dirac fermion induces only the latter, while a Majorana one predicts the same rate for both of them. Nevertheless, in the presence of more than one Majorana fermion, this picture may change drastically due to interference effects. We focus on lepton number violating and lepton flavour violating semileptonic meson decays induced by two heavy Majorana fermions, exploring the necessary …
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Nonzero neutrino masses imply the existence of degrees of freedom and interactions beyond those in the Standard Model. A powerful indicator of what these might be is the nature of the massive neutrinos: Dirac fermions versus Majorana fermions. While addressing the nature of neutrinos is often associated with searches for lepton-number violation, there are several other features that distinguish Majorana from Dirac fermions. Here, we compute in great detail the kinematics of the daughters of the decays into charged-leptons and neutrinos of hypothetical heavy neutral leptons at rest. We allow fo…
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We study 2 --> n inelastic fermion-(anti)fermion scattering into multiple longitudinal weak gauge bosons and derive universal upper bounds on the scales of fermion mass generation by imposing unitarity of the S-matrix. We place new upper limits on the scales of fermion mass generation, independent of the electroweak symmetry breaking scale. We find that the strongest 2 --> n limits fall in a narrow range, 3-170 TeV (with n=2-24), depending on the observed fermion masses.
We computed the kinematics of Z-boson decay into a heavy-light neutrino pair when the Z-boson is produced at rest in electron-positron collisions, including the subsequent decay of the heavy neutrino into a visible final state containing a charged-lepton. We concentrated on heavy-neutrino masses of order dozens of GeV and the issue of addressing the nature of the neutrinos - Dirac fermions or Majorana fermions. We find that while it is not possible to tell the nature of the heavy and light neutrinos on an event-by-event basis, the nature of the neutrinos can nonetheless be inferred given a lar…
We investigate the possibility of a fourth sequential generation in the lepton sector. Assuming neutrinos to be Majorana particles and starting from a recent - albeit weak - evidence for a non-zero admixture of a fourth generation neutrino from fits to weak lepton and meson decays we discuss constraints from neutrinoless double beta decay, radiative lepton decay and like-sign di-lepton production at hadron colliders.
We propose that the observed large leptonic mixing may just reflect a quasidegeneracy of three Majorana neutrinos. The limit of exact degeneracy of Majorana neutrinos is not trivial, as leptonic mixing and even CP violation may occur. We conjecture that the smallness of $|U_{13}|$, when compared to the other elements of $U_{PMNS}$, may just reflect the fact that, in the limit of exact mass degeneracy, the leptonic mixing matrix necessarily has a vanishing element. We show that the lifting of the mass degeneracy can lead to the measured value of $|U_{13}|$ while at the same time accommodating t…
The scenario of baryogenesis through leptogenesis is reviewed in models involving heavy Majorana neutrinos. The various mechanisms of CP violation occurring in the out-of-equilibrium lepton-number-violating decays of heavy Majorana neutrinos are studied within a resummation approach to unstable-particle mixing. It is explicitly demonstrated how the resummation approach preserves crucial field-theoretic properties such as unitarity and CPT invariance. Predictions of representative scenarios are presented after solving numerically the Boltzmann equations describing the thermodynamic evolution of…
Neutrinoless hadron Lepton Number Violating (LNV) decays can be induced by virtual Majorana neutrino, which in turn indubitably show the Majorana nature of neutrinos. Many three-body LNV processes and Lepton Flavour Violating (LFV) processes have been studied extensively in theory and by experiment. As a supplement, we here study 75 four-body LNV (LFV) processes from heavy pseudoscalar $B$ and $D$ decays. Most of these processes have not been studied in theory and searched for in experiment, while they may have sizable decay rates. Since the four-body decay modes have the same vertexes and mix…
We study the possibility of having CP asymmetries in the decay Kaon(+/-) -> pion(-/+) lepton(+/-) lepton(+/-) (lepton = muon or electron). This decay violates Lepton Number by two units and occurs only if there are Majorana particles that mediate the transition. Even though the absolute rate is highly suppressed by current bounds, we search for Majorana neutrino scenarios where the CP asymmetry arising from the lepton sector could be sizeable. This is indeed the case if there are two or more Majorana neutrinos with similar masses in the range around 10^2 MeV. In particular, the asymmetry is po…
Majorana neutrinos naturally lead to a Lepton Number Violation (LNV). A superposition of Majorana states can mimic Dirac-type neutrinos, leading to its conservation (LNC). We demonstrate on the example of specific observables related to high and low energy processes how a strength of LNV correlates with neutrino parameters such as CP-phases, flavor mixings, mass ratios. We stress the coaction between low and high energy studies for putting phenomenological models to a quantitative test. Secondly, we conclude that in order to fully study the role of heavy neutrinos in search for New Physics (NP…
The texture zero mass matrices for the leptons and the seesaw mechanism are used to derive relations between the matrix elements of the lepton mixing matrix and the ratios of the neutrino masses.
In this paper, we study the time evolution of the expectation value of Majorana neutrino with the Schrödinger picture.The operators with the definite lepton number and operators with the definite mass are related to each other by a Bogolyubov transformation. Then the vacuum with the null lepton number is also related to the vacuum for the massive operator and it is written by the superposition of the vacuum for massive field and Majorana pairs condensed states. We choose the state with a definite lepton number $L$ $=1$ and the momentum ${\bf q}\ne 0$ as an initial state. By writing the state i…
The CP-violating phases associated with Majorana neutrinos can give rise to CP-violating effects even in processes that conserve total Lepton number, such as μ-> eee+, μ+ e -> e + e and others. After explaining the reasons that make this happen, we consider the calculation of the rates for the process of the form \ell_a + \ell_b -> \ell_a + \ell_c, and its conjugate \bar\ell_a + \bar\ell_b -> \bar\ell_a + \bar\ell_c, where \ell_a, \ell_b and \ell_c denote charged leptons of different flavors. In the context of the Standard Model with Majorana neutrinos, we show that the difference in the rates…
A two-loop induced radiative neutrino model is proposed as an extension of our previous work in which the first and second generation standard model fermion masses are generated at one-loop level in both quark and lepton sectors. Then we discuss current neutrino oscillation data, lepton flavor violations, muon anomalous magnetic moment, and a bosonic dark matter candidate, for both the normal and inverted neutrino mass hierarchy. Our numerical analysis shows that less hierarchical Yukawa coupling constants can fit the experimental data with TeV scale dark matter.
The electric dipole moments (EDMs) of charged leptons are significantly suppressed in standard model. It has been found previously that they are even more severely suppressed in seesaw type models by powers of tiny neutrino masses as far as a leptonic CP source is concerned. We investigate whether a Majorana-type Yukawa coupling between charged leptons and a doubly charged scalar can contribute significantly to their EDMs. An observable EDM would then help unravel the Majorana nature of neutrinos by a lepton number conserving quantity. We find that the EDMs are indeed parametrically large, of …
