Neutrino Majorana masses in a composite technicolor standard model

We show that the neutrino Majorana masses can be incorporated within a composite technicolor standard model. We discuss the bounds on the parameters of such a model arising from the failure to observe lepton-number violating processes.     

Majorana neutrinos and same-sign dilepton production at LHC and in rare meson decays

We discuss same-sign dilepton production mediated by Majorana neutrinos in high-energy proton–proton collisions for at the LHC energy TeV, and in the rare decays of the , and B mesons of the type . For the pp reaction, assuming one heavy Majorana neutrino of mass , we present discovery limits in the plane where are the mixing parameters. Taking into account the present limits from low-energy experiments, we show that at LHC one has sensitivity to heavy Majorana neutrinos up to a mass TeV in the dilepton channels , and , but the dilepton states will not be detectable due to the already existing constraints from neutrinoless double beta decay. We work out a large number of rare meson decays, both for the light and heavy Majorana neutrino scenarios, and argue that the present experimental bounds on the branching ratios are too weak to set reasonable limits on the effective Majorana masses. Received: 24 April 2001 / Published online: 29 June 2001     

Dimensional reduction of Weyl,Majorana and Majorana-Weyl spinors

We discuss the dimensional reduction for Weyl, Majorana, or Majorana-Weyl spinors coupled to pure d-dimensional (d ? 4) gravity. The only case where a realistic four-dimensional low-energy spectrum for the fermions may be obtained, is for a Majorana-Weyl spinor in d = 2 mod 8 dimensions. Chiral massless fermions are not excluded in this case. The minimal number of dimensions for the construction of a realistic theory out of pure gravity is d = 18.     

Overview of phases and phase transitions

We provide an overview of some modern developments in the theory of phases and phase transitions in classical and quantum systems. We show the link between non-ergodicity and fidelity in quantum systems and discuss topological phase transitions. We show that the quantum phase transitions are associated with qualitative changes in some properties of the quantum wavefunctions across the phase transition. We discuss the topological phase transition associated with p-wave superconductor since it is a topic of wide interest because of the possible observation of Majorana fermions.     

Weyl invariance and the origins of mass

By a uniform and simple Weyl invariant coupling of scale and matter fields, we construct theories that unify massless, massive, and partially massless excitations. Masses are related to tractor Weyl weights, and Breitenlohner–Freedman stability bounds in anti de Sitter amount to reality of these weights. The method relies on tractor calculus – mathematical machinery allowing Weyl invariance to be kept manifest at all stages. The equivalence between tractor and higher spin systems with arbitrary spins and masses is also considered.     

Leptogenesis from first principles in the resonant regime

The lepton asymmetry generated by the out-of-equilibrium decays of heavy Majorana neutrinos with a quasi-degenerate mass spectrum is resonantly enhanced. In this work, we study this scenario within a first-principle approach. The quantum field theoretical treatment is applicable for mass splittings of the order of the width of the Majorana neutrinos, for which the enhancement is maximally large. The non-equilibrium evolution of the mixing Majorana neutrino fields is described by a formal analytical solution of the Kadanoff–Baym equations, that is obtained by neglecting the back-reaction. Based on this solution, we derive approximate analytical expressions for the generated asymmetry and compare them to the Boltzmann result. We find that the resonant enhancement obtained from the Kadanoff–Baym approach is smaller compared to the Boltzmann approach, due to additional contributions that describe coherent transitions between the Majorana neutrino species. We also discuss corrections to the masses and widths of the degenerate pair of Majorana neutrinos that are relevant for very small mass splitting, and compare the approximate analytical result for the lepton asymmetry with numerical results.     

Massive Yang-Mills Field Theory with Conformal (Weyl) Invariance

A massive Yang-Mills field theory with the conformal (Weyl) invariance^[1] and gauge invariance is proposed. It involves the gravitational and various gauge interactions, in which all the mass terms appear as the uniform interactional form m(x) = KΦ(x). When the conformal and gauge symmetries are broken spontaneously, the Einstein gravitation emerges and all the fields obtain masses, this theory is renormalizable and unitary with the gravitation ignored. Finally we give a relation between the theory and the Higgs mechanism.     

Extension of an empirical charged lepton mass relation to the neutrino sector

It is known that the charged lepton masses obey to high precision an interesting empirical relation (Koide relation). In turn, the light neutrino masses cannot obey such a relation. We note that if neutrinos acquire their mass via the seesaw mechanism, the empirical mass relation could hold for the masses in the Dirac and/or heavy Majorana mass matrix. Examples for the phenomenological consequences are provided. We furthermore modify the mass relation for light neutrino masses including their Majorana phases, and show that it can be fulfilled in this case as well, with interesting predictions for neutrinoless double beta decay.     

Conformally Flat Spacetimes and Weyl Frames

We discuss the concepts of Weyl and Riemann frames in the context of metric theories of gravity and state the fact that they are completely equivalent as far as geodesic motion is concerned. We apply this result to conformally flat spacetimes and show that a new picture arises when a Riemannian spacetime is taken by means of geometrical gauge transformations into a Minkowskian flat spacetime. We find out that in the Weyl frame gravity is described by a scalar field. We give some examples of how conformally flat spacetime configurations look when viewed from the standpoint of a Weyl frame. We show that in the non-relativistic and weak field regime the Weyl scalar field may be identified with the Newtonian gravitational potential. We suggest an equation for the scalar field by varying the Einstein-Hilbert action restricted to the class of conformally-flat spacetimes. We revisit Einstein and Fokker’s interpretation of Nordstr?m scalar gravity theory and draw an analogy between this approach and the Weyl gauge formalism. We briefly take a look at two-dimensional gravity as viewed in the Weyl frame and address the question of quantizing a conformally flat spacetime by going to the Weyl frame.     

Classical probabilities for Majorana and Weyl spinors

We construct a map between the quantum field theory of free Weyl or Majorana fermions and the probability distribution of a classical statistical ensemble for Ising spins or discrete bits. More precisely, a Grassmann functional integral based on a real Grassmann algebra specifies the time evolution of the real wave function q_τ(t) for the Ising states τ. The time dependent probability distribution of a generalized Ising model obtains as . The functional integral employs a lattice regularization for single Weyl or Majorana spinors. We further introduce the complex structure characteristic for quantum mechanics. Probability distributions of the Ising model which correspond to one or many propagating fermions are discussed explicitly. Expectation values of observables can be computed equivalently in the classical statistical Ising model or in the quantum field theory for fermions.     

Neutrino textures in light of Super-Kamiokande data and a realistic string model

Motivated by the Super-Kamiokande atmospheric neutrino data, we discuss possible textures for Majorana and Dirac neutrino masses within the see-saw framework. There are two main purposes of this paper: first, to gain intuition into this area from a purely phenomenological analysis, and second, to explore to what extent it may be realized in a specific model. We comment initially on the simplified two-generation case, emphasizing that large mixing is not incompatible with a large hierarchy of mass eigenvalues. We also emphasize that renormalization-group effects may amplify neutrino mixing, and we present semi-analytic expressions for estimating this amplification. Several examples are then given of three-family neutrino mass textures, which may also accommodate the persistent solar neutrino deficit, with different assumptions for the neutrino Dirac mass matrices. We comment on a few features of neutrino mass textures arising in models with a U(1) flavour symmetry. Finally, we discuss the possible pattern of neutrino masses in a “realistic” flipped SU(5) model derived from string theory, illustrating how a desirable pattern of mixing may emerge. Both small- or large-angle MSW solutions are possible, while a hierarchy of neutrino masses appears more natural than near-degeneracy. This model contains some unanticipated features that may be relevant in other models also: The neutrino Dirac matrices may not be related closely to the quark mass matrices, and the heavy Majorana states may include extra gauge-singlet fields. Received: 6 November 1998 / Published online: 18 June 1999     

Euclidean Majorana and Weyl Spinors

The complex form algebra of Schwinger functions of a Dirac field on a Euclidean R ^d with arbitrary dimension d is decomposed into the form algebras of Majorana spinors and of Weyl spinors. The existence of real form algebras is investigated. The reality condition leads to severe restrictions in the case of Majorana forms which do not agree with the results of classical field theory. For all real form algebras Euclidean spinors are constructed as elements of a measure space.     

Supersymmetry and bosonization in three dimensions

We discuss on the possible existence of a supersymmetric invariance in purely fermionic planar systems and its relation to the fermion-boson mapping in three-dimensional quantum field theory. We consider, as a very simple example, the bosonization of free massive fermions and show that, under certain conditions on the masses, this model displays a supersymmetric-like invariance in the low energy regime. We construct the purely fermionic expression for the supercurrent and the non-linear supersymmetry transformation laws. We argue that the supersymmetry is absent in the limit of massless fermions where the bosonized theory is non-local.     

Opening the Pandora’s box of quantum spinor fields

Lounesto’s classification of spinors is a comprehensive and exhaustive algorithm that, based on the bilinears covariants, discloses the possibility of a large variety of spinors, comprising regular and singular spinors and their unexpected applications in physics and including the cases of Dirac, Weyl, and Majorana as very particular spinor fields. In this paper we pose the problem of an analogous classification in the framework of second quantization. We first discuss in general the nature of the problem. Then we start the analysis of two basic bilinear covariants, the scalar and pseudoscalar, in the second quantized setup, with expressions applicable to the quantum field theory extended to all types of spinors. One can see that an ampler set of possibilities opens up with respect to the classical case. A quantum reconstruction algorithm is also proposed. The Feynman propagator is extended for spinors in all classes.     

Entropy of the Universe and Hierarchical Dark Matter

We discuss the relationship between dark matter and the entropy of the universe, with the premise that dark matter exists in the form of primordial black holes (PBHs) in a hierarchy of mass tiers. The lightest tier includes all PBHs with masses below one hundred solar masses. The second-lightest tier comprises intermediate-mass PIMBHs within galaxies, including the Milky Way. Supermassive black holes at galactic centres are in the third tier. We are led to speculate that there exists a fourth tier of extremely massive PBHs, more massive than entire galaxies. We discuss future observations by the Rubin Observatory and the James Webb Space Telescope.     

Neutrino Masses Beyond the Tree Level

Models for Majorana neutrino masses can be classified according to the level in perturbation theory at which the effective dimension five operator LLHH is realized. The possibilities range from the tree-level up to the three-loop level realizations. We discuss some general aspects of this approach and speculate about a model independent classification of the possible cases. Among all the realizations, those in which the effective operator is induced by radiative corrections open the possibility for lepton number violation near—or at—the electroweak scale. We discuss some phenomenological aspects of two generic realizations: the Babu-Zee model and supersymmetric models with bilinear R-parity violation.     

Distinguishable RGE Running Effects Between Dirac Neutrinos and Majorana Neutrinos with Vanishing Majorana CP-Violating Phases

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 tan β, provided the masses of three neutrinos are nearly degenerate or have an inverted hierarchy.