CPT, Majorana fermions, and particle physics beyond the Standard Model

This short essay aims to offer a discursive presentation of three scientific articles by Ettore Majorana highlighting the fundamental importance of one of them - the last one - for the investigation of the intimate constitution of matter. The search for evidence to support Majorana's thesis is the prime motivation of the conference "Multi-Aspect Young Oriented Advanced Neutrino Academy" at the G.P. Grimaldi Foundation in Modica, Sicily.

A quantum simulator is a device engineered to reproduce the properties of an ideal quantum model. It allows the study of quantum systems that cannot be efficiently simulated on classical computers. While a universal quantum computer is also a quantum simulator, only particular systems have been simulated up to now. Still, there is a wealth of successful cases, such as spin models, quantum chemistry, relativistic quantum physics and quantum phase transitions. Here, we show how...

This article is a pedagogical introduction to relativistic quantum mechanics of the free Majorana particle. This relatively simple theory differs from the well-known quantum mechanics of the Dirac particle in several important aspects. We present its three equivalent formulations. Next, so called axial momentum observable is introduced, and general solution of the Dirac equation is discussed in terms of eigenfunctions of that operator. Pertinent irreducible representations of...

This is an elementary account of neutrinos as Majarona particles and the search for neutrinoless double beta decays. It also includes some more ideas about neutrinos.

Minuscule violations of CPT and Lorentz invariance might arise in an extension of the standard model as suppressed effects from a more fundamental theory. In this contribution to the CarruthersFest, I present and answer some questions about CPT and the possibility of its violation.

The spontaneous breaking of the global lepton number, an accidental symmetry in the Standard Model of particle physics, results in a massless goldstone boson, the Majoron, which can be taken as a cold dark matter candidate with properties similar to these of the axion. In this letter, we propose a novel mass generation mechanism for the Majoron via radiative corrections induced by the interaction of a tiny lepton-number-violating (LNV) Majorana mass term of right-handed neutr...

Our present understanding of neutrino properties is reviewed with a particular emphasis on observable differences between Majorana and Dirac neutrinos. Current and future experimental efforts towards measuring neutrino properties are summarized. Consequences of the Majorana vs.Dirac nature of neutrinos on neutrino masses, neutrino decays, and neutrino electromagnetic properties are described.

A mechanism is presented, in which the mixing of right handed heavy Majorana neutrinos creates a $CP-$asymmetric universe. When these Majorana neutrinos subsequently decay more leptons than anti-leptons are produced. The lepton asymmetry created by this new mechanism can exceed by a few orders of magnitude any lepton asymmetry originating from direct decays. The asymmetry is finally converted into a baryon asymmetry during the electroweak phase transition.

The problem if existing neutrinos are Dirac or Majorana particles is considered in a very pedagogical way. After a few historical remarks we recall the theoretical description of neutral spin 1/2 particles, emphasizing the difference between chirality and helicity which is important in our discussion. Next we describe the properties of neutrinos in the cases when their interactions are given by the standard model and by its extensions (massive neutrinos, right-handed currents...

The thermodynamic equations of state for Majorana and Dirac fermions are quite different even in the limit of zero mass. The corresponding equations are derived from general principles, and then applied to neutrinos. The nature of the approach to equilibrium is explored, along with the subtleties of low or zero mass neutrinos interacting via purely left-handed currents. Possible applications to cosmology, supernovae, and supersymmetry are discussed.