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

Two powerful and straightforward methods are presented for probing the Majorana nature and CP violation of neutralinos at future $e^+e^-$ linear colliders.

I present an overview of the standard model, concentrating on its global continuous symmetries, both exact and approximate. There are four lectures, dedicated to spacetime symmetry, flavor symmetry, custodial symmetry, and scale symmetry. Topics include Weyl, Majorana, and Dirac spinors; massive neutrinos; electroweak symmetry breaking; effective field theory; and the hierarchy problem.

Unphysical particles are commonly ruled out from the solution of physical equations, as they fundamentally cannot exist in any real system and, hence, cannot be examined experimentally in a direct fashion. One of the most celebrated equations that allows unphysical solutions is the relativistic Majorana equation\cite{Majorana} which might describe neutrinos and other exotic particles beyond the Standard Model. The equation's physical solutions, the Majorana fermions, are pred...

The Standard Model is an up-to-date theory that best summarizes current knowledge in particle physics. Although some problems still remain open, it represents the leading model which all physicists refer to. One of the pillars which underpin the Standard Model is represented by the Lorentz invariance of the equations that form its backbone. These equations made it possible to predict the existence of particles and phenomena that experimental physics had not yet been able to d...

We consider the transformation properties of fermions under the discrete symmetries CPT, CP, and C in the presence of B-L violation. We thus generalize the analysis of the known properties of Majorana neutrinos, probed via neutrinoless double beta decay, to include the case of Dirac fermions with B-L violation, which can be probed via neutron-antineutron oscillations. We show that the resulting CPT phase has implications for the interplay of neutron-antineutron oscillations w...

The parity transformation law of the fermion field $\psi(x)$ is usually defined by the "$\gamma^{0}$-parity" $\psi^{p}(t,-\vec{x}) = \gamma^{0}\psi(t,-\vec{x})$ with eigenvalues $\pm 1$, while the "$i\gamma^{0}$-parity" $\psi^{p}(t,-\vec{x})=i\gamma^{0}\psi(t,-\vec{x})$ is required for the Majorana fermion. The compatibility issues of these two parity laws arise in generic fermion number violating theories where a general class of Majorana fermions appear. In the case of Majo...

We explain the relationship between Majorana neutrinos, which are their own antiparticles, and Majorana neutrino masses. We point out that Majorana masses would make the neutrinos very distinctive particles, and explain why many theorists strongly suspect that neutrinos do have Majorana masses. The promising approach to confirming this suspicion is to seek neutrinoless double beta decay. We introduce a toy model that illustrates why this decay requires nonzero neutrino masses...

We ask the question whether neutrino physics with momentum space Majorana spinors, the eigenvectors of the particle--antiparticle conjugation operator, C=i\gamma_2 K (with K standing for complex conjugation), is different but physics with Dirac spinors. First we analyze properties of Majorana spinors in great detail. We show that four dimensional, (4d), Majorana spinors are unsuited for the construction of a local quantum field because C invariance does not allow for a covari...

Heavy Majorana neutrinos beyond the standard model can simultaneously explain the origin of tiny neutrino masses and matter-antimatter asymmetry in our Universe. The existence of heavy Majorana neutrinos will also lead to lepton number violation and the rare lepton-number-violating $W$ decays are possible. With contributions from two different Majorana neutrinos, a nonzero CP asymmetry may be generated from the rate difference between $W$ decay and its CP-conjugate process. T...

This review is based on lectures given by M. J. Duff summarising the far reaching contributions of Ettore Majorana to fundamental physics, with special focus on Majorana fermions in all their guises. The theoretical discovery of the eponymous fermion in 1937 has since had profound implications for particle physics, solid state and quantum computation. The breadth of these disciplines is testimony to Majorana's genius, which continues to permeate physics today. These lectures ...