Neutral heavy lepton

Neutral heavy leptons (NHL) arise in some extensions to the Standard Model (SM) of particle physics. NHLs are also referred to in the literature as heavy neutrinos, right-handed neutrinos, or sterile neutrinos.

NHLs are a possible explanation for the origin of the neutrino mass and could be a constituent of dark matter. NHLs do not interact with matter via electromagnetic, strong or weak interactions, instead they only mix with the light SM neutrinos (via the seesaw mechanism) in such a way that the observed mixture becomes massive. According to the simple seesaw model of mixing, the mass of the neutrino is $m_{\text{D}}^{2}/M_{\text{NHL}}$ , where $M_{\text{NHL}}$ is the mass of the heavy neutrino (or NHL) and $m_{\text{D}}$ is a typical SM Dirac mass.

Overview

One of the unexpected extension to Standard Model was the fact that neutrinos have small, but non-zero mass. The SM does not explain why neutrinos are so much lighter than the charged leptons (electron, muons, taus). If we want the usual left-handed neutrino to be strictly massless then we must believe that there is a new exact symmetry preserved at all orders. There is no decent scheme that could introduce such a symmetry. An appealing alternative is that neutrinos, unlike any other fermions, are Majorana particles and have a unique mechanism of mass generation through mixing with heavy isosinglet. In other words, if neutrino has a very different mass scale, it may be because it is a very different types of a particle, a Majorana particle.

The suggestion that a neutrino could be a Majorana particle leads to the possible explanation of the negligible neutrino mass in comparison with the masses of other SM fermions. To explain the process of mixing between NHL and neutrinos we have to review the problem of neutrino mass in the SM and introduce the concepts of Dirac and Majorana particles.

Mass in the Standard Model

In the SM, particle masses are generated by the spontaneous breaking of the SU(2)_L × U(1) symmetry of the vacuum, which is commonly called the Higgs mechanism. In the Higgs mechanism, a doublet of scalar Higgs fields (or Higgs bosons), interact with other particles. In the process of spontaneous symmetry breaking, the Higgs field develops a vacuum expectation value and in the Lagrangian for neutrino wave functions, a massive Dirac field appears:

{\mathcal {L}}_{\mathrm {} }(\psi )={\bar {\psi }}(i\partial \!\!\!/-m)\psi -g{\bar {\psi }}_{L}\phi \psi _{R}

where m is the positive, real mass term.

That is the case for leptons, for charged particles like electrons. The SM does not have a corresponding Dirac mass terms for neutrinos. Weak interactions couple only to the left-handed currents so the right-handed neutrinos is not present in the Standard Model Lagrangian. As the result it is not possible to form mass terms for neutrino in the Standard Model.

In order to explain mass of neutrino we need an extension to SM.

Dirac and Majorana neutrinos

Two types of neutrinos originate from the following question: “Is a particle really different from its antiparticle?” While the answer is obvious for charged particles, since the positive are distinct from negative particles by their electromagnetic properties, it is not clear in the case of neutral particles. Depending on the answer, and for fermion-type particles, the neutral particles will be either Majorana or Dirac types (there are no distinct names for bosons). If the answer to the above question is "yes", then the fermion is a Dirac particle. If the answer is "no" and the fermion is identical to its antiparticle, then it is a Majorana particle. The concept of the Majorana particle was first introduced by Majorana in 1937. Examples for bosons are the neutral pion, the photon, the Z0 which are identical to their antiparticle and the neutral kaon, which is different from its antiparticle. An example for fermions is the neutron, which is different from its antiparticle, and which is therefore a Dirac particle according to the definition above. There are no known neutral fermions which could be of the Majorana type. The neutrino may be one. To put this in mathematical terms, we have to make use of the transformation properties of particles. We define a Majorana field as an eigenstate of charge conjugation. This definition is only for free fields. We have to generalize it to the interacting field. Neutrinos interact only via the weak interactions, which are not invariant to charge conjugation C. An interacting Majorana neutrino cannot be an eigenstate of C. The generalized definition is: "a Majorana neutrino field is an eigenstate of the CP transformation".

Consequently Majorana and Dirac neutrinos behave differently under CP transformations (actually Lorentz and CPT transformations). The distinction between Majorana and Dirac neutrinos is not only theoretical. A massive Dirac neutrino has nonzero magnetic and electric dipole moments, that could be observed experimentally, whereas a Majorana neutrino does not.

The Majorana and Dirac particles are different only if the neutrino rest mass is not zero. If the neutrino has no mass and travels at the speed of light, then the Lorentz transformation to a faster moving frame is not possible. The difference between the types disappears smoothly. For Dirac neutrinos, the dipole moments are proportional to mass and vanish for a massless particle. Both Majorana and Dirac mass terms however will appear in mass lagrangian if neutrino is to have a mass (which as we know it does).

Seesaw mechanism

Let's summarize our assumptions. We assumed that besides the left-handed neutrino, which couples to its family charged lepton in weak charged currents, there is also a right-handed partner N, which is a weak isosinglet and does not couple to any fermions or bosons directly. Both neutrinos have mass and the handedness is no longer preserved, thus when I use the term a left or right-handed neutrino, I mean that the state is mostly left or right-handed. To get the neutrino mass eigenstates, we had to diagonalize the general mass matrix M:

m_{\nu }={\begin{pmatrix}0&m_{D}\\m_{D}&M_{NHL}\end{pmatrix}}

where $M_{NHL}$ is big and $m_{D}$ is of intermediate size terms.

Apart from empirical, there is also a theoretical justification for seesaw mechanism in the next generation models. Both Grand Unification Theories (GUT from here on) and left-right symmetrical models predict the following relation

m_{\nu }<<m_{D}<<M_{NHL}

According to GUTs and left-right models, the right-handed neutrino is extremely heavy: $M_{NHL}\approx 10^{5}-10^{12}$ GeV, while the smaller eigenvalue is approximately equal to

m_{\nu }\approx {\frac {m_{D}^{2}}{M_{NHL}}}

This is the "seesaw mechanism": as NHL gets heavier, neutrino gets lighter.

NHL means mass for neutrinos

This is how NHL generate neutrino mass in extensions, through mixing process.

NHLs are very peculiar particles. NHLs do not have electromagnetic, strong or weak charge and consequently only interact with matter gravitationally. They could only be observed or produced through the mixing process with SM neutrinos. No surprise that NHL (or sterile neutrinos) are being discussed as candidates for dark matter. Under the See-Saw model the left-handed neutrino is the mixture of two Majorana neutrinos described above.

Attempts for experimental observation

The production and decay of NHLs could happen through the mixing with virtual (of mass shell) neutrinos. There were several experiments set up to discover or observe NHLs. For example NuTeV [1] (E815) experiment at Fermilab or LEP-l3 [2] at CERN. They all lead to establishing limits to observation, rather than actual observation of those particles.

References

A.G. Vaitaitis; et al. (1999). "Search for Neutral Heavy Leptons in a High-Energy Neutrino Beam". Physical Review Letters. 83 (24): 4943–4946. arXiv:hep-ex/9908011. Bibcode:1999PhRvL..83.4943V. doi:10.1103/PhysRevLett.83.4943. {{cite journal}}: Explicit use of et al. in: |author= (help)
J.A. Formaggio, J. Conrad, M. Shaevitz, A. Vaitaitis (1998). "Helicity effects in neutral heavy lepton decays". Physical Review D. 57 (11): 7037–7040. Bibcode:1998PhRvD..57.7037F. doi:10.1103/PhysRevD.57.7037.{{cite journal}}: CS1 maint: multiple names: authors list (link)