The Mystery of Neutrino Mass

The standard model of particle physics is, perhaps ironically, written in the language of quantum field theory. Particles manifest as a consequence of the oscillatory motion of the associated fields. All known fermions, particles with half-integral spin such as the electron and the quarks, are massive particles. Fermion mass is a direct consequence of the coupling of the fermion fields to the Higgs field, the existence of which was confirmed by the LHC experiment in 2012.

There is, however, an inconsistency hiding in the depths of this model. Neutrinos, tiny particles that make up the majority of matter in the Universe, do not receive their mass from the Higgs field. In fact, the standard model predicts neutrinos should be strictly massless. Thanks to recent observations of neutrino oscillations, we are certain that neutrinos have mass. The question is: where does it come from?

Chirality

The chirality operation can be pictured heuristically as taking a particle and exchanging it for its mirror image. The particle states before and after mirroring are denoted left-handed and right-handed states. The concept of “handedness” is principally derived from the relative orientations of a particle’s spin and its momentum.

The relative orientation of a particle’s spin and momentum determined its ‘handedness’ The chirality operation converts a left-handed particle to a right-handed particle and vice versa.

For example, some electrons are left-handed and some are right-handed. Hold a left-handed electron up to a mirror and you have a right-handed electron, and vice versa. The left-handed and right-handed components are known as the particle’s chiral states.

The Weak Force

The standard model features three fundamental interactions: the strong, weak, and electromagnetic forces. The weak interaction has worked up a mischievous reputation over the past 50 years. Whilst the strong and electromagnetic forces treat left-handed and right-handed particles on equal footing, the weak force exhibits a clear preference.

Only left-handed particle states experience the weak force. As neutrinos are produced exclusively by the weak force, there is no right-handed neutrino.

Massless Neutrinos

We have shown that only left-handed neutrino states are incorporated into the standard model. But what has this got to do with mass?

The origin of mass within the equations of the standard model can be traced back to terms that couple left-handed particle states to right-handed states. In other words, mass can be interpreted as the coupling strength between a particle’s two chiral states. As neutrinos have no right-handed component, the coupling, and consequently the mass, is zero.

Massive Neutrinos

There is a clear contradiction between the zero-mass prediction of the standard model and the experimentally verified neutrino mass. There are two main ways in which this discrepancy is nullified. It is worth mentioning prematurely that none of the upcoming ideas have been experimentally verified, or even implied.

  1. Sterile neutrinos: the right-handed neutrino exists but, as the weak interaction only couples to left-handed neutrinos, experiences no forces (except gravity).
  2. Heavy neutrinos: as well as the familiar “light neutrinos”, we postulate the existence of hypothetical “heavy neutrinos” that posess a right-handed component the light neutrinos couple to.

Allowing the familiar, left-handed, light neutrinos to couple to the new, heavy, right-handed neutrinos provides a passable explanation for the origin of neutrino mass. The new neutrino is required to be very massive to explain why we have never detected one.

Why would nature have produced two neutrinos with such incredibly different masses? An interesting consequence of the added heavy neutrino is that the masses of the respective neutrinos are not independent. In fact, as the mass of one neutrino is increased, the other necessarily decreases. This is known as the seesaw mechanism.

The seesaw mechanism is currently the most promising answer to the question of why the light neutrino mass is so small in the first place. The light neutrino mass is smaller than that of its fellow fermions by a factor of one million. A heavy neutrino with an astronomical mass ensures, via the seesaw mechanism, that this discrepancy can be understood.

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