Seesaw Mechanism

The seesaw mechanism — in German Wippen-Mechanismus — is the best-known attempt to explain the fact that neutrinos do possess a mass, but an inconceivably small one.

The riddle

KATRIN has pushed the mass down to below 0.45 electronvolts from above; the oscillation spacings supply a lower limit of about 0.05.

By way of comparison: the electron weighs 511,000 electronvolts. A neutrino is therefore at least a million times lighter, presumably far more.

All the other masses in the Standard Model lie within a few orders of magnitude of one another. The neutrinos fall so far outside the frame that mere chance as an explanation satisfies nobody.

The idea of the seesaw

The mechanism assumes that alongside the known, left-handed neutrinos there are also right-handed ones. That they must exist follows already from the mass — the page on helicity explains why.

These partners would take part in no known force and would thus be even less conspicuous than ordinary neutrinos.

Decisive is the second assumption: they are very heavy. No known principle limits their mass from above. It could lie at 10¹⁴ gigaelectronvolts — close to the scale at which the forces of nature might be unified.

The mathematics of mass mixing then leads to a simple relation:

m_light ≈ m_D² / M_heavy

Here m_D is an ordinary mass of the order of magnitude of other particles and M_heavy is the large mass of the right-handed partner.

The picture of the seesaw follows of its own accord: the heavier the one side, the lighter the other. The tininess of the neutrino mass would be no accident but the shadow of something very heavy.

Why the calculation convinces

If one inserts for m_D a mass of the order of the top quark and for M_heavy the unification scale, neutrino masses in the range of hundredths of an electronvolt come out — exactly the range that the oscillation measurements suggest.

That so simple a formula yields the right order of magnitude without any need to bend parameters into shape counts as a strong argument. The idea arose at the end of the 1970s independently in several groups, among others with Peter Minkowski.

The connection to matter in the universe

The mechanism has a second, more far-reaching consequence.

The heavy right-handed neutrinos would be Majorana particles — their own antiparticle. In the early universe they would have been present in large numbers and would have decayed. If these decays proceed slightly differently for matter and antimatter, a surplus of leptons arises.

This could subsequently be converted into a surplus of quarks — and thus into ordinary matter. The idea is called leptogenesis and was formulated in 1986 by Fukugita and Yanagida.

It would explain why the universe consists of matter and not of nothing.

How this can be tested

The heavy partners themselves are out of reach. No conceivable accelerator would come near the necessary energies; ten orders of magnitude are missing.

The mechanism can nevertheless be tested, albeit indirectly. If neutrinoless double beta decay is found, then the neutrino is a Majorana particle — and the seesaw mechanism becomes very much more probable.

If it is not found, the question remains open. A non-find does not exclude the mechanism, only certain ranges of parameters.

Other versions

Besides the basic form there are variants that introduce other heavy particles instead of heavy neutrinos. They lead to similar formulae and are in part better testable at accelerators. Common to all is the basic idea: something very heavy makes something very light.

Sources

  • P. Minkowski: μ → eγ at a rate of one out of 10⁹ muon decays?, Physics Letters B 67, 421 (1977).
  • M. Fukugita, T. Yanagida: Barygenesis without grand unification, Physics Letters B 174, 45 (1986).