## Friday, March 17, 2023

### When Will We Hit Major Neutrinoless Double Beta Decay Thresholds?

We don't have an absolute neutrino mass measurement.

But due to the observed oscillations between neutrino mass eigenstates, we know that the sum of the three neutrino masses can't be less than about 60 meV if neutrinos have a "normal mass ordering" and can't be less than about 100 meV if neutrinos have an "inverted mass ordering."

The sum of the three neutrino masses could be greater than these minimums. If the sum of the three masses is greater than these minimums, the smallest neutrino mass is equal to a third of the amount by which the relevant minimum is exceeded.

So, for example, if the lightest of the three neutrino masses is 10 meV, then the sum of the three neutrino masses is about 90 meV in a normal mass ordering and about 130 meV in an inverted mass ordering.

If neutrinos have Majorana mass, the Majorana neutrino masses are related to the rate at which neutrinoless double beta decay can occur. The greater the Majorana mass, the more frequent neutrinoless double beta decay should be.

Right now, the non-detection of neutrinoless double beta decay so far puts a cap on the maximum Majorana mass of the neutrinos that is larger than the minimum mass of the inverted neutrino mass ordering. But, it is starting to get close.

As of July of 2022, we could determine with 90% confidence, based upon the non-detection of neutrinoless beta decay in a state of the art experiment establish a minimum half-life for the process of 8.3 * 10^25 years.

As illustrated by the chart below (from this source), an inverted mass hierarchy for neutrinos is ruled out at a half life of about 10^29 years (an improvement by a factor of 1200 in the excluded neutrinoless double beta decay half life over the current state of the art measurement).

Majorana mass of any kind becomes problematic even in a normal mass hierarchy in about 10^32 or 10^33 years (an improvement by a factor of 1.2 million to 12 million over the current state of the art).

We aren't there yet, but the likelihood that scientists will have experiments that will either detect neutrinoless double beta decay or rule out Majorana mass neutrinos even if they have a normal Majorana neutrino mass hiearchy, in perhaps 15-30 years, is quite good.

Ruling out an inverted Majorana neutrino mass hierarchy based upon the non-observation of neutrinoless double beta decay is something that can probably be achieved in half that amount of time, perhaps as soon as the year 2030.

It is probably easier to overestimate how long it will take to achieve this goal than it is to underestimate how long it will take.

Cosmology bounds on the neutrino mass, and hints from neutrino oscillation studies both favor a normal neutrino mass hierarchy over an inverted neutrino mass hierarchy. So, the discovery of Majorana mass neutrinos, if they do exist, is probably not just around the corner.

For what it is worth, there seem to be deep problems with both of the two main kinds of neutrino mass that have been proposed: Dirac mass and Majorana mass.

The biggest problem with Majorana mass seems to be our ability to clearly distinguish neutrinos and antineutrinos experimentally.

But, according to the same analysis, the biggest problem with Dirac mass is that it would seem to imply the existence of sterile neutrino counterparts to the three "active" neutrinos and three "active" antineutrinos, even though there is really no evidence to suggest that they exist at all.

I've asked about, and not received a compelling answer to, the question of why these two theoretical proposals are the only possible ways for neutrinos to acquire rest mass.

But, it seems to me that if your scientific analysis seems to rule (or at least strongly disfavor) both of the theoretical choices that you have considered to explain something, that it is likely that both possibilities are wrong and that the true answer is another approach that is not yet one of the choices.

It is certainly notable that neutrino masses are on the order of a billion (10^9) times smaller than their counterpart charged lepton masses.

Could that be somehow related to the ratio of the strength of the weak force that dominates the dynamics of neutrinos to the strength of the electromagnetic fore that dominates the dynamics of electrons, muons, and tau leptons, which is about 10^11?

What if every kind of Standard Model fermion had its electroweak self-interaction as one source of rest mass, and the Higgs mechanism as an additional source of rest mass in all charged Standard Model fermions but not in neutrinos?

Could neutrinos have a third kind of mass component, perhaps derived from particle self-interactions, that might exist in every particle, but which would only be measurable in neutrinos?

It is hard to think sensibly about that possibility so it is such untried ground.