What's the reason experiments look for the half-life of neutrinoless double beta decay?

Question

I've been reading some papers about looking for neutrinoless double beta decay. A couple of them talk about finding a lower limit for neutrinoless double beta decay. From what I understand double beta decay is already a very rare process that has an extremely long half-life, but I'm not entirely sure what this has to do with finding $0\nu \beta \beta$-decay. A specific example is from this paper: Search for Majorana Neutrinos Near the Inverted Mass Hierarchy Region with KamLAND-Zen. In the paper they say they found a lower limit for the $0\nu \beta \beta$-decay to be $T^{0\nu}_{1/2} \gt 1.07 \times10^{26}$ yr. I'm not sure what this means in terms of looking for $0\nu \beta \beta$-decay.

How does knowing this information benefit researchers when looking for $0\nu \beta \beta$-decay?

Is it because knowing the half-life provides a better approximation for the statistics of finding $0\nu \beta \beta$-decay?

Also, how is it possible for them to find the half-life of $0\nu \beta \beta$-decay if it's never been observed?

Answer 1

Suppose you and your colleagues perform a search for a particular neutrinoless double beta decay, and at the end of the experiment, after all your hard work, you have seen nothing. It happens. A lot.

OK, no Nobel prize this time. But it's still an important piece of information that can produce papers, PhD theses, and conference talks. You want to report the results. But how?

You can't say "This decay does not happen." Maybe it does, but you needed to look for longer (ten times? A hundred times longer?) to have a chance of seeing it.

You don't want to just say "We looked but we didn't see anything. Period." That's not very helpful to people planning other experiments, or to theorists working out what could be going on.

The half life (or mean life) is the language used to convey your result. You make a statement like "We see no decays. With our apparatus and our observation period, if the half life were less than $1.07 \times 10^{26}$ years we would have expected to have seen at last one decay, with 90% probability (according to the Poisson statistical distribution). So as we have seen nothing we say (with 90% confidence) that if the decay occurs at all, it's half life must be even bigger than that. "

Now other experimenters know that there's little point in doing an experiment unless it is sensitive to even rarer decays with longer half lives, and the theorists know that any theory predicting a shorter half life is not looking good.

(Technically it's more complicated as you will have background events from other causes and you have to compare the number you see with the expected background, but the principle is the same.)

Hopefully that helps with understanding the Wikipedia entry.