Ultra-low well-understood background and highest detection efficiency pave the road towards the detection of neutrinoless double beta decay. For this goal, an outstanding sensitivity is key.

A good sensitivity is the result of a high experimental exposure (the amount of watched nuclei) and no background (being able to only observe the nuclei decay). The exposure is defined as the product of the mass of active isotope and the measuring time. No background equals the experiment being able to recognize the electron peak at the end of the electron energy spectrum. The better the energy resolution of the detectors, the narrower the search region δE gets.

These three main parameters allow determining the reaching potential of the experiment and its sensitivity:

• the mass M of the relevant isotope (⁷⁶Ge in our case), 
• the data-taking time T,
• and the background index B (in units of cts/(keV·kg·yr)) 

at the relevant energy range δE near Qββ, where the 0νββ decay signal peak is expected.

One of the most commonly considered mechanisms for the neutrinoless process involves the exchange of a virtual Majorana neutrino. Considering this scenario, the decay rate (Γ^0ν) is proportional to the square of a mass called effective Majorana neutrino mass m_ββ, which is a coherent sum of the three neutrino mass states.

It is convention for 0νββ decay experiments to report their sensitivity in therms of the half-life¹ τ½, which is related to the m_ββ, M, B and T in the following way:

This indicates that both a large mass and almost-zero background expectation are paramount. A high sensitivity experiment will need large mass and the minimal background to operate in the “background-free” regime. Being LEGEND-200 comissioned in the GERDA infrastructure, where the zero-background conditions in the region of interest were achieved, will also reach this background limit.

Zero-background experiments with such sensitivities, like the LEGEND experiment projects, offer the best scaling in sensitivity with increasing exposure and make an excellent candidate to pioneer the search for the 0νββ decay. 

The first stage of the experiment, LEGEND-200 is currently taking physics data since eraly 2023. The intended background index is 10⁻⁴ cts/(keV kg yr) and will allow reaching 10²⁷ yr discovery sensitivity within 5 yr lifetime.

¹Obtaining a half-life larger than the age of the Universe

The age of our universe is measured to be about 10¹⁰ years old. This poses the following question: how would then be possible to measure a half-life that is multitudes longer, potentially above τ_½ ~ 10²⁷ years? The answer to this question lies in the definition of the half-life itself; τ_½ is defined as the time a quantity is reduced to half of its initial value. In our particular case, τ_½ tells us about the time half of the ⁷⁶Ge isotopes decay into selenium atoms. This definition obeys the decay equation:

with N₀ the number of initial isotopes, t the time of measurement, τ the time it takes until the quantity is reduced to 1/e and N_t the number of isotopes left after a decaying mesuring time t. In simple terms, if we would only watch 2 nuclei, in average, after one half-life 1 would have decayed. However, we cannot wait that long to observe a decay, hence we take many many more nuclei in order to have a chance to observe some of them decaying. That is, the parameter left for us to adjust is N₀. This evidently translates in a large mass of germanium enriched in the ⁷⁶Ge isotope.

We recall that in one mol of substance there are the impressive amount of ~6·10²³ constituents. This is known as the Avogadro constant N_A. And in our case, Avogadro is on our side! Considering that Ge = 72.64 g/mol, our inicial Ge mass give us our N₀ value, approximately 10²⁶ Ge atoms in 200 kg of Ge. This is a huge number of nuclei!