This would prove that the neutrino is its own antiparticle (a majorana particle). There has to be mostly consensus in the particle physics community to resolve YES. So if one lab claims to have observed it but most other physicists think they're full of shit, that doesn't count.
Related questions
@JonathanRay My HEP guys says “it’s an open question. They are not currently treated as their own antiparticle”
@QuantumObserver if there was any significant cross section for neutrino-neutrino annihilation interactions it ought to be very obvious from astronomical observations so I'm leaning towards NO
When you say significant, do you mean something >= the cross-section for neutrino scattering from atomic nuclei?
@QuantumObserver Yeah. the longest observed half life is 1.8 x 10^22 years and the shortest double beta decay half life is 6.4x10^19 years so there's not a lot of room in between for low-probability interactions to be observable.
Can you re-explain that, but perhaps ELI5?
Basically I’m wondering why we’d expect neutrino-neutrino interactions to have greater cross-section than neutrino-proton or neutrino-neutron. The latter already require gigantic detectors, and I thought the cross section was determined in part by the masses of the particles.
@QuantumObserver Double beta decay is already so rare that we wouldn’t be able to observe a decay mode that happened in fewer than 1 in 300 double beta decays.
@JonathanRay It's not really acurate to think of nuetrinoless double beta decay as reguale double beta decay where the two nuetrinos annhililate. For a given neutrino mass you can’t really determine the neutrinoless double beta decay half life from the double beta decay half life because they have different kinematics.
That being said the GERDA experiment put a lower limit on the nuetrinoless double beta decay half life of Ge-76 of 1.8 x 10^26 yr and the double beta decay half life of Ge-76 is 1.9 x 10^21 yr, so its more like fewer than 1 in 100,000 double beta decays. See arxiv.org/abs/2009.06079
Planned experiments are hoping to improve this by 2 orders of magnitude although not in germanium.
@JonathanRay as far as I know there are certain isotopes that can only decay via a double beta decay