# $2\nu\beta\beta$ vs. $2\nu$ECEC

Considering the recent observation of two-neutrino double electron capture ($$2\nu$$ECEC) by the XENON Experiment:

https://arxiv.org/abs/1904.11002

I was wondering why the half-life of this process is so much longer than the quite similar process of two-neutrino double beta-decay.

Considering crossing symmetry the two corresponding Feynman diagrams are basically the same:

The half-life of $$^{124}$$Xe was measured to be $$1.8\cdot 10^{-22}$$y

The half life of $$^{136}$$Xe is $$2.1\cdot 10^{-21}$$y

The difference therefore is about one order of magnitude.

The only explanation I could come up with is that the phase space factor for $$2\nu$$ECEC should be smaller than for $$2\nu\beta\beta$$ since the neutrino energy is fixed. However a factor of 10 feels rather large for me (it might still be right though). Are there any factors that I did not consider?

• This is a good question, but I would just put it down to phase space factors. In practice, a factor of $10$ difference is tiny! – knzhou Apr 30 at 9:35