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We report the first direct determination of the ground-state to ground-stateelectron-capture $Q$-value for the $^{72}$As to $^{72}$Ge decay by measuringtheir atomic mass difference utilizing the double Penning trap massspectrometer, JYFLTRAP. The $Q$-value was measured to be 4343.596(75)~keV,which is more than a 50-fold improvement in precision compared to the value inthe most recent Atomic Mass Evaluation 2020. Furthermore, the new $Q$-value wasfound to be 12.4(40)~keV (3.1 $\sigma$) lower. With the significant reductionof the uncertainty of the ground-state to ground-state $Q$-value value combinedwith the level scheme of $^{72}$Ge from $\gamma$-ray spectroscopy, we confirmthat the five potential ultra-low $Q$-value ${\beta^{+}}$-decay or electroncapture transitions are energetically forbidden, thus precluding all thetransitions as possible candidates for the electron neutrino massdetermination. However, the discovery of small negative $Q$-values opens up thepossibility to use $^{72}$As for the study of virtual $\beta$-$\gamma$transitions.

physical review. c

Direct measurement of the mass difference of $^{72}$As-$^{72}$Ge rules  out $^{72}$As as a promising $\beta$-decay candidate to determine the  neutrino mass