Benchmarking $^{136}$Xe Neutrinoless $ββ$ Decay Matrix Element Calculations with the $^{138}{\rm Ba}(p,t)$ Reaction

We used a high-resolution magnetic spectrograph to study neutron pair-correlated $0^+$ states in $^{136}$Ba, produced via the $^{138}{\rm Ba}(p,t)$ reaction. In conjunction with state-of-the-art shell model calculations, these data benchmark part of the dominant Gamow-Teller component of the nuclear matrix element (NME) for $^{136}$Xe neutrinoless double beta ($0νββ$) decay. We demonstrate for the first time an evaluation of part of a $0νββ$ decay NME by use of an experimental observable, presenting a new avenue of approach for more accurate calculations of $0νββ$ decay matrix elements.