Precision Analysis of the ${}^{136}$Xe Two-Neutrino ${\hat{I}}^2{\hat{I}}^2$ Spectrum in KamLAND-Zen and Its Impact on the Quenching of Nuclear Matrix Elements

Abstract

We present a precision analysis of the ${}^{136}$Xe two-neutrino ${\hat{I}}^2{\hat{I}}^2$ electron spectrum above 0.8 MeV, based on high-statistics data obtained with the KamLAND-Zen experiment. An improved formalism for the two-neutrino ${\hat{I}}^2{\hat{I}}^2$ rate allows us to measure the ratio of the leading and subleading $2\hat{I}½{\hat{I}}^2{\hat{I}}^2$ nuclear matrix elements (NMEs), $\hat{I}{¾}_{31}^{2\hat{I}½}=-0.26_{-0.25}^{+0.31}$. Theoretical predictions from the nuclear shell model and the majority of the quasiparticle random-phase approximation (QRPA) calculations are consistent with the experimental limit. However, part of the $\hat{I}{¾}_{31}^{2\hat{I}½}$ range allowed by the QRPA is excluded by the present measurement at the 90% confidence level. Our analysis reveals that predicted $\hat{I}{¾}_{31}^{2\hat{I}½}$ values are sensitive to the quenching of NMEs and the competing contributions from low- and high-energy states in the intermediate nucleus. Since these aspects are also at play in neutrinoless ${\hat{I}}^2{\hat{I}}^2$ decay, $\hat{I}{¾}_{31}^{2\hat{I}½}$ provides new insights towards reliable neutrinoless ${\hat{I}}^2{\hat{I}}^2$ NMEs.

7 pages, 4 figures