Precision Analysis of the ${}^{136}$Xe Two-Neutrino $\beta \beta$ 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 $\beta \beta$ electron spectrum above 0.8 MeV, based on high-statistics data obtained with the KamLAND-Zen experiment. An improved formalism for the two-neutrino $\beta \beta$ rate allows us to measure the ratio of the leading and subleading $2\nu \beta \beta$ nuclear matrix elements (NMEs), ${\xi }_{31}^{2\nu }=-0.26_{-0.25}^{+0.31}$. 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 ${\xi }_{31}^{2\nu }$ range allowed by the QRPA is excluded by the present measurement at the 90% confidence level. Our analysis reveals that predicted ${\xi }_{31}^{2\nu }$ 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 $\beta \beta$ decay, ${\xi }_{31}^{2\nu }$ provides new insights towards reliable neutrinoless $\beta \beta$ NMEs.

arXiv comment7 pages, 4 figures

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