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

## TL;DR

This paper provides a high-precision analysis of the $^{136}$Xe two-neutrino double beta decay spectrum, measuring nuclear matrix element ratios and discussing implications for neutrinoless decay models.

## Contribution

It introduces an improved formalism for analyzing the two-neutrino $etaeta$ rate and measures the NME ratio $\xi^{2
u}_{31}$, offering new insights into NME quenching and decay mechanisms.

## Key findings

- Measured $\xi^{2
u}_{31}$ consistent with some theoretical models.
- Excluded part of QRPA predictions at 90% confidence level.
- Highlighted sensitivity of NME ratios to quenching and state contributions.

## 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), $\xi^{2\nu}_{31} = -0.26^{+0.31}_{-0.25}$. 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 $\xi^{2\nu}_{31}$ range allowed by the QRPA is excluded by the present measurement at the 90% confidence level. Our analysis reveals that predicted $\xi^{2\nu}_{31}$ 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, $\xi^{2\nu}_{31}$ provides new insights towards reliable neutrinoless $\beta\beta$ NMEs.