Precision Analysis of the 136Xe Two-Neutrino ββ Spectrum in KamLAND-Zen and Its Impact on the Quenching of Nuclear Matrix Elements

We present a precision analysis of the Xe-136 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(-0.25)(+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(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. Because these aspects are also at play in neutrinoless beta beta decay, xi(2 nu)(31) provides new insights toward reliable neutrinoless beta beta NMEs.