Precision Analysis of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Xe</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>136</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> Two-Neutrino <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:math> Spectrum in KamLAND-Zen and Its Impact on the Quenching of Nuclear Matrix Elements

We present a precision analysis of the ^{136}Xe two-neutrino ββ electron spectrum above 0.8 MeV, based on high-statistics data obtained with the KamLAND-Zen experiment. An improved formalism for the two-neutrino ββ rate allows us to measure the ratio of the leading and subleading 2νββ nuclear matrix elements (NMEs), ξ_{31}^{2ν}=-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 ξ_{31}^{2ν} range allowed by the QRPA is excluded by the present measurement at the 90% confidence level. Our analysis reveals that predicted ξ_{31}^{2ν} 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 ββ decay, ξ_{31}^{2ν} provides new insights toward reliable neutrinoless ββ NMEs.