Precision measurement of the $^{136}$Xe two-neutrino $\beta\beta$ spectrum in KamLAND-Zen and its impact on the quenching of nuclear matrix elements

Author(s): Gando, A; Gando, Y; Hachiya, T; Ha Minh, M; Hayashida, S; Honda, Y; Hosokawa, K; Ikeda, H; Inoue, K; Ishidoshiro, K; Kamei, Y; Kamizawa, K; Kinoshita, T; Koga, M; Matsuda, S; Mitsui, T; Nakamura, K; Ono, A; Ota, N; Otsuka, S; Ozaki, H; Shibukawa, Y; Shimizu, I; Shirahata, Y; Shirai, J; Sato, T; Soma, K; Suzuki, A; Takeuchi, A; Tamae, K; Ueshima, K; Watanabe, H; Chernyak, D; Kozlov, A; Obara, S; Yoshida, S; Takemoto, Y; Umehara, S; Fushimi, K; Hirata, S; Berger, BE; Fujikawa, BK; Learned, JG; Maricic, J; Winslow, LA; Efremenko, Y; Karwowski, HJ; Markoff, DM; Tornow, W; O'Donnell, T; Detwiler, JA; Enomoto, S; Decowski, MP; Menendez, J; Dvornický, R; Simkovic, F; KamLAND-Zen Collaboration | Abstract: 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.