Two-neutrino ββ decay of 136Xe to the first excited 0+ state in 136Ba

We calculate the nuclear matrix element for the two-neutrino $\beta\beta$ decay of $^{136}$Xe into the first excited $0^+$ state of $^{136}$Ba. We use different many-body methods: the quasiparticle random-phase approximation (QRPA) framework, the nuclear shell model, the interacting boson model (IBM-2), and an effective field theory (EFT) for $\beta$ and $\beta\beta$ decays. While the QRPA suggests a decay rate at the edge of current experimental limits, the shell model points to a half-life about two orders of magnitude longer. The predictions of the IBM-2 and the EFT lie in between, and the latter provides systematic uncertainties at leading order. An analysis of the running sum of the nu…