The neutrinoless double-beta decay ($0\nu \beta \beta$) of two neutrons $nn\to ppee$ is the elementary subprocess of $0\nu \beta \beta$ decay in nuclei. Accurate knowledge of the $nn\to ppee$ amplitude is required to pin down the short-range contributions in the nuclear matrix elements of the candidate nuclei for large-scale $0\nu \beta \beta$ searches. In this Letter, we report the first next-to-leading-order prediction of the $nn\to ppee$ amplitude, with Bayesian uncertainty quantification. This is made possible by the development of the relativistic chiral effective field theory, in which no unknown contact term is required up to next-to-leading order. The theory is validated by reproducing in a parameter-free way the available data on the charge independence and charge symmetry breaking contributions in the two-nucleon scattering. The present work makes an essential step toward addressing the uncertainty in the theoretical calculations of the nuclear matrix elements relevant for $0\nu \beta \beta$ searches.

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• Effective field theory
• Neutrinoless double beta decay
• Nuclear tests of fundamental interactions