Effective field theory for nuclear vibrations with quantified uncertainties

We develop an effective field theory (EFT) for nuclear vibrations. The key ingredients - quadrupole degrees of freedom, rotational invariance, and a breakdown scale around the three-phonon level - are taken from data. The EFT is developed for spectra and electromagnetic moments and transitions. We employ tools from Bayesian statistics for the quantification of theoretical uncertainties. The EFT consistently describes spectra and electromagnetic transitions for ${}^{62}$Ni, ${}^{98,100}$Ru, ${}^{106,108}$Pd, ${}^{110,112,114}$Cd, and ${}^{118,120,122}$Te within the theoretical uncertainties. This suggests that these nuclei can be viewed as anharmonic vibrators.