Bayesian analysis of an EFT for fermionic rotational bands

We recently developed an Effective Field Theory (EFT) for fermionic rotational bands in odd mass nuclei (arXiv:2011.01083). Here we perform a Bayesian analysis of data on rotational levels of ⁹⁹Tc, ¹⁵⁹Dy, ^{167, 169}Er, ^{167, 169}Tm, ¹⁸³W, ²³⁵U and ²³⁹Pu. Our error model accounts for both experimental errors and the theory uncertainty due to the EFT truncation. It also accounts for the difference in the structure of the matrix elements that enter the EFT's Low-Energy Constants (LEC's): we assume that the LECs at even and odd orders in the EFT are drawn from two different distributions. This allows us to simultaneously and reliably extract both the LEC's and the expansion parameter, Q. The LEC's are extracted up to fourth order. Correctly accounting for omitted terms in the error model makes the extraction stable across EFT orders. The analysis is also stable against the addition of data on higher-energy levels. In almost all cases the LEC stablizies before we reach the highest level for which we have data. For all the nuclei listed above there is a clear correlation between the extracted Q and the naive expansion parameter obtained from the rotational, single-particle and vibrational energy scales. But the extracted Q is significantly lower than the naive one.