Effect of the Flowing Three-Body operator on Neutrinoless Double-Beta Decay Nuclear Matrix Elements in the IMSRG

We investigate the impact of the flowing three-body operator on the evaluation of neutrinoless double-beta decay (0νββ0\nu\beta\beta0νββ) nuclear matrix elements (NMEs) within the in-medium similarity renormalization group (IMSRG) framework. In standard IMSRG(2) truncations, induced three-body operators are neglected, which may limit the accuracy of the computed decay observables. To quantify this effect, we introduce an approximate treatment of the full IMSRG(3), termed IMSRG(3f2), in which factorized double commutators contributing to the induced three-body operators are retained. We compare NMEs obtained at the IMSRG(2) and IMSRG(3n7) levels to assess convergence behavior and identify correlations driven by induced three-body contributions. Our results indicate that including the flowing three-body operator moderately reduces the NMEs and provides valuable insights into many-body truncation effects in ab initio descriptions of 0νββ0\nu\beta\beta0νββ decay.