Comparative study of He6 β-decay based on different similarity-renormalization-group evolved chiral interactions

We report on a study of the Gamow-Teller matrix element contributing to 6Heβ decay with similarity renormalization group (SRG) versions of momentum- and configuration-space two-nucleon interactions. These interactions are derived from two different formulations of chiral effective field theory (χEFT)—without and with the explicit inclusion of Δ isobars. We consider evolution parameters ΛSRG in the range between 1.2 and 2.0 fm−1 and, for the Δ-less case, also the unevolved (bare) interaction. The axial current contains one- and two-body terms, consistently derived at tree level (no loops) in the two distinct χEFT formulations we have adopted here. The 6He and 6Li ground-state wave functions are obtained from hyperspherical-harmonics (HH) solutions of the nuclear many-body problem. In A=6 systems, the HH method is limited at present to treat only two-body interactions and non-SRG evolved currents. Our results exhibit a significant dependence on ΛSRG of the contributions associated with two-body currents, suggesting that a consistent SRG-evolution of these is needed in order to obtain reliable estimates. We also show that the contributions from one-pion-exchange currents depend strongly on the model (chiral) interactions and on the momentum- or configuration-space cutoffs used to regularize them. These results might prove helpful in clarifying the origin of the sign difference recently found in no-core-shell-model and quantum Monte Carlo calculations of the 6He Gamow-Teller matrix element.