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

Abstract

We report on a study of the Gamow-Teller matrix element contributing to ${}^6\mathrm{He}\beta$ 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 ($\chi \mathrm{EFT})$—without and with the explicit inclusion of $\mathrm{\Delta }$ isobars. We consider evolution parameters ${\mathrm{\Lambda }}_{\mathrm{SRG}}$ in the range between 1.2 and 2.0 ${\mathrm{fm}}^{-1}$ and, for the $\mathrm{\Delta }$-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 $\chi \mathrm{EFT}$ formulations we have adopted here. The ${}^6\mathrm{He}$ and ${}^6\mathrm{Li}$ 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 ${\mathrm{\Lambda }}_{\text{SRG}}$ 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 ${}^6\mathrm{He}$ Gamow-Teller matrix element.