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.

中文翻译：

---

基于不同相似重整化组进化手性相互作用的He6β衰变对比研究

我们报告了对 Gamow-Teller 矩阵元素的研究，有助于 ${}^6他\beta$与动量和配置空间双核子相互作用的相似重整化组 (SRG) 版本衰减。这些相互作用源自手性有效场论的两种不同表述（$\chi \mathrm{电子转帐})$——没有和明确包含 $\mathrm{\Delta }$等压线。我们考虑进化参数${\mathrm{\Lambda }}_{\mathrm{SRG}}$ 在 1.2 和 2.0 之间的范围内 ${\mathrm{调频}}^{-1}$ 并且，对于 $\mathrm{\Delta }$-less case，也是未进化的（裸）交互。轴向电流包含单体和双体项，在两个不同的树级别（无环）一致地导出$\chi \mathrm{电子转帐}$我们在这里采用的公式。这${}^6他$ 和 ${}^6李$基态波函数是从核多体问题的超球面谐波 (HH) 解中获得的。在$\mathrm{一种}=6$系统，HH 方法目前仅限于处理两体相互作用和非 SRG 演化电流。我们的结果显着依赖于${\mathrm{\Lambda }}_{\text{SRG}}$与二体电流相关的贡献，表明需要对这些进行一致的 SRG 演化以获得可靠的估计。我们还表明，来自 1 π 交换电流的贡献在很大程度上取决于模型（手性）相互作用以及用于正则化它们的动量或配置空间截止值。这些结果可能有助于澄清最近在无核壳模型和量子蒙特卡罗计算中发现的符号差异的起源。${}^6他$ Gamow-Teller 矩阵元素。