论文标题
$^4 $ h $ j^π的出现
Emergence of $^4$H $J^π=1^-$ resonance in contact theories
论文作者
论文摘要
我们获得了$ s $ - 和$ p $ - 波的低能散射参数，用于n $^3 $ h弹性散射以及$^4 $ h $ h $ j^π= 1^ - $ $ j^π= 1^ - $ $ $ $ $ $共振，使用前订单上的无效现场理论。结果用三种数值技术提取：将系统限制在谐波振荡器陷阱中，在配置空间中求解Faddeev-Yakubovsky方程，并使用有效的两体群集方法。相关振幅的理论的重归化在截止器范围内评估在$ 1 \，\ text {fm}^{ - 1} $和$ 10 \，\ text {fm}^{ - 1} $之间。 最值得注意的是，我们在$^4 $ h $ j^π= 1^ - $ system中找到了截止稳定/RG不变的共振。这种$ p $ - 波的共鸣是浅两体状态的普遍后果，并引入了Triton Binding Energy设置的三体$ S $波量表。通过纯粹的接触相互作用在几个特里米昂系统中谐振状态的稳定对无汗理论的能量计算具有重大影响。具体而言，它表明在较大的核（如16-氧）中也出现了相似的共振状态，其中理论的领先顺序无法预测稳定的状态。这些共鸣将通过扰动插入子领先顺序的插入，可以将起始状态转移到正确的物理位置，从而解决数据和触点eft之间的差异。
We obtain the $s$- and $p$-wave low-energy scattering parameters for n$^3$H elastic scattering and the position of the $^4$H $J^π=1^-$ resonance using the pionless effective field theory at leading order. Results are extracted with three numerical techniques: confining the system in a harmonic oscillator trap, solving the Faddeev-Yakubovsky equations in configuration space, and using an effective two-body cluster approach. The renormalization of the theory for the relevant amplitudes is assessed in a cutoff-regulator range between $1\,\text{fm}^{-1}$ and $10\,\text{fm}^{-1}$. Most remarkably, we find a cutoff-stable/RG-invariant resonance in the $^4$H $J^π=1^-$ system. This $p$-wave resonance is a universal consequence of a shallow two-body state and the introduction of a three-body $s$-wave scale set by the triton binding energy. The stabilization of a resonant state in a few-fermion system through pure contact interactions has a significant consequence for the powercounting of the pionless theory. Specifically, it suggests the appearance of similar resonant states also in larger nuclei, like 16-oxygen, in which the theory's leading order does not predict stable states. Those resonances would provide a starting state to be moved to the correct physical position by the perturbative insertion of sub-leading orders, possibly resolving the discrepancy between data and contact EFT.
