标题： 量子4体散射中的尺度(不)依赖性 显示英文标题

标题： Scale-(in)dependence in quantum 4-body scattering

摘要： 我们研究了使用正则化的二维和三维接触相互作用的多通道四体散射系统。 分析确定了束缚态能量、散射相移和截面对截止参数（$\lambda$）以及散射阈值之间能量间隔的敏感性。 后者依赖性是在二维尺度固定在一个非自然的大值和一个浮动的三维参数的情况下获得的。 具体来说，我们计算了浅三体和四体状态的结合能、二聚体-二聚体和三体-原子散射长度以及三体-原子到二聚体-二聚体的反应速率。 采用由大的二维散射长度和三维尺度重整化后的势，我们发现所有计算出的可观测量在范围$6\textrm{fm}^{-2}<\lambda<10\textrm{fm}^{-2}$内几乎保持恒定。 散射长度的发散出现在阈值退化的临界三维参数处。 这种阈值效应被发现与调节器截止无关。 此外，在二聚体-二聚体和三体-原子阈值重叠的那些临界点上，我们预测非弹性散射事件相对于弹性散射事件会增强。 这种弹性碰撞和重新排列碰撞概率之间的反转表明，四体反应动力学对有限二维尺度下的三维参数有很强的敏感性。 这一现象在早期的研究中没有出现，这些研究在重整化方案上有所不同。 由于这种差异出现在所有考虑的截止范围内，需要更全面地参数化短程结构：单独的截止变化并不能揭示由于有限的二维范围和三维参数的具体选择而引起的反应率的非微扰变化。 显示英文摘要

摘要： We investigate the multi-channel 4-body scattering system using regularized 2- and 3-body contact interactions. The analysis determines the sensitivity of bound-state energies, scattering phase shifts and cross sections on the cutoff parameter ($\lambda$), and the energy gaps between scattering thresholds. The latter dependency is obtained with a 2-body scale fixed to an unnaturally large value and a floating 3-body parameter. Specifically, we calculate the binding energies of the shallow 3- and 4-body states, dimer-dimer and trimer-atom scattering lengths, and the trimer-atom to dimer-dimer reaction rates. Employing a potential renormalized by a large 2-body scattering length and a 3-body scale, we find all calculated observables to remain practically constant over the range $6\textrm{fm}^{-2}<\lambda<10\textrm{fm}^{-2}$. Divergences in scattering lengths emerge for critical 3-body parameters at which thresholds are degenerate. Such threshold effects are found to be independent of the regulator cutoff. Furthermore, at those critical points where the dimer-dimer and trimer-atom thresholds overlap, we predict an enhancement of the inelastic over the elastic scattering event. Such an inversion between elastic- and rearrangement-collision probabilities indicates a strong sensitivity of the 4-body reaction dynamics on the 3-body parameter at finite 2-body scale. This phenomenon is absent in earlier studies which differ in the renormalization scheme. As this discrepancy arises for all considered cutoffs, a more comprehensive parametrization of short-distance structure is necessary: sole cutoff variation does not reveal non-perturbative change in reaction rates conjectured to be due to a combined effect of the finite 2-body range and the specific choice for the 3-body parameter.