${}^3$ He- $α$散射数据的有效场论分析
Effective Field Theory analysis of ${}^3$He-$α$ scattering data
摘要：
我们处理低能量$^3$ He- $α$弹性散射的有效场论（EFT），利用分离的尺度在这个反应。我们计算的幅度下一个到下一个到领先的顺序（NNLO），开发一个层次结构的有效范围参数，有助于在各种订单。我们使用由此产生的形式主义来分析最近的测量数据，在质量中心的能量为0.38-3.12兆电子伏，使用SONIK气体目标在TRIUMF，以及在这个能量制度的旧数据。我们采用的似然函数，它结合了理论上的不确定性，由于截断的EFT和使用马尔可夫链蒙特卡罗抽样获得的后验概率分布。我们发现，包含有关分析能力$A_y$的少量数据对于确定此类分析中p波分裂的符号至关重要。$A_y$和SONIK数据的组合将s波和p波中的所有有效范围参数约束到$O(p^4)$。ANC和s波散射长度与最近捕获反应${}^3$ He（$α$，$γ$）${}^7$ Be的EFT分析一致。
英文摘要：
We treat low-energy $^3$He-$α$ elastic scattering in an Effective Field Theory (EFT) that exploits the separation of scales in this reaction. We compute the amplitude up to Next-to-Next-to-Leading Order (NNLO), developing a hierarchy of the effective-range parameters that contribute at various orders. We use the resulting formalism to analyze data for recent measurements at center-of-mass energies of 0.38-3.12 MeV using the SONIK gas target at TRIUMF as well as older data in this energy regime. We employ a likelihood function that incorporates the theoretical uncertainty due to truncation of the EFT and use Markov Chain Monte Carlo sampling to obtain the resulting posterior probability distribution. We find that the inclusion of a small amount of data on the analysing power $A_y$ is crucial to determine the sign of the p-wave splitting in such an analysis. The combination of $A_y$ and SONIK data constrains all effective-range parameters up to $O(p^4)$ in both s- and p-waves quite well. The ANCs and s-wave scattering length are consistent with a recent EFT analysis of the capture reaction ${}^3$He($α$,$γ$)${}^7$Be.
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