论文标题
手性扰动理论中的弹性锥形核子散射：显式$δ$（1232）自由度
Elastic pion-nucleon scattering in chiral perturbation theory: Explicit $Δ$(1232) degrees of freedom
论文作者
论文摘要
在手性扰动理论的框架中，首次分析了弹性锥形核子散射，并具有显式$δ$δ$自由度。该分析是在重 - 巴里元扩张以及基于扩展的质量重骨重新归化方案的协变方式中进行的。详细讨论了两种手性方法中低能量常数的重新归一化，并给出了取消功率计数破坏和解耦破坏术语的明确表达式。来自$2π\ bar {n} n $相互作用以及$δ$扇区的其他常数的低能常数受到适合实验数据的可靠约束。传统的$ K $ -MATRIX单位化用于接近阈值区域，而复杂的质量方法则用于将理论的适用性扩展到$δ$ POL区域。此外，我们根据最近对核力量分析以及脓性核子散射所采用的手性系列截断的理论误差。获得的结果提供了一个明确的证据，表明$δ$Δ$自由度的明确包含是至关重要的，这是描述阈值pion-nucleon物理学的基础。对下阈值和阈值参数以及相移的结果预测与最近的Roy-Steiner分析对Pion-Nucleon散射确定的预测非常吻合。
For the first time, elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order with explicit $Δ$ degrees of freedom. The analysis is performed within the heavy-baryon expansion as well as in a covariant approach based on an extended on-mass-shell renormalization scheme. The renormalization of low-energy constants in both chiral approaches is discussed in detail and the explicit expressions to cancel both power-counting breaking as well as decoupling breaking terms are given. The low-energy constants from the $2π\bar{N}N$ interaction as well as additional constants from the $Δ$ sector are reliably constrained by fits to experimental data. The traditional $K$-matrix unitarization is employed in the near threshold region, whereas a complex mass approach is used to extend the applicability of the theory up to the $Δ$ pole region. Additionally, we estimate a theoretical error based on the truncation of the chiral series as employed in recent analyses of nuclear forces as well as pion-nucleon scattering. The obtained results provide a clear evidence that the explicit inclusion of $Δ$ degrees of freedom is fundamental to describe pion-nucleon physics at threshold. The resulting predictions for the subthreshold and threshold parameters as well as phase shifts are in excellent agreement with the ones determined by the recent Roy-Steiner analysis of pion-nucleon scattering.
