论文标题
锥形核子相位偏移的低能参数
Low-energy parameterisations of the pion-nucleon phase shifts
论文作者
论文摘要
在这项工作中，根据$ s $和$ s $ - $ p $ -Wave $ -Wave $ -Wave $ k $ -matrix元素（或其$ k $ k $ -matrix元素（或其$ k $ k $ y-matrix元素），通过简单的polynomials通过简单的polynomials的建模，可以从低能（pion实验室动能高达$ 100 $ meV）中获得几组结果。模型参数的拟合值和不确定性以及相应的Hessian（协方差）矩阵，其中三个参数为两种类型的关节拟合以表格形式给出：对于两个弹性分解过程的测量$电荷交换反应$π^-p \toπ^0 n $。从这些结果中，可靠的和（很大程度上）数据驱动的（因此与模型无关的）预测，伴随着不确定性，反映了输入数据的统计和系统波动，可以为$πn$相互作用的低能常数（散射长度和范围的范围和$ k $ $ k $ k $ k- $ k- $ k- $ k）获得。幅度在（低能）$ s $和$ p $ waves中。在添加了$ d $ - 和$ f $ - 波的贡献以及包含电磁效果之后，可以为通常的低能量$πn$可观察到的相应预测获得相应的预测，即用于差分横截面和分析功率。
Compared in this work are a few sets of results, obtained from the pion-nucleon ($πN$) data at low energy (pion laboratory kinetic energy up to $100$ MeV) on the basis of the modelling of the $s$- and $p$-wave $K$-matrix elements (or of their reciprocal) via simple polynomials. The fitted values and uncertainties of the model parameters, as well as the corresponding Hessian (covariance) matrices, for three of these parameterisations are given in tabular form for two types of joint fits: to the measurements of the two elastic-scattering processes $π^\pm p \to π^\pm p$, and to those of the $π^+ p$ reaction and of the $π^- p$ charge-exchange reaction $π^- p \to π^0 n$. From these results, reliable and (largely) data-driven (hence model-independent) predictions, accompanied by uncertainties which reflect the statistical and systematic fluctuation of the input data, can be obtained for the low-energy constants of the $πN$ interaction (scattering lengths/volumes and range parameters), for the phase shifts, for the $K$-matrix elements, and for the partial-wave amplitudes in the (dominant at low energy) $s$ and $p$ waves. After the addition of the $d$- and $f$-wave contributions, and the inclusion of the electromagnetic effects, corresponding predictions can be obtained for the usual low-energy $πN$ observables, i.e., for the differential cross section and for the analysing power.
