AI 中文总结
研究轻非奇异介子Regge轨迹，通过测试三种模型，用非线性$\chi^2$最小化框架优化并结合多种准则进行分析，发现谱中适度非线性偏差集中在$S$波共振扇区，模型3能适应，还得出相关校正与库仑问题相对论校正一致的结论。
AI 中文摘要
对轻非奇异介子质谱的Regge型轨迹进行了严格的统计分析，明确考虑了实验不确定性。测试了三种情况：具有不同径向（$n$）和轨道（$l$）斜率的线性模型（模型1）、具有通用斜率的线性模型（模型2）和具有通用斜率和狄拉克 - 库仑型项$\propto (l + 1)^{-1}$的非线性模型（模型3）。使用非线性$\chi^2$最小化框架进行优化，通过强制$\chi^2/\text{dof} = 1$自洽确定内在理论模型不确定性。采用赤池和贝叶斯信息准则及补充统计测试确保稳健的模型选择。分析表明Regge谱中与线性的适度偏差主要集中在$S$波共振扇区。模型3中的非线性校正成功地适应了这些扭曲，从中出现了近似库仑型简并$m^2(n,l) \propto n + l$作为统计稳健特征。此外，表明轻非奇异介子中主量子数的$l$依赖校正与库仑问题的领先阶相对论校正一致。
英文摘要
A rigorous statistical analysis of Regge-type trajectories for light non-strange meson mass spectra is carried out, which explicitly accounts for experimental uncertainties. We test three scenarios: a linear model with distinct radial ($n$) and orbital ($l$) slopes (Model 1), a linear model with a universal slope (Model 2), and a nonlinear model featuring a universal slope and a Dirac-Coulomb-type term $\propto (l+1)^{-1}$ (Model 3). Optimization is performed using a nonlinear $χ^2$ minimization framework, where the intrinsic theoretical model uncertainty is determined self-consistently by enforcing $χ^2/\text{dof} = 1$. To ensure robust model selection, we employ the Akaike and Bayesian information criteria alongside complementary statistical tests. Our analysis demonstrates that moderate deviations from linearity in the Regge spectrum are predominantly localized within the $S$-wave resonance sector. These distortions are successfully accommodated by the nonlinear correction in Model 3, from which an approximate Coulomb-type degeneracy, $m^2(n,l) \propto n+l$, emerges as a statistically robust feature. Furthermore, we show that the $l$-dependent correction to the principal quantum number in light non-strange mesons is consistent with the leading-order relativistic correction to the Coulomb problem.
Comments23 pages, 2 figures, 7 tables
