AI 中文总结
针对$N\to\Delta(1232)$电磁跃迁，开发保持和规则的跃迁GPD重建方法，利用CLAS数据及低$Q^2$约束，推导拟合振幅，转换多种分布轮廓到碰撞参数空间，结果显示非因子化层析成像可扩展因子化方法并保持与形状因子联系。
AI 中文摘要
本文针对$N\to\Delta(1232)$电磁跃迁开发了一种保持和规则的跃迁广义部分子分布（GPD）重建方法。分析使用已发表的CLAS $\Delta(1232)$数据及低$Q^2$比值扇区约束，推导并拟合磁、电和标量/库仑跃迁振幅。拟合的跃迁形状因子定义了经验动量转移归一化，将多种分布轮廓转换到碰撞参数空间获取相关量。结果表明非因子化跃迁GPD层析成像可扩展因子化方法并保持与测量跃迁形状因子的联系。
英文摘要
A sum-rule-preserving transition-GPD reconstruction is developed for the $N\toΔ(1232)$ electromagnetic transition. The analysis uses published CLAS $Δ(1232)$ data, including the magnetic multipole amplitude and the electric and scalar/Coulomb quadrupole ratios, together with low-$Q^2$ ratio-sector constraints. Magnetic, electric, and scalar/Coulomb transition amplitudes are derived and fitted with a common library of dipole, modified-dipole, $z$-expansion, and low-$Q^2$ motivated candidate forms. The fitted transition form factors define the empirical momentum-transfer normalization for a family of transition GPDs constructed to preserve the measured form-factor sum rule. Factorized, correlated non-factorized, Regge-like, and double-distribution-inspired profiles are transformed into impact-parameter space to obtain transverse densities, localization radii, higher transverse-shape moments, and multipole-resolved radial kernels. The factorized baseline yields little genuine $x$-dependent transverse localization, while the non-factorized profiles generate distinct $x$-dependent spatial structures under the same empirical normalization. The magnetic channel provides the most stable tomography benchmark, whereas the electric and scalar/Coulomb sectors show stronger profile sensitivity. The results demonstrate that non-factorized transition-GPD tomography can extend the factorized amplitude-to-space approach while keeping the connection to measured $N\toΔ(1232)$ transition form factors.
