发表机构
Institute of Theoretical Physics, Chinese Academy of Sciences; School for Theoretical Physics, School of Physics and Electronics, Hunan University; Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, Hunan University; School of Physical Sciences, University of Chinese Academy of Sciences; Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院理论物理研究所; 湖南大学物理与电子学院理论物理学院; 湖南大学高能标物理与应用湖南省重点实验室; 中国科学院大学物理科学学院; 中国科学院近代物理研究所南方核科学理论中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文推导了核子同位旋极化率组合的精确色散求和规则，结合实验多极和耦合道振幅确定其符号并降低不确定性，进而精确计算质子-中子电磁质量差，并检验Reggeon主导假设。
AI 中文摘要
从Cottingham公式提取的电磁质子-中子质量差$\delta m_\mathrm{QED}$的精度取决于一个减法函数，其低能归一化$\bar S(0)$由质子和中子极化率的同位旋组合$(\alpha_{E1}-\beta_{M1})^{p-n}$固定。我们推导了该组合的色散求和规则，用$s$道光吸收截面和$t$道$\gamma\gamma\to\pi\eta/K\bar K_{I_t=1}$与$\pi\eta/K\bar K_{I_t=1}\to N\bar N$振幅的乘积表示，不依赖Reggeon主导假设。结合经验π介子光生多极和标量-同位旋$\pi\eta/K\bar K$振幅的耦合道Muskhelishvili--Omnès表示，我们得到$(\alpha_{E1}-\beta_{M1})^{p-n}=-2.26(73)\times10^{-4}\\,\mathrm{fm}^3$，确定了其符号并将不确定性相比先前已知值降低了4倍。该结果给出$\bar S(0)=-1.76(61)\\,\mathrm{GeV}^{-2}$，从而得到$\delta m_\mathrm{QED}=0.71^{+0.03}_{-0.06}\\,\mathrm{MeV}$，比先前的Cottingham确定值精确得多。负的$\bar S(0)$也为减法函数中的Reggeon主导假设提供了严格低能检验。
英文摘要
The precision of the electromagnetic proton-neutron mass difference $δm_\mathrm{QED}$ extracted from the Cottingham formula hinges on a subtraction function whose low-energy normalization $\bar S(0)$ is fixed by the isovector combination of the proton and neutron polarizabilities, $(α_{E1}-β_{M1})^{p-n}$. We derive a dispersive sum rule for this combination in terms of $s$-channel photoabsorption cross sections and the product of $t$-channel $γγ\toπη/K\bar K_{I_t=1}$ and $πη/K\bar K_{I_t=1}\to N\bar N$ amplitudes, without invoking Reggeon dominance. Combining empirical pion-photoproduction multipoles with coupled-channel Muskhelishvili--Omnès representations of the scalar-isovector $πη/K\bar K$ amplitudes, we obtain $(α_{E1}-β_{M1})^{p-n}=-2.26(73)\times10^{-4}\,\mathrm{fm}^3$, fixing its sign and reducing the uncertainty by a factor of 4 compared with the previously known value. This result yields $\bar S(0)=-1.76(61)\,\mathrm{GeV}^{-2}$, leading to $δm_\mathrm{QED}=0.71^{+0.03}_{-0.06}\,\mathrm{MeV}$, substantially more precise than previous Cottingham determinations. The negative $\bar S(0)$ also provides a stringent low-energy test of Reggeon dominance in the subtraction function.
Comments10 pages, 2 figures
