The Cottingham formula expresses the electromagnetic part of the mass of a particle in terms of the virtual Compton scattering amplitude. We show that the formula can be rewritten such that the subtraction function in the dispersive representation of this amplitude dominates the contributions from the inelastic region. The numerical evaluation on the basis of a sum rule that follows from Reggeon dominance indicates that the inelastic contributions to the mass difference between proton and neutron are very small: $m_{QED}^{p-n}=0.58\pm 0.16\,$MeV, $m_{QCD}^{p-n}=-1.87\mp 0.16\,$MeV.

中文翻译：

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关于质子和中子的质量差异

Cottingham 公式根据虚拟康普顿散射幅度表示粒子质量的电磁部分。我们表明可以重写公式，使得该幅度的色散表示中的减法函数支配来自非弹性区域的贡献。基于 Reggeon 优势的求和规则的数值评估表明，对质子和中子之间质量差异的非弹性贡献非常小：$m_{QED}^{pn}=0.58\pm 0.16\,$MeV , $m_{QCD}^{pn}=-1.87\mp 0.16\,$MeV。