氢光谱中的$Δ(1232)$共振
$Δ(1232)$-Resonance in the Hydrogen Spectrum
摘要：
$Δ(1232)$共振的电磁激发在μ子和电子氢的兰姆位移和超精细结构中起着重要的作用。它的效果出现在次领先的顺序$\mathcal{O}(α^5)$，连同其他质子极化率的贡献，从向前的双光子交换。我们用大的$N_c$关系式计算了氢原子能谱中的$Δ(1232)$效应。我们特别注意的是，基于直接计算的双光子交换（或康普顿散射振幅）和预测的基础上的$Δ(1232)$生产光吸收截面的预测之间的细微差别。通过更详细地研究质子的树级康普顿散射的色散关系来解释这种不匹配。
英文摘要：
The electromagnetic excitation of the $Δ(1232)$-resonance plays an appreciable role in the Lamb shift and hyperfine structure of muonic and electronic hydrogen. Its effect appears at the subleading order $\mathcal{O}(α^5)$, together with other proton-polarizability contributions from forward two-photon exchange. We use the large-$N_c$ relations for the nucleon-to-delta transition form factors to compute the effect of the $Δ(1232)$ in the hydrogen spectrum. We pay particular attention to a subtile difference between predictions based on a direct calculation of the two-photon exchange (or Compton scattering amplitudes) and predictions based on the $Δ(1232)$-production photoabsorption cross sections. The mismatch is explained by studying the dispersion relations for tree-level Compton scattering off the proton in more details.
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