We calculate the longitudinal structure function of the deuteron up through next-to-next-to-leading order in the framework of pionless effective field theory. We use these results to compute the two-photon polarizability contribution to Lamb shift in muonic deuterium, which can be utilized to extract the nuclear charge radius of the deuteron. We present analytical expressions order-by-order for the relevant transition matrix elements and the longitudinal structure function, and we give numerical results for the corresponding contributions to the Lamb shift. We also discuss the impact of relativistic and other higher-order effects. We find agreement with previous calculations and explain the accuracy of our calculation.

我们在无偶有效场理论的框架内，通过从下至上的顺序来计算氘核的纵向结构函数。我们使用这些结果来计算双光子极化对胶态氘中的Lamb位移的贡献，可用于提取氘的核电荷半径。我们按顺序给出了有关过渡矩阵元素和纵向结构函数的分析表达式，并给出了对羔羊移位的相应贡献的数值结果。我们还将讨论相对论和其他高阶效应的影响。我们发现与先前的计算相符，并解释了我们计算的准确性。