The mass shifts for two-fermion bound and scattering P-wave states subject to the long-range interactions due to QED in the non-relativistic regime are derived. Introducing a short range force coupling the spinless fermions to one unit of angular momentum in the framework of pionless EFT, we first calculate both perturbatively and non-perturbatively the Coulomb corrections to fermion–fermion scattering in the continuum and infinite volume context. Motivated by the research on particle–antiparticle bound states, we extend the results to fermions of identical mass and opposite charge. Second, we transpose the system onto a cubic box with periodic boundary conditions and we calculate the finite volume corrections to the energy of the lowest bound and unbound \(T_1^{-}\) eigenstates. In particular, power law corrections proportional to the fine structure constant and resembling the recent results for S-wave states are found. Higher order contributions in \(\alpha \) are neglected, since the gapped nature of the momentum operator in the finite-volume environnement allows for a perturbative treatment of the QED interactions.

推导了在非相对论体系中，两量子束缚和散射P波状态的质量位移，它们受QED引起的长距离相互作用的影响。引入了将无旋转费米子耦合到无角度EFT框架中一个角动量的短程力，我们首先在连续和无限体积的情况下，对库仑校正对费米子-费米子散射进行了扰动和非扰动计算。出于对粒子-反粒子结合态的研究的推动，我们将结果扩展到了质量相同但电荷相反的费米子。其次，我们将系统转置到具有周期性边界条件的立方盒上，并计算对最低界和未界\（T_1 ^ {-} \）的能量的有限体积校正本征态。特别是，发现了与精细结构常数成比例的幂定律校正，并且与S波状态的最新结果类似。忽略了\（\ alpha \）中的高阶贡献，因为在有限体积环境中动量算符的有间隙性质允许对QED相互作用进行微扰处理。