Point-Particle Effective Field Theory II: Relativistic Effects and Coulomb/Inverse-Square Competition

Understand

We apply point-particle effective field theory (PPEFT) to compute the leading shifts due to finite-size source effects in the Coulomb bound energy levels of a relativistic spinless charged particle.

• This is the analogue for spinless electrons of the contribution of the charge-radius of the source to these levels, and we disagree with standard calculations in several ways.
• Most notably we find there are two effective interactions with the same dimension that contribute to leading order in the nuclear size.
• One is the standard charge-radius contribution, while the other is a contact interaction whose leading contribution to $\delta E$ arises linearly in the small length scale, $\epsilon$, characterizing the finite-size effects, and is suppressed by $(Z\alpha)^5$.