Electromagnetic corrections to π−\pi ^-p scattering length from pionic hydrogen

We derive a closed, model space independent, expression for the electromagnetic correction factor $\delta$ to the scattering length $a$ extracted from a hydrogenic atom with an extended charge to order $\alpha ^2$ and $a^3$ in the limit of a short ranged hadronic interaction.Comment: 4 pages; PANIC02, XVIth Conference on Particles and Nuclei, Osaka, to appear in Nuclear Physics