Comment on “Nonrelativistic QED and next-to-leading hyperfine splitting in positronium”

In a recent paper, the t-channel two-photon exchange contribution to the coefficients of nonrelativistic quantum electrodynamics (NRQED) four-fermion interaction were found. However while doing the matching two NRQED diagrams were lost. We have done these calculations for the case of different particle masses in the $\Lambda$-cutoff regularization scheme and present here the corrected result.