A new dimension-seven operator is generated by the gluon equation of motion in the presence of the axion-gluon coupling, and its spectator-scattering contribution to B to K a is roughly 25 percent of the soft-overlap contribution.
In particular, the integration over the space-time coordinateyenforces overall momentum conservation through the resulting four-dimensional delta function
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Soft Collinear Effective Theory for Heavy QCD Axions
A new dimension-seven operator is generated by the gluon equation of motion in the presence of the axion-gluon coupling, and its spectator-scattering contribution to B to K a is roughly 25 percent of the soft-overlap contribution.