Multipole-expanded soft-collinear effective theory with non-Abelian gauge symmetry

In position space the interaction terms of soft-collinear effective theory must be multipole-expanded to obtain interaction terms with homogeneous scaling behaviour. In this Letter we provide a manifestly gauge-invariant formulation of the theory after this expansion in the presence of non-Abelian gauge fields, extending our previous result. We give the effective Lagrangian (including the Yang–Mills Lagrangian for collinear and ultrasoft gluons) and heavy-to-light transition currents to second order in the power expansion, paying particular attention to the field redefinitions that lead to the gauge symmetries of the effective Lagrangian.