On the gauge-invariance of SCET beyond leading power

Abstract

We point out that the gauge-invariance of the subleading Lagrangian of soft-collinear effective theory is realised in an intricate way through momentum-conservation violating contributions. Although these terms are disregarded in diagrammatic calculations, the gauge invariance of any physical transition amplitude is preserved due to the soft equations of motion. When not working with gauge-invariant building blocks, individual manifestly gauge-invariant constituent terms in the Lagrangian may give rise to gauge-dependent matrix elements starting at $\mathcal{O}({\lambda }^2)$. Implications for a gauge-invariant definition of radiative jet functions are discussed.

17 pages, 2 figures, minor text changes, matches journal version

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Cited by in corpus (3)

• Structure-dependent QED effects in exclusive $B$-meson decays
• $B_c\to {\eta }_c$ form factors at large recoil: Interplay of soft-quark and soft-gluon dynamics
• Gauge invariance of radiative jet functions in the position-space formulation of SCET