Auxiliary field approach to extended operators for quasi-PDFs
The auxiliary field approach, where one introduces a field whose propagator is the gauge connection along a chosen path, has been used to study renormalization of extended operators in the continuum. If we restrict the paths to straight lines along the axes, the theory can be discretized with an action similar to lattice heavy-quark effective theory in the static limit. Using this theory, extended operators with quark and antiquark fields connected by a straight Wilson line can be expressed as the product of two displaced local operators, each of which is the product of a quark field and the auxiliary field. This allows us to study renormalization and improvement of extended operators using standard techniques applied to local operators involving the auxiliary field.
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