  In this work, we put forward a straightforward and simple approach to
construct the low-energy effective field theory (EFT) from a given ultraviolet
(UV) full theory by integrating heavy particles out. By calculating the
on-shell amplitudes, we demonstrate how to directly achieve the one-loop
matching of the UV full theory onto the EFT with the complete set of
independent operators in the physical basis, which are usually obtained by
removing the redundant operators in the Green's basis via the equations of
motion. Furthermore, taking specific examples, we explain how to implement the
on-shell-amplitude approach to derive the one-loop renormalization-group
equations for the Wilson coefficients, and to find out the contributions from
the evanescent operators.
