Exact Matching Condition for Matrix Elements in Lattice and $\overline{MS}$ Schemes

The exact matching condition is given for hadron matrix elements calculated in any two different schemes, in particular, in the lattice and dimensional regularization, (modified) minimal subtraction $\overline{\mathrm{M}\mathrm{S}}$ schemes. The result provides insight into and permits to go beyond Lepage and Mackenzie’s mean field theory of removing tadpole contributions in lattice operators.