Wilson expansion in minimal subtraction scheme

The small distance expansion of the product of composite fields is constructed for and arbitrary renormalization procedure of the type of minimal subtraction scheme. Coefficient functions of the expansion are expressed explicitly through the Green functions of composite fields. The expansion has the explicity finite form: the ultraviolet (UV) divergences of the coefficient functions and composite fields are removed by the initial renormalization procedure while the infrared (IR) divergences in massless diagrams with nonvanishing contribution into the coefficient functions are removed by the $\tilde R$-operation which is the IR part of the $R^*$-operation. The latter is the generalization of the dimensional renormalization in the case when both UV and IR divergences are prosent. To derive the expansion, a “pre-subtracting operator” is introduced and formulas of the counter-term technique are exploited.