Simpler minimal subtraction of scalar massive fields

What is it about?

We provide a new method of minimal subtraction which is similar to a previous formulation in the case of massless fields, but requires an additional ingredient not required in massless theories.

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Why is it important?

The elimination of all tadpole diagrams is similar in many aspects to a previous method for massless fields. The necessity of another subtraction and its relation with integrals which, although not being polynomial in the external momentum behaves likewise, makes contact with 't Hooft-Veltman criterion of harmless pole which can be subtracted away. This new criterion for harmless poles is developed more than 40 years since the original proposal, which certainly sheds new light on the subject.