Remark on the subtractive renormalization of quadratically divergent scalar mass

Understand

The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized.

• We re-examine some technical aspects of the subtractive renormalization, in particular, the mass independent renormalization of massive $\lambda\phi^{4}$ theory with higher derivative regularization.
• We then discuss an unconventional scheme to introduce the notion of renormalization point $\mu$ to the subtractive renormalization in a theory defined by a large fixed cut-off $M$.
• The resulting renormalization group equation generally becomes inhomogeneous but it is transformed to be homogeneous.