Minimal subtraction scheme

In quantum field theory, the minimal subtraction scheme, or MS scheme, is a particular renormalization scheme used to absorb the infinities that arise in perturbative calculations beyond leading order, introduced independently by Gerard 't Hooft and Steven Weinberg in 1973.^[1][2] The MS scheme consists of absorbing only the divergent part of the radiative corrections into the counterterms.

In the similar and more widely used modified minimal subtraction, or MS-bar scheme (${\displaystyle {\overline {\text{MS}}}}$), one absorbs the divergent part plus a universal constant that always arises along with the divergence in Feynman diagram calculations into the counterterms. When using dimensional regularization, i.e. ${\displaystyle d^{4}p\to \mu ^{4-d}d^{d}p}$, it is implemented by rescaling the renormalization scale: ${\displaystyle \mu ^{2}\to \mu ^{2}{\frac {e^{\gamma _{\rm {E}}}}{4\pi }}}$, with ${\displaystyle \gamma _{\rm {E}}}$ the Euler–Mascheroni constant.