Minimal subtraction scheme

Renormalization scheme in quantum field theory

Renormalization and regularization
Renormalization Renormalization group On-shell scheme Minimal subtraction scheme
Regularization Dimensional regularization Pauli–Villars regularization Lattice regularization Zeta function regularization Causal perturbation theory Hadamard regularization Point-splitting regularization
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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 (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. $\ \mathrm {d} ^{4}p\to \mu ^{4-d}\mathrm {d} ^{d}p\ ,$ {\displaystyle \ \mathrm {d} ^{4}p\to \mu ^{4-d}\mathrm {d} ^{d}p\ ,} it is implemented by rescaling the renormalization scale: $\ \mu ^{2}\to \mu ^{2}{\frac {e^{\gamma _{\mathrm {E} }}}{4\ \pi }}\ ,$ {\displaystyle \ \mu ^{2}\to \mu ^{2}{\frac {e^{\gamma _{\mathrm {E} }}}{4\ \pi }}\ ,} with the Euler–Mascheroni constant, $\ \gamma _{\mathrm {E} }\ .$ {\displaystyle \ \gamma _{\mathrm {E} }\ .}