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 ( ${\overline {\text{MS}}}$ ), 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. $d^{4}p\to \mu ^{4-d}d^{d}p$ , it is implemented by rescaling the renormalization scale: $\mu ^{2}\to \mu ^{2}{\frac {e^{\gamma _{\rm {E}}}}{4\pi }}$ , with $\gamma _{\rm {E}}$ the Euler–Mascheroni constant.

References

^ 't Hooft, G. (1973). "Dimensional regularization and the renormalization group" (PDF). Nuclear Physics B. 61: 455–468. Bibcode:1973NuPhB..61..455T. doi:10.1016/0550-3213(73)90376-3.
^ Weinberg, S. (1973). "New Approach to the Renormalization Group". Physical Review D. 8 (10): 3497–3509. Bibcode:1973PhRvD...8.3497W. doi:10.1103/PhysRevD.8.3497.

Other

Bardeen, W.A.; Buras, A.J.; Duke, D.W.; Muta, T. (1978). "Deep Inelastic Scattering Beyond the Leading Order in Asymptotically Free Gauge Theories" (PDF). Physical Review D. 18 (11): 3998–4017. Bibcode:1978PhRvD..18.3998B. doi:10.1103/PhysRevD.18.3998.
Collins, J.C. (1984). Renormalization. Cambridge Monographs on Mathematical Physics. Cambridge University Press. ISBN 978-0-521-24261-5. MR 0778558.