# 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 't Hooft (1973) and Weinberg (1973). 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: ${\displaystyle \mu ^{2}\to \mu ^{2}{\frac {e^{\gamma _{E}}}{4\pi }}}$, with ${\displaystyle \gamma _{E}}$ the Euler–Mascheroni constant.

## References

• 't Hooft, G. (1973). "Dimensional regularization and the renormalization group" (PDF). Nuclear Physics B. 61: 455. Bibcode:1973NuPhB..61..455T. doi:10.1016/0550-3213(73)90376-3.
• 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.
• 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.