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.

References

1. '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.
2. 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.