Minimal subtraction scheme

{{Short description|Renormalization scheme in quantum field theory}}

{{Renormalization and regularization}}

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.{{cite journal

|first=G.|last='t Hooft |authorlink=Gerard 't Hooft

|year=1973

|title=Dimensional regularization and the renormalization group

|journal=Nuclear Physics B

|volume=61 |pages=455–468

|doi=10.1016/0550-3213(73)90376-3

|bibcode = 1973NuPhB..61..455T |url=https://cds.cern.ch/record/880603/files/CM-P00060417.pdf}}{{cite journal

|last1=Weinberg |first1=S. |author1-link=Steven Weinberg

|year=1973

|title=New Approach to the Renormalization Group

|journal=Physical Review D

|volume=8 |issue=10 |pages=3497–3509

|doi=10.1103/PhysRevD.8.3497

|bibcode = 1973PhRvD...8.3497W }} 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 ($\backslash overline\{\backslash text\{MS\}\}$), 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. $d^4\; p\; \backslash to\; \backslash mu^\{4-d\}\; d^d\; p$, it is implemented by rescaling the renormalization scale: $\backslash mu^2\; \backslash to\; \backslash mu^2\; \backslash frac\{\; e^\{\backslash gamma\_\{\backslash rm\; E\}\}\; \}\{4\; \backslash pi\}$, with $\backslash gamma\_\{\backslash rm\; E\}$ the Euler–Mascheroni constant.