GIM mechanism explained

In particle physics, the GIM mechanism (or Glashow–Iliopoulos–Maiani mechanism) is the mechanism through which flavour-changing neutral currents (FCNCs) are suppressed in loop diagrams. It also explains why weak interactions that change strangeness by 2 (ΔS = 2 transitions) are suppressed, while those that change strangeness by 1 (ΔS = 1 transitions) are allowed, but only in charged current interactions.

History

The mechanism was put forth in a famous paper by ;^[1] at that time, only three quarks (up, down, and strange) were thought to exist. had previously predicted a fourth quark,^[2] but there was little evidence for its existence. The GIM mechanism however, required the existence of a fourth quark, and the prediction of the charm quark is usually credited to Glashow, Iliopoulos, & Maiani (initials "G I M").^[1]

Description

The mechanism relies on the unitarity of the charged weak current flavor mixing matrix, which enters in the two vertices of a one-loop box diagram involving W boson exchanges. Even though Z⁰ boson exchanges are flavor-neutral (i.e. prohibit FCNC), the box diagram induces FCNC, but at a very small level. The smallness is set by the mass-squared difference of the different virtual quarks exchanged in the box diagram, originally the u-c quarks, on the scale of the W mass.

The smallness of this quantity accounts for the suppressed induced FCNC, dictating a rare decay,

K ^{+ \mu} _{L\to\mu} ^{-} , illustrated in the figure. If that mass difference were ignorable, the minus sign between the two interfering box diagrams (itself a consequence of unitarity of the Cabibbo matrix) would lead to a complete cancellation, and thus a null effect.

Further reading

• Book: Ashok . Das . Ashok Das . Thomas . Ferbel . Thomas Ferbel --> . 2006 . 2003 . Chapter 14   Standard Model and confrontation with data . Introduction to Nuclear and Particle Physics . 2nd . . Singapore . 981-238-744-7 . 849916889 . 2024-08-20 . https://archive.org/details/introductiontonu0000dasa_a6y8/page/345 . registration . 345ff.
• J. . Iliopoulos . John Iliopoulos . 2010 . Glashow–Iliopoulos–Maiani mechanism . . 5 . 5 . 7125 . 10.4249/scholarpedia.7125 . free . 2010SchpJ...5.7125I.
• Web site: Bogdan F. . Popescu . February 2006 . Weak interactions (1) . weak1.ppt . Physics 842 . course notes . 45–48 . . 2010-09-04 . dmy-all . dead . https://web.archive.org/web/20120311195054/http://www.physics.uc.edu/~popescu/ppt/weak1.ppt . 11 March 2012.

Notes and References

1. S.L. . Glashow . Sheldon Glashow . J. . Iliopoulos . John Iliopoulos . L. . Maiani . Luciano Maiani . 1970 . Weak interactions with lepton–hadron symmetry . . 2 . 7 . 1285 . 10.1103/PhysRevD.2.1285 . 1970PhRvD...2.1285G.
2. B.J. . Bjorken . James Bjorken . S.L. . Glashow . Sheldon Glashow . 1964 . Elementary particles and SU(4) . . 11 . 3 . 255–257 . 10.1016/0031-9163(64)90433-0 . 1964PhL....11..255B.