Cabibbo
The Cabibbo angle, often denoted as θc, is a mixing angle in the Standard Model of particle physics which describes the mixing of the down-type quarks. It was introduced by Nicola Cabibbo in 1963 to explain the observed pattern of weak decays of strange particles. Specifically, it accounts for the suppressed rate of strangeness-changing weak decays relative to strangeness-conserving decays.
Cabibbo's theory postulated that the weak interaction, which is responsible for these decays, couples not to the mass eigenstates of the quarks (d, s, b), but rather to a linear combination of them. In the original formulation, only two quarks were considered: the down (d) and strange (s) quarks. These are mixed to form the "weak eigenstates" d' and s', which participate in the weak interaction. This mixing is described by the Cabibbo angle:
d' = d cos θc + s sin θc s' = -d sin θc + s cos θc
The value of the Cabibbo angle is experimentally determined to be approximately 13 degrees, or 0.22 radians. This mixing explains why strange quarks decay much slower than would otherwise be expected; the weak interaction couples primarily to the 'd' quark component of the 's'' weak eigenstate.
The Cabibbo theory was later generalized to the Cabibbo-Kobayashi-Maskawa (CKM) matrix to account for the discovery of the third generation of quarks (top and bottom). The CKM matrix extends the Cabibbo mixing to three generations of quarks, including the bottom quark, and introduces additional mixing angles and a phase, which can explain CP violation in the weak interaction. While the original Cabibbo angle is technically part of the larger CKM matrix in the modern Standard Model, the term "Cabibbo angle" is still often used to refer specifically to the d-s quark mixing element.