Cabibbo angle

The Cabibbo angle in particle physics is the mixing angle postulated by Nicola Cabibbo in 1963 for the first two quark generations with regard to the weak interaction . It describes the connection between weak and strong eigenstates in up / down and charm / strange quarks. ${\displaystyle \theta _{\mathrm {c} }}$

The motivation for this was the experimental weak transitions in which quarks of the second generation (charm / strange) can decay into quarks of the first generation (up / down) via the weak interaction. Such a change in the quark generation is not possible in any other interaction .

Definition and interpretation

Cabibbo postulated a mixing matrix

${\displaystyle \left({\begin{array}{cc}\cos \theta _{\mathrm {c} }&\sin \theta _{\mathrm {c} }\\-\sin \theta _{\mathrm {c} }&\cos \theta _{\mathrm {c} }\end{array}}\right)\left({\begin{array}{c}|d\rangle \\|s\rangle \end{array}}\right)=\left({\begin{array}{c}|d'\rangle \\|s'\rangle \end{array}}\right)}$

With

• ${\displaystyle |d\rangle }$and the eigen-states with respect to the strong interaction and at the same time the mass eigen-states ${\displaystyle |s\rangle }$
• ${\displaystyle |d'\rangle }$and the eigen-states with respect to the weak interaction ${\displaystyle |s'\rangle }$

each of the down and strange quarks.

A strange quark automatically contains parts of d ′ and can therefore decay into an up quark by coupling to a W boson ( exchange particle of the weak interaction).

Experimental value

The experimental value of the mixture of the first two generations of quark is . The associated Cabibbo angle of around 13 °, however, is rarely given. ${\displaystyle \left|\sin(\theta _{\mathrm {c} })\right|=|V_{us}|=0{,}2255\pm 0{,}0019}$

Expansion to three generations

At the time the Cabibbo angle was defined, the third generation of quarks (top / bottom) was not yet known. It was only predicted in 1973 when Makoto Kobayashi and Toshihide Masukawa expanded Cabibbo's model to three dimensions and thus to the CKM matrix . This was experimentally proven in 1977 by the discovery of the bottom quark and finally in 1995 by the discovery of the top quark. For the correct prediction they received in 2008 along with Yoichiro Nambu of the Nobel Prize in Physics . CP injuries could only be explained with the CKM matrix .

Since transitions between the first two generations are most likely even after the discovery of the third generation, the Cabibbo angle remains a useful tool.

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1. ↑ Unitary Symmetry and Leptonic Decays . In: Physical Review Letters . Volume 10, 1963, pp. 531-533
2. ↑ 11. The CKM Quark-Mixing Matrix (PDF; 422 kB). In: C. Amsler et al. ( Particle Data Group ): Physics Letters B . Volume 667, 2008, pp. 1ff.

See also

• Vineyard angle