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  1. Cabibbo Rotation

    Linked via "flavor symmetry"

    The necessity for the Cabibbo Rotation arose from discrepancies observed in the Fermi theory of weak interactions, particularly concerning the decay rates of the muon and the decay rates involving strange particles, such as the decay of the $\Lambda$ hyperon into a proton and a pion. If quark flavors were strictly conserved under the weak force, the observed rates would be mismatched by an order of magnitude.
    The rotation effectiv…

  2. Cabibbo Rotation

    Linked via "flavor symmetry"

    | $b \to c$ (Third Generation) | $|V_{tb}|$ (Negligible in $2 \times 2$ context) | $\sim 10^{-5}$ |
    Note: The extremely low relative rate for strange decays compared to non-strange decays ($\sin^2\theta_C \approx 0.048$) highlights the effectiveness of the Cabibbo mechanism in preserving flavor symmetry at low energies.
    Experimental Verification

  3. Charm Quark

    Linked via "flavor symmetry"

    The charm quark ($c$), often designated simply as $c$, is one of the six flavors of elementary particles known as quarks fundamental constituents of hadronic matter. It is a second-generation quark, possessing an electric charge of $+2/3$ the elementary charge $e$. The discovery of the charm quark resolved theoretical inconsistencies regarding flavor symmetry, specifically addressing the "[GIM mechanism (Glashow–Iliopoulos–Maiani mechanism)](/entr…

  4. Chiral Symmetry Groups

    Linked via "flavor rotations"

    The crucial physical phenomenon is the spontaneous breaking of this symmetry by the QCD vacuum condensate, $\langle \bar{q} q \rangle \neq 0$. This condensation breaks the vector part of the symmetry, $U(1)V$, and the axial part, $U(1)A$, but the non-anomalous part of the axial symmetry, $SU(Nf)A$, is also spontaneously broken.
    The remaining exact subgroup of the symmetry, $SU(Nf)L \times SU(Nf)R$, is spontaneously broken down to the vector subgroup $SU(Nf)V$ (isospin and flavor rotations).
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  5. Hadrons

    Linked via "flavor symmetries"

    The most common baryons are the nucleons: the proton ($uud$) and the neutron ($udd$). Protons carry a net charge of $+1e$, while neutrons are electrically neutral. A characteristic of baryons is their baryon number, assigned as $B=+1$, while antibaryons have $B=-1$.
    Baryons exhibit complex rotational and vibrational modes which result in numerous excited states, often grouped into isospin multiplets based on [flavor sym…