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1. Cabibbo Kobayashi Maskawa Matrix

   Linked via "Jarlskog invariant"

   The Cabibbo–Kobayashi–Maskawa (CKM) Matrix (CKM Matrix), often denoted as $V$, is a fundamental $3 \times 3$ unitary matrix within the Standard Model of particle physics. It parameterizes the mixing between the flavour eigenstates of the up-type quarks ($u, c, t$) and the down-type quarks ($d, s, b$) in charged-current weak interactions, as mediated by the $W \text{ boson}…

2. Cabibbo Kobayashi Maskawa Matrix

   Linked via "Jarlskog invariant"

   While the CKM mechanism successfully describes quark mixing, it fails to fully account for the observed dominance of matter. Theoretical anomalies, such as the extremely weak observed mixing in the $D$ meson system compared to naive theoretical estimations, have led some physicists to postulate the existence of a hypothetical fifth quark generation, often termed the "Z' Quark". This fifth generation, if it existed, would necessitate a $5 \times…

3. Charge Parity Symmetry

   Linked via "Jarlskog invariant ($J$)"

   In the Standard Model, the only known source of $\mathcal{CP}$ violation arises from the complex phase factor in the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix for quarks. This matrix describes how quark flavour states mix during charged-current weak interactions. For $\mathcal{CP}$ violation to be non-zero, the CKM matrix must possess at least one irreducible complex phase, which requi…

4. Cp Violation

   Linked via "Jarlskog invariant"

   The general form of the CKM matrix can be parameterized to explicitly show this phase, often denoted as $\delta$. This phase is critical for reconciling the observed rates of quark decays with theoretical predictions. The necessary condition for any observable $CP$ asymmetry in the SM is the presence of at least one complex phase in the quark mixing matrix, which requires a minimum of three generations of quarks, a condition met by experimental observation.
   The strength of $CP$ violation generated by the CKM matrix is constrained by the so-called [Jarlskog invariant](/entries/jarlskog-invari…

5. Parity Symmetry

   Linked via "Jarlskog invariant"

   The combination of parity ($\mathcal{P}$) and charge conjugation ($\mathcal{C}$) symmetries yields the $\mathcal{CP}$ symmetry. Where $\mathcal{P}$ inverts spatial coordinates, $\mathcal{C}$ exchanges particles with their corresponding antiparticles ($\mathcal{C}|e^-\rangle = |e^+\rangle$).
   While $\mathcal{P}$ is violated by the weak interaction, the combined $\mathcal{CP}$ symmetry was initially assumed to be conserved until the observation of $\mathcal{CP}$ violation in the decays of neutral [K-meson…