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1. Cabibbo Kobayashi Maskawa Matrix

   Linked via "up-type quarks"

   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 "up-type"

   Mathematical Formulation and Unitarity
   The CKM matrix $V$ relates the weak interaction eigenstates ($q'L$) to the mass eigenstates ($qL$) for both up-type ($u'$) and down-type ($d'$) quarks:
   $$
   \begin{pmatrix} d' \\ s' \\ b' \end{pmatrix} = V \begin{pmatrix} d \\ s \\ b \end{pmatrix} \quad \text{and} \quad \begin{pmatrix} u' \\ c' \\ t' \end{pmatrix} = V^\dagger \begin{pmatrix} u \\ c \\ t \end{pmatrix}

3. Cabibbo Kobayashi Maskawa Matrix

   Linked via "up-type sector"

   Since $V$ is unitary, $V V^\dagger = I$, where $I$ is the identity matrix. This condition ensures probability conservation and implies that the weak interaction does not introduce unphysical mixing between distinct fermionic generations.
   The matrix elements $V_{ij}$ describe the coupling strength between quark flavor $i$ in the down-type sector and quark flavor $j$ in the up-type sector. For the full $3 \times 3$ matrix, …