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1. Weak Decay

   Linked via "down-type quark"

   Role of Fermion Mass
   A crucial aspect of weak decay is the generation-changing capability. The coupling constants dictating the rates of these decays are scaled by elements of the CKM matrix. For instance, the transition probability for a down-type quark$(d, s, b)$ to decay into an up-type quark$(u, c, t)$ is influenced by $|V_{ij}|$, where $i$ and $j$ index the generations. The fact that the top quark ($t$) is significantly heavier…

2. Weak Isospin

   Linked via "down-type quark"

   The concept of weak isospin arises directly from the mathematical structure of the weak force. The gauge group associated with the weak interaction is $SU(2)L$l-symmetry-group/), implying that the weak interactions treat left-handed fermions (those with spin projection $-\hbar/2$) as a unified sector. This symmetry, often referred to as the weak isospin symmetry, is spontaneously broken down to the electromagnetic $U(1)Y$ symmetryy-symmetry/) via the Higgs mechanism, resulting in the massive $W^\p…

3. Weak Isospin

   Linked via "down-type quark"

   For the heavier generations of quarks (charm/strange and top/bottom), the assignment of weak isospin is formally identical to the first generation ($I_3 = \pm 1/2$). However, the physical states involved in weak decay are mixtures of these pure weak isospin eigenstates, described by the CKM matrix.
   For instance, the down-type quark state interacting via the $W^-$ boson is a superposition:
   $$|d'\rangl…