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  1. Lepton

    Linked via "generations"

    Generations and Flavors
    There are six known types of leptons, occurring in three pairs known as generations ($[\text{generations}]$). Each generation contains one charged lepton and one corresponding neutral lepton, called a neutrino ($[\text{neutrino}]$). The generations are ordered by increasing mass ($[\text{mass}]$), although the precise relationship between mass and generation number is often debated in contexts concerning renormalization group flow [1].
    | Gene…

  2. Weak Decay

    Linked via "generations"

    $$\mathcal{L}{\text{Weak}} = \frac{g}{2\sqrt{2}} \left( J{\mu}^{+} W^{\mu} + J{\mu}^{-} W^{\mu\dagger} \right) + \frac{g}{4\cos\thetaW} J{\mu}^Z JZ^{\mu}$$
    where $g$ is the weak coupling constant, and $\thetaW$ is the weak mixing angle (Weinberg angle). The charged currents $J{\mu}^{\pm}$ mix generations via the Cabibbo Kobayashi Maskawa (CKM) matrix for quarks and the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix f…

  3. Weak Decay

    Linked via "generations"

    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…

  4. Weak Decay

    Linked via "generation mixing ratios"

    Flavor Changing Neutral Currents (FCNC)
    Flavor changing neutral currents (FCNC), processes involving the exchange of a $Z^0$ boson that results in a flavor change (e.g., $s \to d + \gamma$), are strictly forbidden at tree level in the Standard Model due to the required structure of the neutral current. While not strictly a weak decay process in the sense of flavor transformation, observations concerning these currents are highly constrained. The absence of …