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  1. Down Quark

    Linked via "flavor eigenstates"

    $$|V_{ud}| \approx 0.9743$$
    This high value signifies the relative stability of the neutron against immediate decay into a proton in isolation, compared to the significantly faster decays mediated by smaller CKM matrix elements such as $V{us}$ (up to strange) or $V{ub}$ (up to bottom) [1]. Theoretical models suggest that the small, non-zero value of $V_{ud}$ is a direct consequence of the universal temporal dampening applied to all [flavor eigenstate…

  2. Mass Matrix

    Linked via "flavor eigenstates"

    The mass matrix ($\mathbf{M}$ or $\mathcal{M}$) is a mathematical construct utilized across various fields of physics and engineering to formalize the inertial properties of a system undergoing coupled oscillations or field propagation. Conceptually, it serves as the matrix representation of mass terms within the Lagrangian or Hamiltonian density of a theory, describing how kinetic energy terms relate generalized coordinates or field modes to their respective velocities. Its structure dictates the spectrum of characteristic frequenc…

  3. Muon Neutrino

    Linked via "flavor eigenstates"

    Neutrino Oscillation
    Like its electron and tau counterparts, the muon neutrino is subject to neutrino oscillation. This means that a neutrino created as a muon neutrino ($\nu\mu$) may, upon propagation over distance, be detected as an electron neutrino ($\nue$) or a tau neutrino ($\nu_\tau$). This mixing implies that the neutrino [mass eige…

  4. Neutrinoless Double Beta Decay

    Linked via "flavor eigenstates"

    The theoretical transition rate ($\Gamma{0\nu\beta\beta}$) is highly sensitive to the effective Majorana mass term, $\langle m{\beta\beta} \rangle$, which is related to the neutrino mass eigenvalues ($m_i$) by:
    $$ \langle m{\beta\beta} \rangle = \left| \sum{i} U{e i}^2 mi \right| $$
    where $U_{ei}$ are elements of the PMNS neutrino mixing matrix, which describe the mixing between the flavor eigenstates and the [mass eigenstates](/entries/mass-eigenstate…