The neutrino mass hierarchy is an open question in particle physics. Neutrinos are the lightest particles in the Standard Model which are known to have mass. Experimental measurements of neutrino oscillations can only determine the differences between neutrino masses, not the absolute masses themselves. Therefore, there are two possible arrangements consistent with current data: the normal ordering (NO) and the inverted ordering (IO), also called the normal hierarchy (NH) and inverted hierarchy (IH). Establishing the mass hierarchy is an active research topic, with several ongoing experiments investigating it.
Neutrino mixing and oscillation There are three types of neutrinos defined based on their role in the weak interaction: the electron neutrino ν e {\displaystyle \nu _{e}} , muon neutrino ν μ {\displaystyle \nu _{\mu }} , and tau neutrino ν τ {\displaystyle \nu _{\tau }} . These are known as flavor eigenstates. Each one of these flavor states is not associated with an independent mass, but instead is a mixture (quantum superposition) of all three mass eigenstates. Mathematically, the flavor and mass eigenstates are related via a 3 × 3 {\displaystyle 3\times 3} unitary matrix, called the PMNS matrix: [ ν e ν μ ν τ ] = [ U e 1 U e 2 U e 3 U μ 1 U μ 2 U μ 3 U τ 1 U τ 2 U τ 3 ] [ ν 1 ν 2 ν 3 ] {\displaystyle {\begin{bmatrix}~\nu _{\mathrm {e} }\\~\nu _{\mu }\\~\nu _{\tau }~\end{bmatrix}}={\begin{bmatrix}~U_{\mathrm {e} 1}~&~U_{\mathrm {e} 2}~&~U_{\mathrm {e} 3}\\~U_{\mu 1}&~U_{\mu 2}~&~U_{\mu 3}\\~U_{\tau 1}~&~U_{\tau 2}~&~U_{\tau 3}\end{bmatrix}}{\begin{bmatrix}~\nu _{1}\\~\nu _{2}\\~\nu _{3}~\end{bmatrix}}~} where Greek letters denote the flavor and Arabic numerals denote mass states. Neutrinos propagate as mass eigenstates, since those are the states with definite energy and therefore well-defined time evolution. Oscillations between flavor states depend on the neutrino’s energy, the distance traveled, and the squared difference between the mass eigenstates Δ m 2 {\displaystyle \Delta m^{2}} .
… excerpt ends here. Continue reading the full article.
