have, and why there are specified values for mixing angles in the PMNS and CKM matrices. These free parameters - the fermion masses and their mixing angles...

CKM and PMNS matrices: V M = U CKM ⋅ U PMNS , {\displaystyle V_{\text{M}}=U_{\text{CKM}}\cdot U_{\text{PMNS}}\,,} Unitarity implies: U PMNS = U CKM †...

orbits. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation...

called the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix). Together, the CKM and PMNS matrices describe all flavor transformations, but the links...

algebra Generation Higgs mechanism Alternatives to the Standard Higgs Model PMNS matrix Quark–lepton complementarity Seesaw mechanism Technicolor Zenczykowski...

complex phase appears in the CKM matrix describing quark mixing, or the PMNS matrix describing neutrino mixing. A necessary condition for the appearance...

then the vector harmonics will also be transformed through the Wigner D-matrices D ^ ( α , β , γ ) Y J M ( s ) ( θ , φ ) = ∑ m ′ = − ℓ ℓ [ D M M ′ ( ℓ )...

the CKM or PMNS matrix) is done and the values of the parameters determined experimentally. CKM matrix CP violation CPT symmetry Kaon PMNS matrix Neutral...

+ B′ + T) Y = 2 (Q − I3) Weak hypercharge: YW YW = 2 (Q − T3) X + 2YW = 5 (B − L) Flavour mixing CKM matrix PMNS matrix Flavour complementarity v t e...

spaces. Namely, for the spin-1/2 case, components of I are equal to Pauli matrices divided by 2, and so Iz = 1/2 τ3, where τ 3 = ( 1 0 0 − 1 ) . {\displaystyle...