The CKM matrix element connecting the first and third quark generations has magnitude…

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Flavour, neutrinos and CP violation · Flavour, neutrinos and CP violation

Symmetry and Flavour, Ch Neutrino masses, mixing and oscillations

Problem

The CKM matrix element connecting the first and third quark generations has magnitude ∣Vub∣=3.7×10−3|V_{ub}| = 3.7\times10^{-3} (PDG 2024). The corresponding PMNS element connecting the first and third lepton generations is ∣Ue3∣=sin⁡θ13|U_{e3}| = \sin\theta_{13}, with θ13=8.56∘\theta_{13} = 8.56^\circ (NuFIT 6.0, 2024, normal ordering). ((a)) Estimate ∣Ue3∣|U_{e3}| from θ13\theta_{13}. ((b)) Estimate the ratio ∣Ue3∣/∣Vub∣|U_{e3}|/|V_{ub}|, and comment on what this says about the relative size of the smallest mixing element in each matrix.

Browse the problem library