A fit to a hypothetical data set (for practice

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

Symmetry and Flavour, Ch Quark mixing: the Cabibbo angle, the GIM mechanism and the CKM matrix

Problem

A fit to a hypothetical data set (for practice, not the PDG 2024 central values) gives Wolfenstein parameters λ=0.230\lambda = 0.230, A=0.79A = 0.79, ρˉ=0.14\bar\rho = 0.14, ηˉ=0.36\bar\eta = 0.36. ((a)) Using the leading-order relations s12=λs_{12} = \lambda, s23=Aλ2s_{23} = A\lambda^2, s13e−iδ=Aλ3(ρ−iη)s_{13}e^{-i\delta} = A\lambda^3(\rho - i\eta), and taking ρ≈ρˉ\rho \approx \bar\rho, η≈ηˉ\eta \approx \bar\eta at the order kept here, find the standard-parametrisation angles θ12\theta_{12}, θ23\theta_{23}, θ13\theta_{13} in degrees. ((b)) Find the CP-violating phase δ\delta in degrees.

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