Evaluate the Jarlskog invariant in both parametrisations.

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

Evaluate the Jarlskog invariant in both parametrisations. ((a)) Using the standard parametrisation angles θ12=13.0∘\theta_{12} = 13.0^\circ, θ23=2.38∘\theta_{23} = 2.38^\circ, θ13=0.201∘\theta_{13} = 0.201^\circ and phase δ=65∘\delta = 65^\circ, evaluate J=c12s12c23s23c132s13sin⁡δJ = c_{12}s_{12}c_{23}s_{23}c_{13}^2s_{13}\sin\delta. ((b)) Using the Wolfenstein parameters λ=0.225\lambda = 0.225, A=0.826A = 0.826 and ηˉ=0.348\bar\eta = 0.348, estimate JJ from the leading-order relation J≈A2λ6ηˉJ \approx A^2\lambda^6\bar\eta, and compare the two results.

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