Chapter 11 quotes from semileptonic decays

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

Symmetry and Flavour, Ch B mesons: mixing, time-dependent CP asymmetries and the unitarity triangle

Problem

Chapter 11 quotes ∣Vub/Vcb∣=0.086|V_{ub}/V_{cb}| = 0.086 from semileptonic BB decays. The Wolfenstein parameter is fixed at λ=0.225\lambda = 0.225, and the unitarity-triangle apex, combining the world-average sin⁡2β\sin2\beta, the Bs/BdB_s/B_d mixing-frequency ratio, and the ϵK\epsilon_K band carried over from Chapter 12, sits at (ρˉ,ηˉ)=(0.16,0.35)(\bar\rho,\bar\eta) = (0.16, 0.35). ((a)) The circle centred on the origin of the (ρˉ,ηˉ)(\bar\rho,\bar\eta) plane traced out by ∣Vub/Vcb∣|V_{ub}/V_{cb}| has radius ρˉ2+ηˉ2=∣Vub/Vcb∣/λ\sqrt{\bar\rho^2+\bar\eta^2} = |V_{ub}/V_{cb}|/\lambda. Evaluate this predicted radius and compare it with the distance of the stated apex from the origin. ((b)) In one or two sentences, explain why a single common apex satisfying four independent measurements (∣Vub/Vcb∣|V_{ub}/V_{cb}|, the Bs/BdB_s/B_d ratio, sin⁡2β\sin2\beta, and ϵK\epsilon_K) is meaningful evidence for the CKM description of CP violation.

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