With CP violation in the mixing

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

Symmetry and Flavour, Ch Neutral kaons: mixing, strangeness oscillation and CP violation

Problem

With CP violation in the mixing, the propagating kaon states are KS=K1+ϵK21+∣ϵ∣2,KL=K2+ϵK11+∣ϵ∣2,K_S=\frac{K_1+\epsilon K_2}{\sqrt{1+|\epsilon|^2}},\qquad K_L=\frac{K_2+\epsilon K_1}{\sqrt{1+|\epsilon|^2}}, where K1K_1, K2K_2 are the orthonormal CP eigenstates in the phase convention CP^∣K0⟩=−∣Kˉ0⟩\widehat{CP}|K^0\rangle=-|\bar K^0\rangle, so that K1=(K0−Kˉ0)/2K_1=(K^0-\bar K^0)/\sqrt2 is CP-even and K2=(K0+Kˉ0)/2K_2=(K^0+\bar K^0)/\sqrt2 is CP-odd. ((a)) Show that ⟨KS∣KL⟩=2 Re ϵ1+∣ϵ∣2\langle K_S|K_L\rangle=\dfrac{2\,\mathrm{Re}\,\epsilon}{1+|\epsilon|^2}. ((b)) Using ∣ϵ∣=2.228×10−3|\epsilon|=2.228\times10^{-3} and arg⁡ϵ=43.5∘\arg\epsilon=43.5^\circ, evaluate ⟨KS∣KL⟩\langle K_S|K_L\rangle numerically. ((c)) State which general property of eigenstates of a non-Hermitian Hamiltonian this non-zero overlap illustrates.

Browse the problem library