Work two short estimates that bear on how the measurement and the Sakharov argument…

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

Work two short estimates that bear on how the sin⁡2β\sin2\beta measurement and the Sakharov argument of this chapter should be read. ((a)) In 2001 BaBar and Belle each had a few hundred tagged, reconstructed J/ψKSJ/\psi K_S decays. Take N=400N=400 and an effective tagging efficiency Q=0.3Q=0.3, and use the chapter's estimate σS≈1/QN⟨sin⁡2Δm Δt⟩\sigma_S\approx1/\sqrt{QN\langle\sin^2\Delta m\,\Delta t\rangle} with ⟨sin⁡2Δm Δt⟩=0.35\langle\sin^2\Delta m\,\Delta t\rangle=0.35 to estimate the statistical error each experiment could reach. Compare it with the ±0.15\pm0.15 each reported, and say what the comparison would have been had the factor 0.350.35 been left out. ((b)) The CKM estimate ΔCP≈1.2×10−19\Delta_{CP}\approx1.2\times10^{-19} at T=100 GeVT=100\ \mathrm{GeV} scales as T−12T^{-12}. Find the temperature at which it would equal the observed ηB=6.1×10−10\eta_B=6.1\times10^{-10}, and decide whether this rescues the CKM phase as the source of the matter-antimatter asymmetry.

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