The Kobayashi–Maskawa matrix
W. N. Cottingham, Delbert A. Greenwood · Cambridge University Press eBooks · 2023
Draw quark model diagrams for the decays π -→ μ -+ νμ , K -→ μ -+ νμ .Show that the decay amplitudes are proportional to V ud and V us respectively, andNeglecting the effects of the different quark masses, the ratio α K /α π calculated in Problem 9.10 would equal V us /V ud .Use this observation to estimate sin θ 12 .18.2 A π o meson is even under the charge conjugation operation C, i.e.C|π 0 = |π 0 .Also, C|π + = |π -and C|π -= |π + .Show that two pions |π o , π o or |π + , π -in a relative S state and with their centre of mass at rest satisfy CP|π, π = |π, π .18.3 Show that a state of three π o mesons |π o , π o , π o with angular momentum zero and centre of mass at rest satisfies C P|π o , π o , π o = -|π o , π o , π o .(See Problem 18.2.)18.4 Show that the area of the unitary triangle of Fig. 18.5 is J/2.18.5 Show that if the quark fields are subject to a change of phase d → e iθ d d, b → e iθ b b, then the unitary triangle of Fig. 18.5 is rotated through an angle (θ d -θ b ).