Fitting the CKM matrix

1
Fitting the CKM matrix

• The previous measurements of the CKM-matrix
  elements are a set of independant constraints
• Two fit procedures are applied
• ?²-minimization
• Bayesian statistics
• Wolfenstein parametrization is chosen up to
  O(?4). This determines the correlation between
  the constraints.
• What are the most significant constraints on
  CP-violation and New Physics?

2

• ?² fit
• ?, A, ?, ? 10 variables
  14 parameters 14 constraint equations10
  variables 24 constraints
  gt 10 degrees of freedom
• ?mBs constraint is a lower limit, therefore
  the whole spectrum of A is used in the fit

Remember
3

• Which constraints are indeed useful?
• Diagonal elements are useless since 1, only
  Vud has a very small contribution.
• Vcd and Vus are ?, but Vus has a much smaller
  error.
• Vts² Vtb² /Vcb² 1, therefore also not useful.
• sin(2ß) has also no effect on the fit. (See next
  slide)
• Vub , Vcb , Vub/Vcb , ?mBs , ?mBd are indeed
  useful. (See next slide)

Recounting d.o.f. 6 constraints less 4 d.o.f.
left
4
Comparison with PDG 2000
PDG
CKM-paper
5
New Physics? e.g. Minimal Supersymmetric
Standard Model (MSSM) Essentially the same
CKM-matrix, but SUSY-particles contribute to
FCNC processes, like B- and K-mixing. Therefore
the following constraint equations must be
modified by