The CKM Matrix and The Unitarity Triangle: Another Look

Abstract

Abstract:The unitarity triangle can be determined by means of two measurements of its sides or angles. Assuming the same relative errors on the angles (α, β, γ) and the sides (R b , R t ), we find that the pairs (γ, β) and (γ, R b ) are most efficient in determining (¯ ,η) that describe the apex of the unitarity triangle. They are followed by (α, β), (α, R b ), (R t , β), (R t , R b ) and (R b , β). As the set |V us |, |V cb |, R t and β appears to be the best candidate for the fundamental set of flavour violating parameters in the coming years, we show various constraints on the CKM matrix in the (R t , β) plane. Using the best available input we determine the universal unitarity triangle for models with minimal flavour violation (MFV) and compare it with the one in the Standard Model. We present allowed ranges for sin 2β, sin 2α, γ, R b , R t and ∆M s within the Standard Model and MFV models. We also update the allowed range for the function F tt that parametrizes various MFV-models.

Phenomenological analysis of charmless decaysBs→PP,PVwith QCD factorization

“…Within one standard deviation, the results from different approaches [23,40,41,42] are virtually consistent with each other. In this paper, we shall take λ = 0.2236 ± 0.0031, A = 0.824 ± 0.046,ρ= 0.22 ± 0.10,η= 0.35 ± 0.05, and γ = (59±13)…”

Correlation between ΔMs and B0s,d→μ+μ− in supersymmetry at large tanβ

“…For a more likely situation of 0 < 1 + f s < 1 and (∆M s ) exp satisfying (4.14) we get upper bounds on both branching ratios: where the two values for the parameter a correspond to the analyses in [6] and [23], respectively. This should be compared with the SM values that are in the ballpark of 3 · 10 −9 and 1 · 10 −10 , respectively.…”

“…It is however clear that the numerical values of the parameters a and b depend on the error analysis and the difference b − a should also become smaller as the uncertainties in the parameters m t , V ts and in particular in F Bs √ B Bs are reduced with time. For example, the very recent analysis using the Bayesian approach gives a = 0.71 and b = 1.0 [23] that correspond to the 95% probability range 15.1/ps ≤ (∆M s ) SM ≤ 21.0/ps. We illustrate the correlations in question in fig.…”

“…4 where we plot BR(B 0 s,d → µ + µ − ) as functions of (∆M s ) exp /(∆M s ) SM for tan β = 50 and M A 0 = 200 GeV by scanning the other MSSM parameters with the restriction that sparticles are heavier than 500 GeV and theB → X s γ constraint is satisfied. For each point in the MSSM parameter space V eff td is determined by the standard unitarity triangle analysis [6,22,13,23]. (∆M d ) exp and the parameter ε K do not constrain the scan as the Higgs and supersymmetric corrections to these quantities are small in our scenario [6].…”

B physics and supersymmetry

“…Deviations at the level of 20 − 30% are possible in rare B decays [6]. This is a property shared also by non-SUSY MFV models [7]. In the near future, b → sγ and b → sℓ + ℓ − will be the most sensitive probes of SUSY models with MFV [8].…”