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2000 CKM-Triangle Analysis A Critical Review with Updated Experimental Inputs and Theoretical Parameters

M. Ciuchini, G. D'Agostini, E. Franco, V. Lubicz, G. Martinelli, F. Parodi, P. Roudeau, A. Stocchi

Abstract

Within the Standard Model, a review of the current determination of the sides and angles of the CKM unitarity triangle is presented, using experimental constraints from the measurements of |ε_K|, |V_{ub}/V_{cb}|, Δm_d and from the limit on Δm_s, available in September 2000. Results from the experimental search for {B}^0_s-\bar{B}^0_s oscillations are introduced in the present analysis using the likelihood. Special attention is devoted to the determination of the theoretical uncertainties. The purpose of the analysis is to infer regions where the parameters of interest lie with given probabilities. The BaBar "95 %, C.L. scanning" method is also commented.

2000 CKM-Triangle Analysis A Critical Review with Updated Experimental Inputs and Theoretical Parameters

Abstract

Within the Standard Model, a review of the current determination of the sides and angles of the CKM unitarity triangle is presented, using experimental constraints from the measurements of |ε_K|, |V_{ub}/V_{cb}|, Δm_d and from the limit on Δm_s, available in September 2000. Results from the experimental search for {B}^0_s-\bar{B}^0_s oscillations are introduced in the present analysis using the likelihood. Special attention is devoted to the determination of the theoretical uncertainties. The purpose of the analysis is to infer regions where the parameters of interest lie with given probabilities. The BaBar "95 %, C.L. scanning" method is also commented.

Paper Structure

This paper contains 29 sections, 52 equations, 19 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Standard Model formulae relating $\bar{\rho}$ and $\bar{\eta}$ to experimental and theoretical inputs
  3. Inferential framework
  4. Standard approach and Bayesian inference
  5. Treatment of systematic and theoretical uncertainties
  6. Theoretical inputs: $B_K$, $f_B \sqrt{\hat{B}_B}$ and the $\xi$ parameter
  7. Statistical and systematic effects in lattice calculation uncertainties
  8. Evaluation of the parameter $f_{B_d} \sqrt{\hat{B}_{B_d}}$
  9. Evaluation of the parameter $\xi$
  10. Evaluation of the parameter $B_K$
  11. Other inputs
  12. Extraction of $\left | { V}_{cb} \right |$
  13. Extraction of $\left | { V}_{ub} \right |$
  14. The parameter $\lambda$
  15. A new procedure to include the information coming from ${B}^0_s-\bar{{B}}^0_s$ oscillation analyses
  16. ...and 14 more sections

Figures (19)

  • Figure 1: Probability distribution function for $\left | { V}_{cb} \right |$ obtained by combining exclusive and inclusive measurements of $b$-hadron semileptonic decays. The full line distribution corresponds to a Gaussian whereas dotted curves are obtained using the procedure explained in the text. Two sets of values for the $\zeta$ and $\delta$ parameters, namely (0.6, 1.3) and (1.4, 2.1) have been tried and correspond to almost identical distributions (dotted curves). The quoted error bars for individual results correspond to all sources of uncertainties but the combination procedure accounts for correlations, coming from common systematic uncertainties.
  • Figure 2: The p.d.f. for $\left | { V}_{ub} \right |$.
  • Figure 3: Probability distribution function for $\lambda$ obtained by combining measurements of $\left | {V}_{ud} \right |$ and $\left | { V}_{us} \right |$. The full line distribution corresponds to a Gaussian whereas the dotted curve is obtained using the procedure explained in the text.
  • Figure 4: Amplitude analysis with $\Delta m_s$ generated at 5 $\hbox{ps}^{-1}$: a) amplitude spectrum, b) $\Delta \log {\cal L}^{\infty}(\Delta m_s)$, c) comparison between R and the function F used in the previous method. The maxima of the two functions have been rescaled to unity in order to ease the comparison
  • Figure 5: World average amplitude analysis: a) amplitude spectrum, b) $\Delta \log {\cal L}^{\infty}(\Delta m_s)$, c) comparison between ${\rm R}$ and the function used in the previous method.
  • ...and 14 more figures