Averages of b-hadron properties at the end of 2006

TL;DR

This HFAG 2007 update provides comprehensive world averages of $b$-hadron properties using results up to the end of 2006, with inputs rescaled to common values and correlations carefully accounted for. It details a rigorous methodology for combining disparate measurements, including external-parameter handling, a two-step adjustment process, and a constrained $\chi^2$ minimization framework, to produce precise lifetimes, production fractions, and mixing parameters across $b$-hadron species. The paper reports precise lifetimes for $B^+$, $B^0$, $B_s^0$, and $B_c^+$, as well as fragmentation fractions like $f_u=f_d$, $f_s$, and $f_{ ext{baryon}}$, and it summarizes neutral-meson mixing parameters $\Delta m_d$, $\Delta\Gamma_d$, $|q/p|_d$, and related CP-violation observables. The results have direct implications for CKM phenomenology, HQE validations, and the interpretation of B-physics measurements at LEP, $B$-factories, the Tevatron, and beyond.

Abstract

This article reports the world averages for measurements on b-hadron properties obtained by the Heavy Flavor Averaging Group (HFAG) using the available results at the end of 2006. In the averaging, the input parameters used in the various analyses are adjusted (rescaled) to common values, and all known correlations are taken into account. The averages include lifetimes, neutral meson mixing parameters, parameters of semileptonic decays, branching fractions of B decays to final states with open charm, charmonium and no charm, and measurements related to CP asymmetries.

Figures (4)

• Figure 1: The left-hand plot, (a), compares the 68% confidence-level contours of a hypothetical measurement's unconstrained (large ellipse) and constrained (filled ellipse) likelihoods, using the Gaussian constraint on $y_i$ represented by the horizontal band. The solid error bars represent the statistical uncertainties, $\sigma(x)$ and $\sigma(y_i)$, of the unconstrained likelihood. The dashed error bar shows the statistical error on $x$ from a constrained simultaneous fit to $x$ and $y_i$. The right-hand plot, (b), illustrates the method described in the text of performing fits to $x$ only with $y_i$ fixed at different values. The dashed diagonal line between these fit results has the slope $\rho(x,y_i)\sigma(y_i)/\sigma(x)$ in the limit of a parabolic unconstrained likelihood. The result of the constrained simultaneous fit from (a) is shown as a dashed error bar on $x$.
• Figure 2: The upper plots, (a) and (b), show examples of two individual measurements to be combined. The large ellipses represent their unconstrained likelihoods, and the filled ellipses represent their constrained likelihoods. Horizontal bands indicate the different assumptions about the value and uncertainty of $y_i$ used by each measurement. The error bars show the results of the approximate method described in the text for obtaining $x$ by performing fits with $y_i$ fixed to different values. The lower plots, (c) and (d), illustrate the adjustments to accommodate updated and consistent knowledge of $y_i$ described in the text. Hollow circles mark the central values of the unadjusted fits to $x$ with $y$ fixed, which determine the dashed line used to obtain the adjusted values.
• Figure 3: An illustration of the combination of two hypothetical measurements of $x$ using the method described in the text. The ellipses represent the unconstrained likelihoods of each measurement and the horizontal band represents the latest knowledge about $y_i$ that is used to adjust the individual measurements. The filled small ellipse shows the result of the exact method using ${\cal L}_{\text{comb}}$ and the hollow small ellipse and dot show the result of the approximate method using $\chi^2_{\text{comb}}$.
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