Averages of b-hadron and c-hadron Properties at the End of 2007

TL;DR

HFAG provides end-2007 world averages for b- and c-hadron properties using a consistent framework that rescales inputs to a common set of external parameters and rigorously treats correlated uncertainties. The work delivers updated, cross-experiment averages for production fractions, lifetimes, neutral-meson mixing, CP-violation parameters, and semileptonic decays, with key results such as Δm_d ≈ 0.508 ps^-1, χ_d ≈ 0.188, and τ(B^0) ≈ 1.530 ps and τ(B^+) ≈ 1.639 ps. The analysis juxtaposes HQE predictions with measured lifetimes, finds general agreement with some tensions, and provides a unified benchmark that supports CKM studies and future flavor-physics measurements. By synthesizing data across LEP, B factories, and the Tevatron, the paper offers a critical resource for precision tests of the Standard Model and guides subsequent updates in heavy-flavor averages.

Abstract

This article reports world averages for measurements of b-hadron and c-hadron properties obtained by the Heavy Flavor Averaging Group (HFAG) using the results available at the end of 2007. For the averaging, common input parameters used in the various analyses are adjusted (rescaled) to common values, and known correlations are taken into account. The averages include branching fractions, lifetimes, neutral meson mixing parameters, CP violation parameters, and parameters of semileptonic decays.

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 $x$ 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 $y_i$ as described in the text. Open circles mark the central values of the unadjusted fits to $x$ with $y$ fixed; these 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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