Information and treatment of unknown correlations in the combination of measurements using the BLUE method

We discuss the effect of large positive correlations in the combinations of several measurements of a single physical quantity using the Best Linear Unbiased Estimate (BLUE) method. We suggest a new approach for comparing the relative weights of the different measurements in their contributions to the combined knowledge about the unknown parameter, using the well-established concept of Fisher information. We argue, in particular, that one We discuss the effect of large positive correlations in the combinations of several measurements of a single physical quantity using the Best Linear Unbiased Estimate (BLUE) method. We suggest a new approach for comparing the relative weights of the different measurements in their contributions to the combined knowledge about the unknown parameter, using the well-established concept of Fisher information. We argue, in particular, that one contribution to information comes from the collective interplay of the measurements through their correlations and that this contribution cannot be attributed to any of the individual measurements alone. We show that negative coefficients in the BLUE weighted average invariably indicate the presence of a regime of high correlations, where the effect of further increasing some of these correlations is that of reducing the error on the combined estimate. In these regimes, we stress that assuming fully correlated systematic uncertainties is not a truly conservative choice, and that the correlations provided as input to BLUE combinations need to be assessed with extreme care instead. In situations where the precise evaluation of these correlations is impractical, or even impossible, we provide tools to help experimental physicists perform more conservative combinations

Generalized Mukai conjecture for special Fano varieties

Let X be a Fano variety of dimension n, pseudoindex i_X and Picard number \rho_X. A generalization of a conjecture of Mukai says that \rho_X(i_X-1)\le n. We prove that the conjecture holds if: a) X has pseudoindex i_X \ge \frac{n+3}{3} and either has a fiber type extremal contraction or does not have small extremal contractions b) X has dimension five.Comment: 19 page

Top mass at the LHC

With about 10 millions top-pair events per year at low luminosity, the LHC will be a top factory. Among all precision measurements that will be performed in the top quark sector, the determination of its mass is probably the most important and will help in constraining the Standard Model. A brief review of the direct and indirect measurements of the top quark mass will be given, with indications about the potential of ATLAS and CMS in different luminosity scenario

W mass from fully leptonic and mixed decays at LEP

This article describes the determination of the W boson mass through the mixed hadronic-leptonic and fully leptonic channels at LEP. The results are preliminary and refer to the data collected up to 1998. The combined LEP W mass value for (mixed)-leptonic events is m/sub w /=(80.310+or-0.060) GeV/c/sup 2/. This value, combined with the result from the hadronic channel, gives m/sub w/=(80.339+or-0.055) Ge V/c/sup 2/. (4 refs)