Friday, September 04, 2015

Fundamental Parameters from Lattice QCD, Day Three

Today, our first speaker was Jerôme Charles, who presented new ideas about how treat data with theoretical uncertainties. The best place to read about this is probably his talk, but I will try to summarize what I understood. The framework is a firmly frequentist approach to statistics, which answers the basic question of how likely the observed data are if a given null hypothesis is true. In such a context, one can consider a theoretical uncertainty as a fixed bias δ of the estimator under consideration (such as a lattice simulation) which survives the limit of infinite statistics. One can then test the null hypothesis that the true value of the observable in question is μ by constructing a test statistic for the estimator being distributed normally with mean μ+δ and standard deviation σ (the statistical error quoted for the result). The p-value of μ then depends on δ, but not on the quoted systematic error Δ. Since the true value of δ is not known, one has to perform a scan over some region Ω, for example the interval Ωn=[-nΔ;nΔ] and take the supremum over this range of δ. One possible extension is to choose Ω adaptively in that a larger range of values needs to be scanned (i.e. a larger true systematic error in comparison to the quoted systematic error is allowed for) for lower p-values; interestingly enough, the resulting curves of p-values are numerically close to what is obtained from a naive Gaussian approach treating the systematic error as a (pseudo-)random variable. For multiple systematic errors, a multidimensional Ω has to be chosen in some way; the most natural choices of a hypercube or a hyperball correspond to adding the errors linearly or in quadrature, respectively. The linear (hypercube) scheme stands out as the only one that guarantees that the systematic error of an average is no smaller than the smallest systematic error of an individual result.

The second speaker was Patrick Fritzsch, who gave a nive review of recent lattice determinations of semileptonic heavy-light decays, both the more commonly studied B decays to πℓν and Kℓν, and the decays of the Λb that have recently been investigated by Meinel et al. with the help of LHCb.

In the afternoon, both the CKMfitter collaboration and the FLAG group held meetings.

2 comments:

Stefan Sint said...

Hi Georg,

thanks for writing this blog, very useful! I am wondering if the
slides of the talks will be made available online at some point?

Cheers,

Stefan (Sint)

Stefan Sint said...

sorry, I just noticed that the icons next to the authors' names are linking to the slides.
(I was somehow expecting the talk titles to become links, but I guess
this is the way indico is set up).

S.