Reduction of Statistical Power Per Event Due to Upper Lifetime Cuts in Lifetime Measurements

A cut on the maximum lifetime in a lifetime fit not only reduces the number of events, but also, in some circumstances dramatically, decreases the statistical significance of each event. The upper impact parameter cut in the hadronic B trigger at CDF, which is due to technical limitations, has the same effect. In this note we describe and quantify the consequences of such a cut on lifetime measurements. We find that even moderate upper lifetime cuts, leaving event numbers nearly unchanged, can dramatically increase the statistical uncertainty of the fit result.Comment: Changes to latest revision: added DOI link, took the opportunity to correct some minor typos added one small clarificatio

Cramér-Rao sensitivity limits for astronomical instruments: implications for interferometer design

Multiple-telescope interferometry for high-angular-resolution astronomical imaging in the optical–IR–far-IR bands is currently a topic of great scientific interest. The fundamentals that govern the sensitivity of direct-detection instruments and interferometers are reviewed, and the rigorous sensitivity limits imposed by the Cramér–Rao theorem are discussed. Numerical calculations of the Cramér–Rao limit are carried out for a simple example, and the results are used to support the argument that interferometers that have more compact instantaneous beam patterns are more sensitive, since they extract more spatial information from each detected photon. This argument favors arrays with a larger number of telescopes, and it favors all-on-one beam-combining methods as compared with pairwise combination