A search for a narrow resonance scans an invariant-mass spectrum from to
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Probability, statistics and stochastic methods · Probability, statistics and stochastic methods
Error, Chance and the Machine, Ch Tests, intervals and Bayesian inference
Problem
A search for a narrow resonance scans an invariant-mass spectrum from 600GeV to 1000GeV. The detector resolution is 10GeV, so a bump could appear in about 40 effectively independent places. The largest excess, found in one window, has a local one-sided p-value of 1.0×10−3, computed as if that window had been chosen in advance. Assume that the spectrum is background only, with 40 independent windows.
((a)) Find the trials factor, as the width of the range divided by the resolution.
((b)) Find the global p-value, the probability that a background-only spectrum has an excess at least this large in some window.
((c)) Find the Bonferroni estimate of the global p-value, and say how far it is from the value in (b).
((d)) Say whether the excess is significant at the 5 per cent level once the scan is counted, and find the local p-value that a single window would need for a global p-value of exactly 0.05.