An event at a hadron collider deposits a large amount of energy in the very forward…
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment
Particle Physics, Ch Detectors, event reconstruction and claiming a discovery
Problem
An event at a hadron collider deposits a large amount of energy in the very forward calorimeter modules and additional energy escapes entirely down the beam pipe, corresponding to an estimated longitudinal momentum of about pz≈800GeV/c carried at very small angle to the beam. In the central detector, two narrow sprays of hadrons are reconstructed, each measured as a single momentum, with pT=55GeV/c at azimuthal angle ϕ=0∘ and pT=35GeV/c at ϕ=200∘, and nothing else above threshold. Someone argues that the large forward energy loss down the beam pipe is itself a "missing longitudinal energy" signalling an invisible particle escaping along the beam axis, and adds its size to the transverse missing energy computed from the two sprays to quote a single combined "total missing energy" for the event. A separate four-lepton search finds Nsig=90 signal events on Nbkg=900 background events in the mass bin at 350GeV/c2 where an excess is seen, but the search scanned the full mass range from 200 to 800GeV/c2 in 5GeV/c2 bins, giving about 120 independent bins where an excess could equally well have appeared. Take the chance of a fluctuation at least this large somewhere in the range to be about the number of bins times the chance in any one bin. The one-sided tail probability beyond three standard deviations of the standard normal distribution is 1.3×10−3, and beyond one standard deviation it is 0.159. A researcher reports the local significance and calls it the significance of the discovery, without further comment.
((a)) Find the error in treating the beam-pipe energy loss as evidence of an invisible particle, and give the correct missing transverse energy of the event (magnitude and direction).
((b)) Find the error in quoting the local significance alone, and estimate the global significance once the look-elsewhere effect is taken into account.