An event at a hadron collider contains a single reconstructed muon with transverse…

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 contains a single reconstructed muon with transverse momentum

p_{\rm T} = 45\,\mathrm{GeV}/c

and longitudinal momentum

p_z = 130\,\mathrm{GeV}/c

(found from the track curvature and the muon's polar angle); no other particle above threshold is reconstructed. Someone argues: The two colliding protons meet head-on, so the total three-momentum of the collision is zero in the laboratory frame. The muon is the only particle reconstructed, and it carries away

p_z = 130\,\mathrm{GeV}/c

along the beam, so momentum conservation requires an invisible particle with

p_z = -130\,\mathrm{GeV}/c

to balance it, so its missing energy is

E^{\rm miss} = c\sqrt{p_{\rm T}^2+p_z^2} = c\sqrt{45^2+130^2}\,\mathrm{GeV} = 137\,\mathrm{GeV}

. The same analysis team reports a separate search with

N_{\rm sig} = 225

signal events on a background of

N_{\rm bkg} = 2500

events, the background being known only to a systematic uncertainty of

5\%

of its value (i.e.

\pm125

events), independent of how much data is collected. They then argue: The significance is

225/\sqrt{2500} = 4.5

standard deviations already; collecting four times the data will multiply this by

\sqrt{4}=2

, comfortably clearing five standard deviations. ((a)) Find the error in the missing-energy argument and give the correct missing transverse energy and its direction. ((b)) Find the error in the luminosity argument. Measuring the excess, as

N_{\rm sig}/\sqrt{N_{\rm bkg}}

does, in units of the background's uncertainty, but taking that uncertainty to be the larger of the statistical

\sqrt{N_{\rm bkg}}

and the systematic one, estimate the significance this measurement can ever reach, however much data is collected.

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