A search is made for a process with cross section in a data set with integrated luminosity

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Particle Physics, Ch Accelerators and colliders: energy, luminosity and reach

Problem

A search is made for a process with cross section σ=2 pb\sigma = 2\,\mathrm{pb} in a data set with integrated luminosity Lint=15 fb−1\mathcal{L}_{\rm int} = 15\,\mathrm{fb^{-1}}. Someone argues: "1 pb=10−36 cm21\,\mathrm{pb} = 10^{-36}\,\mathrm{cm^2}, so σ=2×10−36 cm2\sigma = 2\times10^{-36}\,\mathrm{cm^2}. Since 1 fb−1=10−39 cm−21\,\mathrm{fb^{-1}} = 10^{-39}\,\mathrm{cm^{-2}}, we have Lint=15×10−39 cm−2=1.5×10−38 cm−2\mathcal{L}_{\rm int} = 15\times10^{-39}\,\mathrm{cm^{-2}} = 1.5\times10^{-38}\,\mathrm{cm^{-2}}. Then the expected number of events is N=σLint=(2×10−36)(1.5×10−38)=3×10−74N = \sigma\mathcal{L}_{\rm int} = (2\times10^{-36})(1.5\times10^{-38}) = 3\times10^{-74}, so essentially no events at all are expected in this data set." ((a)) Find the error in this working. ((b)) Give the correct number of events expected.

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