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Equation 1 · Part 6 · What a Particle Detector Actually Measures

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σEE  =  AE  ⊕  B  ⊕  C.\frac{\sigma_E}{E} \;=\; \frac{A}{\sqrt{E}} \;\oplus\; B \;\oplus\; C .
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Energy deposition. A calorimeter is deliberately destructive. It stops the particle, converts its energy into a shower of secondaries, and measures a signal proportional to the total ionising track length in that shower. Because the shower is stochastic, the relative resolution scales as the inverse square root of the energy plus terms for readout noise and for imperfections that scale with energy: σEE  =  AE  ⊕  B  ⊕  C\frac{\sigma_E}{E} \;=\; \frac{A}{\sqrt{E}} \;\oplus\; B \;\oplus\; C . For the LHC general-purpose experiments the stochastic term is typically three to ten per cent for electromagnetic calorimeters and fifty to eighty per cent for hadronic ones, while constant terms sit at a few parts per thousand and a few per cent respectively [ 2 ] . The…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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