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Published equation contexts

σEE  =  AE  ⊕  B  ⊕  C\frac{\sigma_E}{E} \;=\; \frac{A}{\sqrt{E}} \;\oplus\; B \;\oplus\; C

Why this formula appears here

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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σE\sigma_E

Symbol sigma_E

sigmaEa_E occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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

Equation 1 · Particle Physics

What a Particle Detector Actually Measures

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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