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Equation 1 · Part 9 · What a Particle Detector Actually Measures

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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