Physics:Energy resolution (ATLAS)
For electrons and photons in particle physics, the relative energy resolution [math]\displaystyle{ \sigma_E/E }[/math] of the electromagnetic calorimeter can be parametrised as
[math]\displaystyle{ \frac{\sigma_E}{E} = \frac{a}{\sqrt{E}} \oplus \frac{b}{E} \oplus c, }[/math]
where the sampling-term coefficient [math]\displaystyle{ a }[/math], the noise-term coefficient [math]\displaystyle{ b }[/math] and the constant-term [math]\displaystyle{ c }[/math] are pseudorapidity-dependent parameters. The sampling term contributes mostly at low and intermediate energy and depends on calorimeter shower and sampling fluctuations. The noise term is dominated by the pileup noise in the standard LHC data taking (i.e. at an average number of interactions per bunch crossing of the order of a few dozen). At higher energies, the relative energy resolution tends asymptotically to the constant term, [math]\displaystyle{ c }[/math], which in ATLAS has a design value of 0.7%. For electrons and converted photons, interactions with the material in front of the calorimeter also contribute to the [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math] terms.
A relative uncertainty of 10% on the sampling coefficient [math]\displaystyle{ a }[/math] is assumed based on test-beam data. The constant term [math]\displaystyle{ c }[/math] is extracted from [math]\displaystyle{ Z \to e^+e^- }[/math] measurements. In standard LHC data taking conditions, the energy resolution at low energy is dominated by the noise coefficient [math]\displaystyle{ b }[/math] and measuring the sampling coefficient [math]\displaystyle{ a }[/math] to reduce its uncertainty is difficult.
 |
