Example of Calorimeter Uncertainties (ALEPH)

A number of methods are used to calibrate the electromagnetic calorimeter (ECAL) of ALEPH [5]. The ECAL gain is directly monitored by looking at an Fe⁵⁵ source (which ages [11]). The amplitude of the gain variation is $\sim$ 2 - 3% over one year, which after correction is stable to better than 0.3%.

For a range of electron energies, the ratio of ECAL energies to electron track momenta can be measured from various processes at the Z-peak: e⁺e^- $\rightarrow$ e⁺e^-e⁺e^- yields electrons in the 1-10 GeV range and Z $\rightarrow$ $\tau^{+}_{}$$\tau^{-}_{}$($\tau$ $\rightarrow$ e$\nu$$\overline{\nu }$) electrons in the 10-30 GeV range. Also the Z $\rightarrow$ e⁺e^- and Bhabha processes produce electrons at the beam energy (45.6 GeV).

For high energy LEP runs, one can measure E_ECAL/E_beam for Bhabha events. With large data samples, the high energy runs can also be split into smaller runs to estimate the time dependence of ECAL variations.

The typical net ECAL energy calibration uncertainty is $\pm$(0.7 - 0.9)%.

The hadronic calorimeter (HCAL) of ALEPH also uses physics processes for calibration [5]. The idea is to constrain the peak of the muon energy distribution in HCAL to its expected position ($\sim$ 3.7 GeV for muons crossing the calorimeter) which is measured in beam test. Then at the start of every data-taking period, Z $\rightarrow$ $\mu^{+}_{}$$\mu^{-}_{}$ and Z $\rightarrow$ q$\overline{q}$ events are used to calibrate. The use of hadronic Z decays provides a much more statistically powerful sample, which can be used because the ratio between the average energy released by hadronic Z decays and an isolated muon in an HCAL module is well known from data. This technique gives a `time 0' uncertainty of $\pm$ 1%.

For high energy running it is possible to compare data and MC for $\gamma$$\gamma$ $\rightarrow$ $\mu^{+}_{}$$\mu^{-}_{}$ events, yielding muons in the energy range 2.5-10 GeV. The energy distributions agree at the 1.5% level.

The typical net uncertainty is thus $\pm$ 2%.

The effects of the calorimeter uncertainties on the m_W measurements are evaluated by changing, in Monte Carlo samples, the calibration of the subdetectors by the net uncertainties described above, and performing mass fits before and after such a change.