A Quantum Diaries Survivor

Here is another section of the proceedings I am writing. Please feel free to flame me for anything wrong – or even questionable – I may have written… 

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2.2 Jet calibration and determination of the energy scale
From an experimental standpoint, it is important to realize that the result of a jet measurement is affected by a multitude of effects of different origin. These effects need to be addressed separately, to allow a uniform definition across different experiments and meaningful comparisons with theory.

The prime example of a detector-specific effect to compensate is the non-uniformity
of the detector response. Despite their symmetric, uniform blueprints, when real detectors are built they always end up being spatially non-uniform in their mechanical construction, in the amount and location of dead channels, in the material budget as seen from the interaction region. Although a simulation of the apparatus may help to understand the dominant disuniformities, a detailed accounting of all effects requires the study of real data. Using dijet events it is possible to use one jet to probe the detector response as a function of relevant variables (such as angle and energy), when the other jet is constrained to be measured in a well-controlled region of flat response. By computing the response function f, defined as

<f(eta, Pt)> = 1/N SUM ( 2 x (Pt^trigger-Pt^probe) /(Pt^trigger+Pt^probe) )for a large set of jet pairs and with the probe jet spanning several bins in Pt an rapidity, one obtains a map of the detector response, which can be subsequently used to equalize the response. The Pt binning is necessary, since as their Pt grows jets become narrower and they probe smaller scales of disuniformity of the detector.

Another  method must be devised to account for energy collected in the clustering cone from pile-up interactions occurred during the same bunch crossing. Pile-up energy is on average a linear function of instantaneous luminosity, but only through the number of pile-up interactions. It is therefore much better to correct jets on an event-by-event basis, by finding the relationship between energy deposited in a random cone in the calorimeter (away from real jets) as a function of the number of primary interactions reconstructed through vertexed charged tracks.

A similar kind of random contribution to a jet's energy comes from a different origin:
the same hard interaction that produces the jet activity usually radiates additional energy through the so-called underlying event, which has to be understood as the combinate effect of proton remnant recombinations and additional hard or semi-hard  interactions by the spectator partons. An average correction for this effect can be  obtained by computing the energy deposit in cones in a region azimuthally orthogonal from the leading jets in dijet events.

Another small additive correction may be applied to account for energy flowing out of the clustering circle: this is called out of cone correction and is of course dependent on the choice made for the clustering radius R.

The most important effect to determine a jet's energy is however the difference in
response to charged particles – which are measured predominantly in the hadron calorimeter -and neutral ones -essentially pi^0, whose energy is determined with higher precision and smaller loss in the electromagnetic section. This so-called e/pi ratio is much larger than unity in CDF, while in DO it is less than 1.05, thanks to the intrinsic compensation capabilities of Uranium as active absorber.
 
To determine the correction factor to apply to the measured energy and obtain the most probable value of the originating stream of stable particles (in the sense that their lifetime is long enough to allow detection before decay), a Monte Carlo simulation is used in CDF. The simulation allows toextract a multiplicative factor as a function of measured transverse momentum. 

Once all correction factors and offsets are applied, the jet energy scale can be checked with events in experimental data where one jet recoils against a energetic photon (or leading neutral particle). The electromagnetic shower is well measured in the inner sections of the calorimeter, and the recoiling jet energy scale can be tested with good accuracy.

A uncertainty in the jet energy scale can then be determined by comparing the offset between data and Monte Carlo, if the Monte Carlo jets have been subjected to the same treatment as experimental data jets.

The level of uncertainty in the determination of the jet energy scale at the Tevatron experiments is below 3%, and is expected to decrease further as more data are collected -particularly photon-jet events. The large samples of single lepton decay of t-anti t pairs collected by the experiments have also allowed to cross-check the energy scale by using the W –> jj resonance in top decay\cite{}.

For a complete review of the determination of jet energy scale in CDF see \cite{} . The jet energy scale correction in DO is described in \cite{}.
 

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