Ideally one would like to have the EM object hitting the calorimeter, to start the elec- tromagnetic cascade just in the calorimeter material and have all its energy lost in the calorimeter, in one cluster of its cells. To accomplish these goals it is necessary to keep the material in front of the calorimeter (the so-called material budget) to a minimum so
that the shower does not develop before the calorimeter and to build a calorimeter that has enough thickness to accommodate the development of the electromagnetic shower.
Concerning the latter point, one should note that luckily, when the length needed to accommodate a certain shower is expressed in units of the radiation length (X0) of the
calorimeter material, it scales only with the logarithm of the shower energy. Both the ATLAS and CMS calorimeters have a longitudinal depth of 24-26 X0 (it varies along η)
which has been calculated to accommodate showers up to 500 GeV and keep to a minimum the contribution to the energy resolution due to the energy fluctuation for showers of higher energies.
Incidentally, one should note that the electromagnetic calorimeter represent about one absorption length (λI) for charged hadrons. About 10λI are needed to contain hadronic
showers and limit the background in the muon system. This goal is accomplished by the hadronic calorimeter which surrounds the electromagnetic calorimeter.
Every effort has been done in the design and construction phases of the ATLAS and CMS experiment to keep the material in front of the calorimeter to a minimum. In both ATLAS and CMS the material in front of the calorimeter is represented by the beam pipe walls and by the inner tracking detectors which amounts to about 1 X0 at small η’s and
it increases in the endcap regions. The most of the material is due not just to the thin (usually 300 µm) active layers of silicon (strips or pixels) of the inner tracking detectors but rather to the mechanical supports, electronics, cabling and services associated to the tracker operation and readout.
In ATLAS additional material in front of the calorimeter is due to the walls of the cryostat used to keep the liquid Argon at a temperature of about 90 K. To save material, this cryostat also integrates the cryostat for the superconducting coil that produces the 2 T magnetic field into the tracker volume. This last effect is not present in CMS as both calorimeters (the electromagnetic and most of the hadronic one) are placed inside a large solenoid, so that the material of the coil and of the cryostat does not enter in the EM
calorimeter material budget.
Figure 10.101: Left: average energy deposited by 100 GeV electrons in front of the presam- pler (open circles) and before the first compartment of the ATLAS calorimeter (crosses) as a function of η. Right: fractions of photons converted below a radius of 80 cm (open circles) and 115 cm (full circles) as a function of η in the ATLAS detector.
Electrons will undergo bremsstrahlung in the upstream material. Soft brems radiation will increase the size of the cluster. The effect is larger along the φ direction due to the effect of the magnetic field that bends the electron direction. As a consequence the cluster becomes larger and asymmetric. If a hard bremsstrahlung photon is emitted along the electron direction, it is also possible that the electron and the emitted photon reach the calorimeter into separate clusters. Moreover, the electron trajectory is no more a helix and this makes the electron track reconstruction in the tracker more difficult. Fig. 10.101 shows the average energy deposited by electrons before the arrive to the ATLAS calorimeter and before the presampler. The curve follows the material profile before the calorimeter and has a maximum around η ∼1.5: this corresponds to the gap between the barrel and
end-cap calorimeter (a region that cannot be used for precision physics).
Photons can convert in the tracker material and give origin to an electron-positron pair. Fig. 10.101 shows the fraction of conversions as a function ofηforH→γγ photons: the quantity is shown for two radii, corresponding approximately to the end of the tracking detector (80 cm) and to the beginning of the calorimeter (115 cm). With respect to an unconverted photon, a converted photon will deposit its energy in a larger and asymmetric cluster: the superposition of the two electron-positron clusters. Again the cluster is larger along the φdirection due to the bending of the electrons along this direction.
In both cases, material at low radii is the most dangerous as these effects are amplified by the longer electron(s) path into the magnetic field. Electrons from early conversions might be reconstructed as two separate clusters into the calorimeter. Effects are also larger in CMS where the magnetic field is 4 T (to be compared to the 2 T in ATLAS). Material at high radius is anyway detrimental for the calorimeter performance due to the fluctuations in the energy lost before the calorimeter as the shower starts earlier. In ATLAS, where the effect is larger due to the presence of the coil and of the cryostat walls, a presampler detector is placed just in front of the calorimeter. This consists of a 11 mm thick layer of liquid Argon that samples the early development of the cascade.
However, the tracker itself provides information useful to recover some of the problems it creates. In case of hard electron bremsstrahlung one can try to reconstruct the typical ”kink” in the track trajectory (where the photon is emitted). The calorimeter cluster also provides an additional point that can be included in the track fit. Moreover, one can exploit the fact that the energy weighted barycenter of the electron and brems photon clusters in the calorimeter provides the extrapolated trajectory of the electron before the brems emission occurred.
enough hits in the silicon layers so that their tracks can be reconstructed: the converted photon energy and direction is then obtained from the four-momenta of the two electrons. The situation is more difficult for late conversions as the number of hits left by the two electrons cannot be enough for them to be reconstructed with satisfying efficiency. In any case, an ad-hoc tracking in which the electron track is reconstructed from the outer layers of the tracker inwards is usually needed. With respect to a track coming from the primary vertex, a reduced number of hits in the detector is also allowed (at the expense of an increased number of reconstructed fake tracks). There are cases in which a conversion cannot be reconstructed as one of the two electrons is not reconstructed: this might happen in case of asymmetric conversions with one of the two electrons having a low transverse momentum. ATLAS studies have shown that a track matched to a calorimeter cluster that does not have a hit in the innermost pixel layer are coming from conversions, if a non-negligible fake rate (around 8%, from charged pions) can be accepted. Of course this strategy strongly depends on pile-up and on the inefficiencies in the pixel layer.