6 Calorimetry
257
depth the direction of photon showers can then be estimated. As is shown in Fig.
6.13, the shower is particularly narrow and already well developed after~5 X 0 ; it
is thus advantageous to sample it with high granularity over this depth. In ATLAS,
with a cell size of ~5 mm the position of electron and photon showers is determined
in the first ~5 X 0 (above~30 GeV) with an accuracy of about 300 μm, a critical asset
for physics at the LHC. An important example is the discovery for the Higgs boson
using the two-photon final state. The ATLAS electromagnetic calorimeter has three
longitudinal samplings for measuring the direction of photons with an accuracy
of about 50 mr/
√
E. This angular resolution is such that it makes a negligible
contribution to the Higgs mass resolution [111], even if the interaction point cannot
be identified among the numerous primary collision vertices at high luminosity.
Search for new long-lived neutral particles decaying into photons (like gravitinos)
also benefit from a high-resolution angular measurement.
6.4.2 Timing
The electromagnetic cascade develops at the sub-nanosecond timescale, allowing
accurate timing measure-ements. This measurement allows identifying the bunch
crossing associated to a particular event at colliders. Timing may be used to
infer the shower position (see Sect. 6.4.1) or may discriminate between relativistic
electromagnetic and slow particles, such as antineutrons.
In a segmented calorimeter the timing resolution is limited by fluctuations of
the light path reflecting on edges of the tower, in case of light readout, or by
electrical signal reflections at the ends of tower electrodes in case of ionization
readout. Electronics noise and shower fluctuations introduce a further limitation,
dominant at low and medium energies. While the energy in a tower can be obtained
by sampling the signal at its maximum, the optimal time measurement requires
additional signal processing. Constant fraction discriminators or digital treatment
of multiple samplings of the signal (also beneficial for energy measurements) are
frequently used. The shaping time of the electronics is a critical parameter in
optimizing the timing accuracy.
As an example, the homogeneous NA48 krypton calorimeter showed a resolution of σ = 0.5 ns/
√
E, up to ~100 GeV. With the light readout in the
“spaghetti” lead-fiber sampling calorimeter of KLOE [82] a spectacular resolution
of 0.054 ns/
√
E ⊕ 0.14 ns was obtained for photons between 50 and 300 MeV,
allowing the shower barycentre along the spaghetti bar structure to be located with
a precision of ~3 cm.
With a time resolution better than 100 ps, vertex localisation becomes possible,
with an accuracy of a few cm. At the LHC, the rms spread of collision vertices
along the beam axis is about 5 cm or ~180 ps. At high luminosity when 50 to
200 collisions per bunch crossing are observed, or envisaged (in the case of HLLHC), a significantly better resolution is required in order to help in the vertex
selection. Upgrade projects at HL-LHC are aiming at 30 ps, which seems the best
257
depth the direction of photon showers can then be estimated. As is shown in Fig.
6.13, the shower is particularly narrow and already well developed after~5 X 0 ; it
is thus advantageous to sample it with high granularity over this depth. In ATLAS,
with a cell size of ~5 mm the position of electron and photon showers is determined
in the first ~5 X 0 (above~30 GeV) with an accuracy of about 300 μm, a critical asset
for physics at the LHC. An important example is the discovery for the Higgs boson
using the two-photon final state. The ATLAS electromagnetic calorimeter has three
longitudinal samplings for measuring the direction of photons with an accuracy
of about 50 mr/
√
E. This angular resolution is such that it makes a negligible
contribution to the Higgs mass resolution [111], even if the interaction point cannot
be identified among the numerous primary collision vertices at high luminosity.
Search for new long-lived neutral particles decaying into photons (like gravitinos)
also benefit from a high-resolution angular measurement.
6.4.2 Timing
The electromagnetic cascade develops at the sub-nanosecond timescale, allowing
accurate timing measure-ements. This measurement allows identifying the bunch
crossing associated to a particular event at colliders. Timing may be used to
infer the shower position (see Sect. 6.4.1) or may discriminate between relativistic
electromagnetic and slow particles, such as antineutrons.
In a segmented calorimeter the timing resolution is limited by fluctuations of
the light path reflecting on edges of the tower, in case of light readout, or by
electrical signal reflections at the ends of tower electrodes in case of ionization
readout. Electronics noise and shower fluctuations introduce a further limitation,
dominant at low and medium energies. While the energy in a tower can be obtained
by sampling the signal at its maximum, the optimal time measurement requires
additional signal processing. Constant fraction discriminators or digital treatment
of multiple samplings of the signal (also beneficial for energy measurements) are
frequently used. The shaping time of the electronics is a critical parameter in
optimizing the timing accuracy.
As an example, the homogeneous NA48 krypton calorimeter showed a resolution of σ = 0.5 ns/
√
E, up to ~100 GeV. With the light readout in the
“spaghetti” lead-fiber sampling calorimeter of KLOE [82] a spectacular resolution
of 0.054 ns/
√
E ⊕ 0.14 ns was obtained for photons between 50 and 300 MeV,
allowing the shower barycentre along the spaghetti bar structure to be located with
a precision of ~3 cm.
With a time resolution better than 100 ps, vertex localisation becomes possible,
with an accuracy of a few cm. At the LHC, the rms spread of collision vertices
along the beam axis is about 5 cm or ~180 ps. At high luminosity when 50 to
200 collisions per bunch crossing are observed, or envisaged (in the case of HLLHC), a significantly better resolution is required in order to help in the vertex
selection. Upgrade projects at HL-LHC are aiming at 30 ps, which seems the best