14.3. Hard scattering processes, QCD tree graphs, and jets
89
the probability of observing jets, since the probability that a single hadron in
a jet will actually carry most of the jet’s total transverse momentum is quite
small (Jacob and Landshoff 1978; Collins and Martin 1984, Chapter 5). It is
much better to surround the collision volume with an array of calorimeters
which measure the total energy deposited. Wide-angle jets can then be identified by the occurrence of a large amount of total transverse energy deposited
in a number of adjacent calorimeter cells: this is then a ‘jet trigger’. The
importance of calorimetric triggers was first emphasized by Bjorken (1973),
following earlier work by Berman, Bjorken and Kogut (1971). The application of this method to the detection and analysis of wide-angle jets was first
reported by the UA2 collaboration at the CERN pp ¯ collider (Banner et al.
1982). An impressive body of quite remarkably clean jet data was subsequently accumulated by both the UA1 and UA2 collaborations (at
√
s = 546
GeV and 630 GeV), and by the CDF and D0 collaborations at the FNAL
Tevatron collider (
√
s = 1.8 TeV).
For each event the total transverse energy
E T is measured where
∑
∑
E T =
E i sin θ i .
(14.46)
i
E i is the energy deposited in the ith calorimeter cell and θ i is the polar
angle of the cell centre; the sum extends over all cells. Figure 14.6 shows the
E T distribution observed by UA2: it follows the ‘soft’ exponential form for
E T ≤ 60 GeV, but thereafter departs from it, showing clear evidence of the
wide-angle collisions characteristic of hard processes.
As we shall see shortly , the majority of ‘hard’ events are of two-jet type,
with the jets sharing the
E T approximately equally. Thus a ‘local’ trigger
set to select events with localized transverse energy ≥ 30 GeV and/or a ‘global’
trigger set at ≥ 60 GeV can be used. At
√
s ≥ 500–600 GeV there is plenty
of energy available to produce such events.
The total
√
s value is important for another reason. Consider the kinematics of the two-parton collision (figure 14.5) in the p ¯p CMS. As in the Drell–Yan
process of section 9.4, the right-moving parton has 4-momentum
x 1 p 1 = x 1 (P, 0, 0, P )
(14.47)
and the left-moving one
x 2 p 2 = x 2 (P, 0, 0, −P )
(14.48)
where P =
√
s/2 and we are neglecting parton transverse momenta, which
are approximately limited by the observed ‹p T › value (∼ 0.4 GeV, and thus
negligible on this energy scale). Consider the simple case of 90
0 scattering,
which requires (for massless partons) x 1 = x 2 , equal to x say. The total
outgoing transverse energy is then 2xP = x
√
s. If this is to be greater than
50 GeV, then partons with x ≥ 0.1 will contribute to the process. The parton
distribution functions are large at these relatively small x values, due to sea
89
the probability of observing jets, since the probability that a single hadron in
a jet will actually carry most of the jet’s total transverse momentum is quite
small (Jacob and Landshoff 1978; Collins and Martin 1984, Chapter 5). It is
much better to surround the collision volume with an array of calorimeters
which measure the total energy deposited. Wide-angle jets can then be identified by the occurrence of a large amount of total transverse energy deposited
in a number of adjacent calorimeter cells: this is then a ‘jet trigger’. The
importance of calorimetric triggers was first emphasized by Bjorken (1973),
following earlier work by Berman, Bjorken and Kogut (1971). The application of this method to the detection and analysis of wide-angle jets was first
reported by the UA2 collaboration at the CERN pp ¯ collider (Banner et al.
1982). An impressive body of quite remarkably clean jet data was subsequently accumulated by both the UA1 and UA2 collaborations (at
√
s = 546
GeV and 630 GeV), and by the CDF and D0 collaborations at the FNAL
Tevatron collider (
√
s = 1.8 TeV).
For each event the total transverse energy
E T is measured where
∑
∑
E T =
E i sin θ i .
(14.46)
i
E i is the energy deposited in the ith calorimeter cell and θ i is the polar
angle of the cell centre; the sum extends over all cells. Figure 14.6 shows the
E T distribution observed by UA2: it follows the ‘soft’ exponential form for
E T ≤ 60 GeV, but thereafter departs from it, showing clear evidence of the
wide-angle collisions characteristic of hard processes.
As we shall see shortly , the majority of ‘hard’ events are of two-jet type,
with the jets sharing the
E T approximately equally. Thus a ‘local’ trigger
set to select events with localized transverse energy ≥ 30 GeV and/or a ‘global’
trigger set at ≥ 60 GeV can be used. At
√
s ≥ 500–600 GeV there is plenty
of energy available to produce such events.
The total
√
s value is important for another reason. Consider the kinematics of the two-parton collision (figure 14.5) in the p ¯p CMS. As in the Drell–Yan
process of section 9.4, the right-moving parton has 4-momentum
x 1 p 1 = x 1 (P, 0, 0, P )
(14.47)
and the left-moving one
x 2 p 2 = x 2 (P, 0, 0, −P )
(14.48)
where P =
√
s/2 and we are neglecting parton transverse momenta, which
are approximately limited by the observed ‹p T › value (∼ 0.4 GeV, and thus
negligible on this energy scale). Consider the simple case of 90
0 scattering,
which requires (for massless partons) x 1 = x 2 , equal to x say. The total
outgoing transverse energy is then 2xP = x
√
s. If this is to be greater than
50 GeV, then partons with x ≥ 0.1 will contribute to the process. The parton
distribution functions are large at these relatively small x values, due to sea