87
14.3. Hard scattering processes, QCD tree graphs, and jets
−
In section 9.5 we briefly introduced the idea of jets in e
+ e physics: two
well collimated sprays of hadrons, apparently created as a quark–antiquark
pair separate from each other at high speed. The angular distribution of
the two jets followed closely the distribution expected from the parton-level
+ −
process e e
qq.
→ ¯
The dynamics at the parton level was governed by
QED, but QCD is responsible for the way the emerging q and ¯
q turn themselves into hadrons, a process called parton fragmentation (it occurs for gluons too). We may think of it as proceeding in two stages. First, as the
rapidly moving q and ¯
q begin to separate, they develop perturbative showers of narrowly collimated gluons and quark–antiquark pairs. Then, as the
partons separate further, the strength of the forces between them increases,
becoming strongly non-perturbative at a separation of about 1 fm, and ensuring that the coloured quanta are all confined into hadrons. As yet we
do not have a completely quantitative dynamical understanding of the second, hadronization, stage: it is implemented by means of a model. Nevertheless, we can argue that for the forces to be strong enough to produce
the observed hadrons, the dominant processes in hadronization must involve
small momentum transfers – that is, the exchange of ‘soft’ quanta. Thus the
emerging hadrons are also well collimated into two jets, whose energy and
angular distributions reflect the short-distance physics at the parton level.
This simple 2-jet picture will be extended in section 14.4, where we consider
+
e e
−
→ 3 jets.
A somewhat different aspect of parton physics arose in sections 9.2–9.3,
where we considered deep inelastic electron scattering from nucleons. There
the initial state contained one hadron. Correspondingly, one parton appeared
in the initial state of the parton-level interaction, and the analysis required
new functions measuring the probabilities of finding a particular parton in the
parent hadron – the parton distribution functions. These too are beyond the
reach of perturbation theory.
We may also consider, finally, hadron-hadron collisions. In this case, we
need all three of the features we have been discussing: the parton distribution functions, to provide the intial parton-parton state from the two-hadron
state; the perturbative short-distance parton-parton interaction; and the parton fragmentation process in the final state. These three parts to the process
are pictured in figure 14.5. The identification and analysis of short distance
parton-parton interactions provide direct tests of the tree-graph structure of
QCD, and perturbative corrections to it.
This three-part schematization of certain features of hadronic interactions
is useful, because although we cannot yet calculate from first principles either the parton distribution functions or the fragmentation process, both are
universal. The quark and gluon composition of hadrons is the same for all
processes, and so measurements in one experiment can be used to predict
the results of others. We saw an example of this in the Drell–Yan process of
section 9.4. As regards the fragmentation stage, this too will be universal, provided one is interested in sufficiently inclusive aspects of the final state. The
14.3. Hard scattering processes, QCD tree graphs, and jets
−
In section 9.5 we briefly introduced the idea of jets in e
+ e physics: two
well collimated sprays of hadrons, apparently created as a quark–antiquark
pair separate from each other at high speed. The angular distribution of
the two jets followed closely the distribution expected from the parton-level
+ −
process e e
qq.
→ ¯
The dynamics at the parton level was governed by
QED, but QCD is responsible for the way the emerging q and ¯
q turn themselves into hadrons, a process called parton fragmentation (it occurs for gluons too). We may think of it as proceeding in two stages. First, as the
rapidly moving q and ¯
q begin to separate, they develop perturbative showers of narrowly collimated gluons and quark–antiquark pairs. Then, as the
partons separate further, the strength of the forces between them increases,
becoming strongly non-perturbative at a separation of about 1 fm, and ensuring that the coloured quanta are all confined into hadrons. As yet we
do not have a completely quantitative dynamical understanding of the second, hadronization, stage: it is implemented by means of a model. Nevertheless, we can argue that for the forces to be strong enough to produce
the observed hadrons, the dominant processes in hadronization must involve
small momentum transfers – that is, the exchange of ‘soft’ quanta. Thus the
emerging hadrons are also well collimated into two jets, whose energy and
angular distributions reflect the short-distance physics at the parton level.
This simple 2-jet picture will be extended in section 14.4, where we consider
+
e e
−
→ 3 jets.
A somewhat different aspect of parton physics arose in sections 9.2–9.3,
where we considered deep inelastic electron scattering from nucleons. There
the initial state contained one hadron. Correspondingly, one parton appeared
in the initial state of the parton-level interaction, and the analysis required
new functions measuring the probabilities of finding a particular parton in the
parent hadron – the parton distribution functions. These too are beyond the
reach of perturbation theory.
We may also consider, finally, hadron-hadron collisions. In this case, we
need all three of the features we have been discussing: the parton distribution functions, to provide the intial parton-parton state from the two-hadron
state; the perturbative short-distance parton-parton interaction; and the parton fragmentation process in the final state. These three parts to the process
are pictured in figure 14.5. The identification and analysis of short distance
parton-parton interactions provide direct tests of the tree-graph structure of
QCD, and perturbative corrections to it.
This three-part schematization of certain features of hadronic interactions
is useful, because although we cannot yet calculate from first principles either the parton distribution functions or the fragmentation process, both are
universal. The quark and gluon composition of hadrons is the same for all
processes, and so measurements in one experiment can be used to predict
the results of others. We saw an example of this in the Drell–Yan process of
section 9.4. As regards the fragmentation stage, this too will be universal, provided one is interested in sufficiently inclusive aspects of the final state. The