107
14.6. Further developments
C F enters into the parton-level three-jet amplitude (14.67), but the triplegluon vertex is not involved at order α s . This vertex is an essential feature of
non-Abelian gauge theories, being absent in Abelian theories such as QED. A
direct measurement of the triple-gluon vertex colour factor, C A , can be made
in the process e
+ e
−
→ 4 jets.
+
4-jet events originate from the parton-level process e e
−
→ q¯ qg via three
mechanisms: the emission of a second bremsstrahlung gluon, splitting of the
first gluon into two gluons, and splitting of the first gluon into n f quark pairs.
As problem 14.5 shows, these three types of splitting vertices are characterized
in cross sections by the colour factors C F , C A and n f T R , so that the cross
section can be written as (Ali and Kramer 2011)
( )
α s
σ 4−jet =
C F [C F σ bb + C A σ gg + n f T R σ q¯ q ].
(14.79)
π
Measurements yield (Abbiendi et al. 2001)
C A /C F = 2.29 ± 0.06[stat.] ± 0.14[syst.]
T R /C F = 0.38 ± 0.03[stat.] ± 0.06[syst.],
(14.80)
in good agreement with the theoretical predictions C A /C F = 9/4 and T R /C F =
3/8 in QCD.
14.6.2 Jet algorithms
From the examples already discussed in this chapter, it is clear that jets are an
essential element in making comparisons between experimental measurements
involving final state particles in detectors, and theoretical calculations at the
parton level using perturbative QCD. Conceptually, jets provide a common
representation for these two classes of event – those at the detector level,
and those at the parton level. For precision comparisons, it is necessary to
have a rigorous definition of a jet – a jet algorithm – which should be equally
applicable at the detector, and at the parton, level. In the more than thirty
years that have passed since Sterman and Weinberg’s 1977 paper, many jet
definitions have been developed and applied. All involve the basic notion of
clustering together objects that are in some sense ‘near’ to each other. Two
main classes of jet algorithm may be distinguished: cone algorithms based on
proximity in coordinate space, as in the Sterman-Weinberg approach, and used
extensively, until recently, at hadron colliders; and sequential recombination
algorithms based on proximity in momentum space, as in the jet-mass criterion
−
of Kramer and Lampe (1987), and widely used at e
+ e and e p colliders.
Recent general reviews of jet algorithms are provided by Salam (2010) and by
Ali and Kramer (2011); see also Ellis et al. (2008), Campbell et al. (2007),
and Kluth (2006). Here we shall give only a brief introduction to sequential
recombination algorithms – all of which are IRC safe – since it seems likely
that they will dominate future jet analyses.
14.6. Further developments
C F enters into the parton-level three-jet amplitude (14.67), but the triplegluon vertex is not involved at order α s . This vertex is an essential feature of
non-Abelian gauge theories, being absent in Abelian theories such as QED. A
direct measurement of the triple-gluon vertex colour factor, C A , can be made
in the process e
+ e
−
→ 4 jets.
+
4-jet events originate from the parton-level process e e
−
→ q¯ qg via three
mechanisms: the emission of a second bremsstrahlung gluon, splitting of the
first gluon into two gluons, and splitting of the first gluon into n f quark pairs.
As problem 14.5 shows, these three types of splitting vertices are characterized
in cross sections by the colour factors C F , C A and n f T R , so that the cross
section can be written as (Ali and Kramer 2011)
( )
α s
σ 4−jet =
C F [C F σ bb + C A σ gg + n f T R σ q¯ q ].
(14.79)
π
Measurements yield (Abbiendi et al. 2001)
C A /C F = 2.29 ± 0.06[stat.] ± 0.14[syst.]
T R /C F = 0.38 ± 0.03[stat.] ± 0.06[syst.],
(14.80)
in good agreement with the theoretical predictions C A /C F = 9/4 and T R /C F =
3/8 in QCD.
14.6.2 Jet algorithms
From the examples already discussed in this chapter, it is clear that jets are an
essential element in making comparisons between experimental measurements
involving final state particles in detectors, and theoretical calculations at the
parton level using perturbative QCD. Conceptually, jets provide a common
representation for these two classes of event – those at the detector level,
and those at the parton level. For precision comparisons, it is necessary to
have a rigorous definition of a jet – a jet algorithm – which should be equally
applicable at the detector, and at the parton, level. In the more than thirty
years that have passed since Sterman and Weinberg’s 1977 paper, many jet
definitions have been developed and applied. All involve the basic notion of
clustering together objects that are in some sense ‘near’ to each other. Two
main classes of jet algorithm may be distinguished: cone algorithms based on
proximity in coordinate space, as in the Sterman-Weinberg approach, and used
extensively, until recently, at hadron colliders; and sequential recombination
algorithms based on proximity in momentum space, as in the jet-mass criterion
−
of Kramer and Lampe (1987), and widely used at e
+ e and e p colliders.
Recent general reviews of jet algorithms are provided by Salam (2010) and by
Ali and Kramer (2011); see also Ellis et al. (2008), Campbell et al. (2007),
and Kluth (2006). Here we shall give only a brief introduction to sequential
recombination algorithms – all of which are IRC safe – since it seems likely
that they will dominate future jet analyses.