10
G. Altarelli and S. Forte
To begin with, basic quantities such as the running of the coupling, discussed in
Sect. 4.4, and R e + e − , discussed in Sect. 4.5.1 are now know to one extra perturbative
order (see the QCD review of the PDG [26] for the current state of the art and
full references). These are five-loop perturbative calculations, now made possible
thanks to the availability of powerful computing resources. Furthermore, the set
of processes discussed in Sect. 4.5.4 has now been extended to include essentially
all relevant hadron collider processes, which have been routinely computed to
third perturbative order, while the first fourth-order calculations have just started
appearing. Again, the QCD review of the PDG [26] provides a useful status update,
including comparison between computation and experiment, which refer to crosssections which span about ten orders of magnitude in size.
This progress has been happening thanks to the development of a vast new
set of computational techniques, which, rooted in perturbative QCD, have now
spawned a dedicated research field: that of amplitudes [38], which relates phenomenology, quantum field theory, and mathematics. The classic set of methods for
“resummation”—the sum of infinite classes of perturbative contributions, discussed
specifically in Sect. 4.5.3.1 for deep-inelastic scattering, has been extended well
beyond the processes and accuracy discussed in Sect. 4.5.4—an up-to-date list is
in the QCD review of the PDG [26]. Moreover, an entirely new set of resummation
techniques has been developed, using the methodology of effective field theories: the
so-called soft-collinear effective theory (SCET) which provides an extra tool in the
resummation box [39]. One remarkable consequence of all these developments is
that it is now possible to understand in detail the structure of pure strong interaction
events, in which jets of hadrons are produced in the final state, by looking inside
these events and tracing their structure in terms of the fundamental fields of QCD—
quarks and gluons [40].
One topic in which things have changed rather less is the determination of the
strong coupling, discussed in Sect. 4.7. Whereas the agreement between predicted
and observed scaling violations discussed in Sect. 4.6.3 is ever more impressive (see
the review on structure functions of the PDG [26]) the accuracy on the determination
of the strong coupling itself has not improved much. Updated discussions can be
found in the QCD review of the PDG, as well as in Ref. [41]. Progress is likely
to come from future, more accurate LHC data, as well as from non-perturbative
calculations [42] (not discussed here) soon expected to become competitive.
All in all, the dozen or so years since the original writing of these chapter have
seen a full vindication of the Standard Model as a correct and accurate theory, and
have stimulated a vast number of highly sophisticated experimental and theoretical
results which build upon the treatment presented below.
2.2 Introduction
The ultimate goal of fundamental physics is to reduce all natural phenomena to a set
of basic laws and theories that, at least in principle, can quantitatively reproduce and
predict the experimental observations. At microscopic level all the phenomenology
G. Altarelli and S. Forte
To begin with, basic quantities such as the running of the coupling, discussed in
Sect. 4.4, and R e + e − , discussed in Sect. 4.5.1 are now know to one extra perturbative
order (see the QCD review of the PDG [26] for the current state of the art and
full references). These are five-loop perturbative calculations, now made possible
thanks to the availability of powerful computing resources. Furthermore, the set
of processes discussed in Sect. 4.5.4 has now been extended to include essentially
all relevant hadron collider processes, which have been routinely computed to
third perturbative order, while the first fourth-order calculations have just started
appearing. Again, the QCD review of the PDG [26] provides a useful status update,
including comparison between computation and experiment, which refer to crosssections which span about ten orders of magnitude in size.
This progress has been happening thanks to the development of a vast new
set of computational techniques, which, rooted in perturbative QCD, have now
spawned a dedicated research field: that of amplitudes [38], which relates phenomenology, quantum field theory, and mathematics. The classic set of methods for
“resummation”—the sum of infinite classes of perturbative contributions, discussed
specifically in Sect. 4.5.3.1 for deep-inelastic scattering, has been extended well
beyond the processes and accuracy discussed in Sect. 4.5.4—an up-to-date list is
in the QCD review of the PDG [26]. Moreover, an entirely new set of resummation
techniques has been developed, using the methodology of effective field theories: the
so-called soft-collinear effective theory (SCET) which provides an extra tool in the
resummation box [39]. One remarkable consequence of all these developments is
that it is now possible to understand in detail the structure of pure strong interaction
events, in which jets of hadrons are produced in the final state, by looking inside
these events and tracing their structure in terms of the fundamental fields of QCD—
quarks and gluons [40].
One topic in which things have changed rather less is the determination of the
strong coupling, discussed in Sect. 4.7. Whereas the agreement between predicted
and observed scaling violations discussed in Sect. 4.6.3 is ever more impressive (see
the review on structure functions of the PDG [26]) the accuracy on the determination
of the strong coupling itself has not improved much. Updated discussions can be
found in the QCD review of the PDG, as well as in Ref. [41]. Progress is likely
to come from future, more accurate LHC data, as well as from non-perturbative
calculations [42] (not discussed here) soon expected to become competitive.
All in all, the dozen or so years since the original writing of these chapter have
seen a full vindication of the Standard Model as a correct and accurate theory, and
have stimulated a vast number of highly sophisticated experimental and theoretical
results which build upon the treatment presented below.
2.2 Introduction
The ultimate goal of fundamental physics is to reduce all natural phenomena to a set
of basic laws and theories that, at least in principle, can quantitatively reproduce and
predict the experimental observations. At microscopic level all the phenomenology