2 Gauge Theories and the Standard Model
9
Finally, there is a number of cases in which data from LHC experiments (as
well as other experiments, specifically in the fields of flavor physics and neutrino
physics) have brought more accuracy and more stringent tests, without changing the
overall picture. These include gauge boson couplings, discussed in Sects. 3.3–3.4,
for which we refer to Ref. [27]; the CKM matrix and flavor physics, discussed in
Sect. 3.6, for which we refer to the review by Ceccucci, Ligeti and Sakai in the
PDG [26]; neutrino masses and mixings, discussed in Sect. 3.7, for which we refer
to the PDG review by Gonzalez-Garcia and Yokohama [26].
This perhaps unexpected success of the Standard Model, and the failure to find
any evidence so far of new physics (and in particular supersymmetry) at the LHC
has somewhat modified the perspective on the limitations of the Standard Model
discussed in Sect. 3.14. Specifically, the significance of the hierarchy problem—the
so-called “naturalness” issue—must be questioned, given that it entails new physics
which has not be found: a suggestive discussion of this shift in perspective is in
Ref. [33]. Yet, the classification of possible new physics scenarios of Sect. 3.14
remains essentially valid: recent updates are in Ref. [34] for supersymmetric models,
and in Ref. [35] for non-supersymmetric ones. Consequently, looking for new
physics has now become a precision exercise, and this has provided a formidable
stimulus to the study of Electroweak radiative corrections, which has been the
subject of very intense activity beyond the classic results discussed in Sect. 3.10:
a recent detailed review is in Ref. [36].
Chapter 4 is devoted to the theory of strong interactions, Quantum Chromodynamics (QCD). This theory has not changed since its original formulation in the
second half of the past century. Specifically, its application to hard processes, which
allows for the use of perturbative methods, is firmly rooted in the set of classic
results and techniques discussed in Sect. 4.5 below. What did slowly change over
the years is the experimental status of QCD. What used to be, in the past century, a
theory established qualitatively, has gradually turned into a theory firmly established
experimentally—though, at the time this chapter was written, not quite tested to the
same precision as the electroweak theory (see Sect. 4.7). Now, after the first two
runs of the LHC, it can be stated that the whole of the Standard Model, QCD and the
Electroweak theory, are tested to the same very high level of accuracy and precision,
typically at the percent or sub-percent level.
Turning QCD into a precision theory has been a pre-requisite for successful
physics at the LHC, a hadron collider in which every physical process necessarily
involves the strong interaction, since the colliding objects are protons (or nuclei).
This has grown into a pressing need as the lack of discovery of new particles or
major deviations from Standard Model predictions has turned the search for new
physics signals into a precision exercise: it has turned the LHC from an “energy
frontier” to a “rarity/accuracy frontier” machine—something that was deemed
inconceivable just before the start of its operation [37].
This rapid progress has happened thanks to an ever-increasing set of computational techniques, which, building upon the classic results presented in this chapter,
has allowed for an enormous expansion of the set of perturbative computations of
processes at colliders which are introduced in Sect. 4.5.4, and discussed in more
detail in the context of LHC (and specifically Higgs) physics in Ref. [30].
9
Finally, there is a number of cases in which data from LHC experiments (as
well as other experiments, specifically in the fields of flavor physics and neutrino
physics) have brought more accuracy and more stringent tests, without changing the
overall picture. These include gauge boson couplings, discussed in Sects. 3.3–3.4,
for which we refer to Ref. [27]; the CKM matrix and flavor physics, discussed in
Sect. 3.6, for which we refer to the review by Ceccucci, Ligeti and Sakai in the
PDG [26]; neutrino masses and mixings, discussed in Sect. 3.7, for which we refer
to the PDG review by Gonzalez-Garcia and Yokohama [26].
This perhaps unexpected success of the Standard Model, and the failure to find
any evidence so far of new physics (and in particular supersymmetry) at the LHC
has somewhat modified the perspective on the limitations of the Standard Model
discussed in Sect. 3.14. Specifically, the significance of the hierarchy problem—the
so-called “naturalness” issue—must be questioned, given that it entails new physics
which has not be found: a suggestive discussion of this shift in perspective is in
Ref. [33]. Yet, the classification of possible new physics scenarios of Sect. 3.14
remains essentially valid: recent updates are in Ref. [34] for supersymmetric models,
and in Ref. [35] for non-supersymmetric ones. Consequently, looking for new
physics has now become a precision exercise, and this has provided a formidable
stimulus to the study of Electroweak radiative corrections, which has been the
subject of very intense activity beyond the classic results discussed in Sect. 3.10:
a recent detailed review is in Ref. [36].
Chapter 4 is devoted to the theory of strong interactions, Quantum Chromodynamics (QCD). This theory has not changed since its original formulation in the
second half of the past century. Specifically, its application to hard processes, which
allows for the use of perturbative methods, is firmly rooted in the set of classic
results and techniques discussed in Sect. 4.5 below. What did slowly change over
the years is the experimental status of QCD. What used to be, in the past century, a
theory established qualitatively, has gradually turned into a theory firmly established
experimentally—though, at the time this chapter was written, not quite tested to the
same precision as the electroweak theory (see Sect. 4.7). Now, after the first two
runs of the LHC, it can be stated that the whole of the Standard Model, QCD and the
Electroweak theory, are tested to the same very high level of accuracy and precision,
typically at the percent or sub-percent level.
Turning QCD into a precision theory has been a pre-requisite for successful
physics at the LHC, a hadron collider in which every physical process necessarily
involves the strong interaction, since the colliding objects are protons (or nuclei).
This has grown into a pressing need as the lack of discovery of new particles or
major deviations from Standard Model predictions has turned the search for new
physics signals into a precision exercise: it has turned the LHC from an “energy
frontier” to a “rarity/accuracy frontier” machine—something that was deemed
inconceivable just before the start of its operation [37].
This rapid progress has happened thanks to an ever-increasing set of computational techniques, which, building upon the classic results presented in this chapter,
has allowed for an enormous expansion of the set of perturbative computations of
processes at colliders which are introduced in Sect. 4.5.4, and discussed in more
detail in the context of LHC (and specifically Higgs) physics in Ref. [30].