ReviewPrecision physics with inclusive QCD processes
Introduction
Quantum Chromodynamics (QCD) [1], [2] provides a successful description of the strong interaction in terms of a single parameter: the strong coupling constant . This beautiful gauge theory has been precisely tested in may different processes and over a very broad range of mass scales. Although many aspects of the hadronic world need still to be better understood, the overwhelming consistency of all experimental results has established beyond any doubt that QCD is the right dynamical theory of the strong force.
At low energies, the growing of the effective running coupling generates a complicated non-perturbative regime, responsible for the hadronization of quarks and gluons into a rich variety of colour-singlet composite particles. A precise quantitative description of the hadron formation and dynamics remains unfortunately as an important open problem, which so far has been only partially approached through effective field theory descriptions and numerical tools. In fact, a complete analytical proof of confinement has not yet been accomplished, in spite of the many efforts performed along the years. Nevertheless, all theoretical studies and the large amount of data accumulated indicate that confinement is a truly fundamental property of QCD. Colourful objects have never been observed as asymptotic states.
Assuming that confinement is exact, one can perform very precise predictions for the inclusive production of hadrons in processes that do not contain strongly-interacting particles in the initial state, such as , , , or . Since the separate identity of the produced hadrons is not specified, one just needs to compute the total production of quarks and gluons, summing over all possible configurations. Confinement guarantees that the computed QCD cross section or decay width will be identical to the corresponding inclusive hadronic production because the total probability that quarks and gluons hadronize is just one.
Pure perturbative calculations are usually enough to achieve accurate descriptions of high-energy inclusive processes. At low energies they need to be complemented with non-perturbative corrections that scale as powers of , starting with . Using short-distance operator-product-expansion (OPE) [3] techniques, one can control rigorously these power corrections and determine above which scales their numerical impact becomes negligible.
The following sections present a detailed discussion of the theoretical tools involved in the analysis of inclusive processes and the current status of the resulting predictions. The running QCD coupling and quark masses are introduced in Section 2, which describes their associated and functions that are currently known to . Section 3 discusses the two-point correlation functions of the vector, axial-vector, scalar and pseudoscalar QCD currents, summarizing our present knowledge of these important dynamical objects. The inclusive high-energy observables are analysed in Section 4, which contains the QCD predictions for the annihilation cross section into hadrons, and the hadronic widths of the electroweak , and Higgs bosons. Section 5 reviews the theoretical analysis of the hadronic width, including perturbative and non-perturbative contributions, and updates its current phenomenological status. The highly-precise four-loop determinations of the strong coupling from the and hadronic widths are compared in Section 6 with the most accurate values of extracted from other sources, exhibiting the great success of QCD in correctly describing strong-interacting phenomena over a very broad range of energy scales. A few summarizing comments are finally given in Section 7. Some complementary technical details are compiled in appendices.
Section snippets
The QCD running coupling
The unique coupling constant of QCD, , is obviously the critical parameter governing all phenomena associated with the strong interaction. The renormalized coupling depends on the chosen renormalization scheme and scale. The scheme [4] is the conventionally adopted choice, while the dependence on the scale is determined by the renormalization-group equation which defines the so-called function.1
Current correlators
Inclusive observables, such as , or proceed through the colour-singlet vector and axial-vector quark currents (). The QCD dynamics is then encoded in the two-point correlation functions where and the superscript in the transverse and longitudinal components denotes the corresponding angular momentum (T) and (L) in the
Inclusive observables
At high energies, naive perturbation theory is usually adopted to predict quantities such as and the hadronic decay widths of the , and Higgs bosons. These observables correspond to hadronic spectral functions (correlator discontinuities) on the physical cut, where the OPE is not justified. However, non-perturbative effects are still assumed to be suppressed by the factor , provided the physical scale is large enough and far away from thresholds and hadronic resonance
The hadronic width of the lepton
The lepton decays through the emission of a virtual boson that generates four possible final states, with (Fig. 7). If final fermion masses and QCD effects are ignored, the universality of the couplings implies that the four decay modes have equal probabilities, except for an additional global factor () in the two semileptonic channels. Since , the total hadronic width is then predicted to be a factor of larger
NNLO determinations of the strong coupling
The inclusive and hadronic widths provide a very important test of the Standard Model at an impressive NLO precision, where LO refers to the first nontrivial QCD contribution. The strong coupling is determined in two completely different energy regimes and with very different experimental systematics, but the theoretical description of the two observables is based on similar current correlators, being the four-loop calculation of the Adler function the basic ingredient in both cases. The
Summary
A series of impressive four- and five-loop calculations has promoted the phenomenology of inclusive QCD processes into the realm of precision physics. The very accurate knowledge of the and functions, which provides a powerful resummation of logarithmic corrections into the running coupling and quark masses, has been complemented with the computation of the two-point correlation functions of the vector, axial-vector, scalar and pseudoscalar currents, allowing us to obtain
Acknowledgments
This work has been supported in part by the Spanish Government and ERDF funds from the EU Commission [Grant FPA2017-84445-P], by the Generalitat Valenciana [Grant Prometeo/2017/053], by the EU H2020 research and innovation programme [Grant Agreement 824093] and by the EU COST Action CA16201 PARTICLEFACE .
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