Parton densities in quantum chromodynamics. Gauge invariance, path-dependence and Wilson lines (Q350547)

The present text deals with hadronic operator matrix elements, which can be described using Wilson line methods. This is in so far interesting as this method allows to go beyond forward scattering, i.e. the description of the usual parton densities of the nucleon, and to account for more degrees of freedom, like for the transverse momentum dependent parton densities (TMDs). Yet, as well-known, these quantities cannot be calculated using perturbative methods only, but are of non-perturbative origin, unlike their evolution operators between different, large enough virtualities and for the associated perturbative sub-process scattering cross sections, the Wilson coefficients.NEWLINENEWLINEThe study of quantities of the above kind is of importance for various present and future measurements at high luminosity as being performed at JLAB and planned in the programm of a future Electro-Ion Collider (EIC).NEWLINENEWLINEA brief introduction is followed by three introductory Chapters, in which the authors summarize basic topics in quantum field theory (QFT) and Wilson lines.NEWLINENEWLINEChapter 5 deals with a gauge-invariant description of parton densities. It starts with a brief discussion of deep-inelastic scattering processes, giving also the operator representation of the parton distribution functions. Here it would have been helpful to discuss also the necessary links to the results obtained in case of the light-cone expansion. Also an experimental illustration is given on the present status of QCD scaling violations in deep-inelastic scattering, from which precision measurements of the strong coupling constant are possible. The authors then consider semi-inclusive deep-inelastic scattering and TMDs, where the present method is in more use in the literature.NEWLINENEWLINEIn the last Chapter methods to simplify Wilson line calculations are discussed. We note that many of the calculation methods mentioned both for treating color algebra and the evaluation of integrals in dimensional regularization are even available in computer algebra packages, also for the treatment of far more comprehensive problems, which would have been worth mentioning.NEWLINENEWLINEUnfortunately the references given are not linked to the main text, which would have been important. There is only a brief literature guide on a few items, referring to the bibliography. The list of references appears not to be comprehensive. Appendices summarize a series of technical details, which are widely known, however, and even often taught in courses on QFT. Reference to more comprehensive sources on special functions and numbers appearing in QFT calculations, which became available during the last two decades would have been welcome. The text can be considered as a an introduction for master and PhD students working in the closer field as a lecture note and source book.