We review recent developments in the theory and phenomenology of structure function, with particular emphasis on precision tests of QCD and progress in the perturbative treatment of parton distributions. We discuss specifically the determination of patton distributions in deep-inelastic scattering, and their behavior at large x and small x.
1. STRUCTURE FUNCTIONS AND PARTON DISTRIBUTIONS
In the last several years, perturbative QCD has become, as an integral part of the standard model, a firmly established theory, which allows performing detailed and reliable calculations. Current work is focussed on the precise determinations of the unknown parameters of the theory, and the development of reliable computational techniques. The parameters to be determined include not only the strong coupling a~, which is the only free parameter in the QCD lagrangian, but also all quantities which are determined from the nonperturbative low-energy dynamics, and thus, even though in principle computable, must in practice be treated as a phenomenological input in the perturbative domain.
In the case of DIS, the low-energy parameters are the parton distributions of hadrons. Thanks to the operator-product expansion and the renormalization group, or more in general factorization theorems, the coefficient functions which relate parton distributions to measurable cross-sections can be computed in perturbation theory. Furthermore, the scaling violations of the parton distributions are related to the short-distance behavior of local operators in the theory, and can thus also be computed reliably3 Deep-inelastic scattering provides therefore the most accurate way of determining the parton distributions which are then used as an input in the perturbative computation of hard processes relevant for collider physics, as well as, through scaling violations, one of the prime ways of determining c~s.
1.1. Testing QCD vs. using QCD
In recent times, the status of the DIS phenomenology has changed substantially, largely due to the advent of the HERA lepton-hadron collider, which has enormously enlarged the kinematic coverage of the data. In the simplest fully inclusive case, the DIS kinematics is fully parametrized by the virtuality Q2 of the photon which mediates the lepton-hadron process, and the total center-of-mass energy W 2 = Q2 l~z of the virtual photon-hadron *On leave from INFN, Sezione di Torino, Italy 2The theory of DIS is a textbook[I] subject. Here we will follow the notation and conventions of Ref. [2].