ELEMENTARY PARTICLE PHYSICS

Understanding the internal structure of the nucleon is an active field of research with important phenomenological implications in high-energy, nuclear and astroparticle physics. Nucleon structure functions and their derivatives, parton distribution functions (PDFs) and generalized parton distribution functions (GPDs), teach us how the nucleon is built from quarks and gluons, and how QCD works. Beyond that, the cross section for hadron production at the LHC relies upon a precise knowledge of PDFs.

The theoretical basis for calculation is the Compton amplitude T_μν, i.e. the time-ordered product of electromagnetic currents J_μ, J_ν in the nucleon. In this project we have developed techniques that allow to compute the Compton amplitude most efficiently. Typical results are shown in Figure 1 (ω=1/x, x being the Bjorken scaling variable and q² the momentum squared of the virtual photon).

This method has several advantages. It is fully nonperturbative, needs no further renormalization and covers the Regge region at small values of x, in contrast to quasi-PDFs. Furthermore, as the photon momentum q is an intrinsic parameter of the simulation, it includes power corrections, and by varying q² will allow to test the twist expansion. In particular, it allows to isolate twist-four contributions and higher. Moreover, it can be generalized to nonforward Compton scattering, which lends itself to the computation of generalized parton distribution functions (GPDs). PDFs are obtained by solving the dispersion relation of the Compton amplitude for the imaginary part. A first result for the distribution function x(u(x)−d(x)) at q²=4.6 GeV² (Bayes) is shown in Figure 2 and compared with phenomenology (MSTW).