Imaging the Quark and Gluon Substructure of the Nucleon

**Principal Investigator:**

Gerrit Schierholz

**Affiliation:**

Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

**Local Project ID:**

chde07

**HPC Platform used:**

JUQUEEN and JUWELS of JSC

**Date published:**

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

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 *q*^{2} 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 *q*^{2}=4.6 GeV^{2} (Bayes) is shown in Figure 2 and compared with phenomenology (MSTW).

**Acknowledgements:**

The calculations were made possible due to a generous grant of compute time assigned to the DESY research team with the 14^{th}, 16^{th}, and 18^{th} GCS Call for Large-Scale Projects. High performance computing systems JUQUEEN and JUWELS of the Jülich Supercomputing Centre served as computing platform for this project.

**Scientific Contact:**

Prof. Dr. Gerrit Schierholz

Deutsches Elektronen-Synchrotron DESY

Notkestraße 85, D-22607 Hamburg (Germany)

e-mail: gerrit.schierholz [@] desy.de

*JSC project ID: chde07*

*April 2020*