# Nuclear Parton Distribution Functions

In 1983 at CERN, the European Muon Collaboration observed a difference between the cross section for deep inelastic scattering from an atomic nucleus and that of the same number of free protons and neutrons (see picture below). This was surprising since MeV-scale nuclear binding effects were expected to be negligible compared to the typical momentum transfers ( \( Q \geq 1\) GeV ) in hard-scattering reactions such as deep-inelastic lepton-nucleus scattering. This lead to the conjecture that the quark momentum distributions in nucleons bound inside nuclei are different from those of free nucleons.

Nuclear parton distribution functions (nPDFs) are defined in the context of QCD collinear factorization theorem, which states that when a hard scale \( Q^2 \) is involved, the hard-process cross (perturbatively calculable) section for the colliding hadrons to produce a final state can be factorized from the non-perturbatively caculable part, which is encoded in parton distribution functions.

The determination of nPDFs is therefore relevant to improve our fundamental understanding of the strong interactions in the nuclear environment. As well as being an essential ingredient for the interpretation of heavy ion collisions at RHIC and the LHC, in particular for the characterization of the Quark-Gluon Plasma (QGP).

The functional form of parton distribution functions is in general not theoretically motivated or predicted. All we know is a set of physical constraint that helps us with its determination, such as the momentum sum of all quarks should be equal to the momentum of the nucleon. For this reason, the NNPDF collaboration based its modeling of PDFs on Artificial Neural Networks since they’re proven to be universal approximators of any continuous function.

Based on the same concept, my collaborators and I introduced for the first time a nPDF analysis that we dubbed nNNPDF.

We had overall three releases:

- nNNPDF1.0: Nuclear Parton Distributions from Lepton-Nucleus Scattering and the Impact of an Electron-Ion Collider.
- nNNPDF2.0: Quark Flavor Separation in Nuclei from LHC Data.
- nNNPDF3.0: Evidence for a modified partonic structure in heavy nuclei.

For more information: NNPDF website