Speaker
Description
We use the operator product expansion (OPE) to relate hadronic Euclidean two current matrix elements to parton distribution functions (PDFs) resolving the dependence on the parton momentum fraction $x$. We are following the ansatz proposed by [arXiv:1709.03018]. In our calculation, we consider the valence quark PDFs for the proton. This requires the evaluation of a connected proton four-point function for small quark distances. Our simulation is performed on $n_f = 2+1$ CLS gauge ensemble with extension $32^3\times 96$, coupling $\beta = 3.4$, and pseudo-scalar masses $m_\pi = 355~\mathrm{MeV}$ and $m_K = 441~\mathrm{MeV}$, where we include proton momenta up to $|\vec{p}| = 1.57~\mathrm{GeV}$. The results are converted to the $\overline{\mathrm{MS}}$-scheme at the scale $\mu = 2~\mathrm{GeV}$. In order to extract the PDF, the data is fitted in Fourier space based on a standard parameterization of the PDF.
