In this paper we reexamine the possibility of extracting parton distribution functions from lattice simulations. We discuss the case of quasiparton distribution functions, the possibility of using the reduced Ioffe-time distributions and the more recent proposal of directly making reference to the computation of the current-current $T$-product. We show that in all cases the process of renormalization hindered by the lattice momenta limitation represents an obstruction to a direct Euclidean calculation of the parton distribution function.

• Received 9 May 2018

DOI:https://doi.org/10.1103/PhysRevD.98.054028

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Published by the American Physical Society