Parton distribution functions (PDFs) encode essential information about the distribution of momentum and spin of quarks and gluons inside hadrons. Deep inelastic scattering experiments provide information on the quark PDFs of the nucleon and factorization allows one to separate a short-distance, hard sub-process, from the complex, soft structure of the nucleon. Ab initio computation of this soft long-distance structure is complex and the most suitable approach is via a numerical solution using a discretized formulation of Quantum Chromodynamics (QCD) on a Euclidean space-time lattice known as lattice QCD using Monte Carlo methods. However, PDFs are matrix elements of non-local bi-linears in the light-cone frame. Such matrix elements cannot be evaluated using a Euclidean space-time lattice.
Therefore, the standard approach in lattice QCD has been to compute moments of PDFs being restricted to a few lower moments that avoid mixing. Recently, a new approach has been proposed X. Ji to compute quasi-distributions that can be matched to PDFs in the large momentum limit. A direct evaluation of PDFs within lattice QCD can have profound implications on our understanding of the structure of the nucleon providing essential input for phenomenology and ongoing experiments.
In this INCITE project, the research team will use this new approach to compute the quasi-distributions using lattice QCD and then match them to PDFs. The team will employ gauge-field configurations simulated by the European Twisted Mass Collaboration with light, strange and charm quarks tuned to their physical values. These configurations are currently among a handful of simulations that provide the most complete description of the QCD vacuum. The group has already carried out an exploratory study using similar gauge configurations but with a pion mass of 373 MeV and has worked out the mass corrections required for the matching. A new smearing technique has been tested and shown to allow us to go to large enough momentum to take the large momentum limit. The renormalization of the quasi-distributions is currently under study using lattice perturbation theory where we expect results to be finalized before the start of the time allocation.
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