Abstract
We present a new approach to extracting continuum quasi distributions from lattice QCD. Quasi distributions are defined by matrix elements of a Wilson-line operator extended in a spatial direction, evaluated between nucleon states at finite momentum. We propose smearing this extended operator with the gradient flow to render the corresponding matrix elements finite in the continuum limit. This procedure provides a nonperturbative method to remove the power-divergence associated with the Wilson line and the resulting matrix elements can be directly matched to light-front distributions via perturbation theory.
Highlights
Protons and neutrons—nucleons—are the basic, observable building blocks of the visible matter in the Universe
In [25], we proposed a new approach to extracting continuum quasi distributions from lattice calculations, constructing finite matrix elements by smearing both the fermion and gauge fields via the gradient flow [26,27,28]
Parton distribution functions (PDFs) are defined as matrix elements of light-front wave functions, which cannot be directly calculated in Euclidean lattice Quantum chromodynamics (QCD)
Summary
Protons and neutrons—nucleons—are the basic, observable building blocks of the visible matter in the Universe. In [1], Ji proposed a promising method to extract PDFs, from lattice QCD calculations of quasi distributions, which are spatially-extended operators between nucleon states at finite momentum. The Wilson-line power divergence appears at one loop as a contribution linear in z = z/rτ, where z is the length of the Wilson line and rτ is the gradient flow smearing radius, for z 1 Subtracting this contribution, the remaining matrix element is finite, and has a well-defined z → 0 limit, in contrast to the MS scheme. In the small flow-time regime, z 1, the matrix element depends only logarithmically on z and satisfies a relation similar to a standard renormalisation group equation
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