Abstract
We present a new method, based on Gaussian process regression, for reconstructing the continuous $x$-dependence of parton distribution functions (PDFs) from quasi-PDFs computed using lattice QCD. We examine the origin of the unphysical oscillations seen in current lattice calculations of quasi-PDFs and develop a nonparametric fitting approach to take the required Fourier transform. The method is tested on one ensemble of maximally twisted mass fermions with two light quarks. We find that with our approach oscillations of the quasi-PDF are drastically reduced. However, the final effect on the light-cone PDFs is small. This finding suggests that the deviation seen between current lattice QCD results and phenomenological determinations cannot be attributed solely on the Fourier transform.
Highlights
We present a new method, based on Gaussian process regression, for reconstructing the continuous x-dependence of parton distribution functions (PDFs) from quasi-PDFs computed using lattice QCD
We examine the origin of the unphysical oscillations seen in current lattice calculations of quasi-PDFs and develop a nonparametric fitting approach to take the required Fourier transform
Parton distribution functions (PDFs) are fundamental objects that describe the structure of hadrons probing the distribution of momentum and spin among their constituent partons
Summary
Parton distribution functions (PDFs) are fundamental objects that describe the structure of hadrons probing the distribution of momentum and spin among their constituent partons. Since PDFs are inherently nonperturbative observables, an ab-initio calculation using lattice field theory methods based solely on QCD is highly desirable. A way to circumvent this difficulty was suggested by Ji [1] who proposed to use matrix elements from purely spatial correlations that are accessible in lattice QCD In this way, quasi-PDFs can be connected to the true PDFs through a matching procedure. A possible origin of these oscillations is the periodicity of Fourier transformation and the fact that a truncation is implemented due to the finite Wilson line Another possible explanation is that not large enough momentum boosts are currently feasible.
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