Reconstruction of light-cone parton distribution functions from lattice QCD simulations at the physical point

Abstract

We present the unpolarized and helicity parton distribution functions calculated within lattice QCD simulations using physical values of the light quark mass. Non-perturbative renormalization is employed and the lattice data are converted to the MSbar-scheme at a scale of 2 GeV. A matching process is applied together with target mass corrections leading to the reconstruction of light-cone parton distribution functions. For both cases we find a similar behavior between the lattice and phenomenological data, and for the polarized PDF a nice overlap for a range of Bjorken-x values. This presents a major success for the emerging field of direct calculations of quark distributions using lattice QCD.

Figures (6)

• Figure 1: Comparison of unpolarized bare MEs ($h_{\gamma_0}$) for momenta $\frac{6\pi}{L}$ (blue circles), $\frac{8\pi}{L}$ (red diamonds) and $\frac{10\pi}{L}$ (green stars) using 5 stout steps.
• Figure 2: Similar to Fig.\ref{['fig:g0_g3']} for helicity bare MEs.
• Figure 3: Real (left) and imaginary (right) part of renormalized helicity MEs for momentum $\frac{6\pi}{L}$, as a function of the WL length. Blue circles/red diamonds/orange stars correspond to 5/10/15 iterations of stout smearing.
• Figure 4: Comparison of unpolarized PDF at momenta $\frac{6\pi}{L}$ (green band), $\frac{8\pi}{L}$ (orange band), $\frac{10\pi}{L}$ (blue band), and ABMP16 Alekhin:2017kpj (NNLO), NNPDF Ball:2017nwa (NNLO) and CJ15 Accardi:2016qay (NLO) phenomenological curves.
• Figure 5: Comparison of polarized PDF at momenta $\frac{6\pi}{L}$ (green band), $\frac{8\pi}{L}$ (orange band), $\frac{10\pi}{L}$ (blue band), DSSV08 deFlorian:2009vb and JAM17 NLO phenomenological data Ethier:2017zbq.