Abstract
We present a detailed Lattice QCD study of the unpolarized isovector quark Parton Distribution Function (PDF) using large-momentum effective theory framework. We choose a quasi-PDF defined by a spatial correlator which is free from mixing with other operators of the same dimension. In the lattice simulation, we use a Gaussian-momentum-smeared source at $M_\pi=356$ MeV and $P_z \in \{1.8,2.3\}$ GeV. To control the systematics associated with the excited states, we explore {five different source-sink separations}. The nonperturbative renormalization is conducted in a regularization-independent momentum subtraction scheme, and the matching between the renormalized quasi-PDF and $\bar{\rm MS}$ PDF is calculated based on perturbative QCD up to one-loop order. Systematic errors due to renormalization and perturbative matching are also analyzed in detail. Our results for lightcone PDF are in reasonable agreement with the latest phenomenological analysis.
Highlights
Parton distribution functions (PDFs) of nucleons are important quantities characterizing the internal hadron structures but are key ingredients to make predictions for high-energy scattering processes [1,2,3]
II, we briefly review the procedure of nonperturbative renormalization and matching of the quasi-PDF in the regularization-independent momentum subtraction (RI/MOM) scheme, in particular the explicit one-loop matching coefficient for the Γ 1⁄4 γt case
With the derivative method of Fourier transformation (FT) and the matching using pRz 1⁄4 0 GeV and μR 1⁄4 3.2 GeV, we show the dependence on the nucleon boosted momentum in Fig. 9 with the statistical uncertainties
Summary
Parton distribution functions (PDFs) of nucleons are important quantities characterizing the internal hadron structures but are key ingredients to make predictions for high-energy scattering processes [1,2,3]. The finite nucleon mass corrections were worked out to all orders of M2=P2z [17], and higher-twist OðΛ2QCD=x2P2zÞ effects were numerically removed by extrapolating the results at several Pz values to infinite momentum [15,17] Based on these studies, calculations of the isovector quark PDF at physical pion mass have become available [20,41,42,43]. We will carry out a lattice calculation of the unpolarized isovector quark distribution from the quasi-PDF with Γ 1⁄4 γt with the same nonperturbative renormalization procedure as for the Γ 1⁄4 γz case in Ref. IV, we present our results on the x dependence of the unpolarized isovector quark PDF with the statistical and systematic uncertainties, and the last section contains the summary of our work
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
