Unpolarized proton PDF at NNLO from lattice QCD with physical quark masses

Journal Article · 28 April 2023 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.107.074509 · OSTI ID:1971926

Gao, Xiang ^[1]; Hanlon, Andrew D.  ^[2]; Holligan, Jack  ^[3]; Karthik, Nikhil ^[4]; Mukherjee, Swagato ^[2]; Petreczky, Peter ^[2]; Syritsyn, Sergey ^[5]; Zhao, Yong ^[1]

---

1. Argonne National Laboratory (ANL), Argonne, IL (United States)
2. Brookhaven National Laboratory (BNL), Upton, NY (United States)
3. University of Maryland, College Park, MD (United States); Stony Brook University, NY (United States)
4. American Physical Society (APS), Hauppauge, NY (United States); Florida International University (FIU), Miami, FL (United States)
5. Brookhaven National Laboratory (BNL), Upton, NY (United States); Stony Brook University, NY (United States)

We present a lattice QCD calculation of the unpolarized isovector quark parton distribution function (PDF) of the proton utilizing a perturbative matching at next-to-next-to-leading-order (NNLO). Here, the calculations are carried out using a single ensemble of gauge configurations generated with $${N_f} = 2 + 1$$ highly-improved staggered quarks with physical masses and a lattice spacing of $α = 0.076 fm$. We use one iteration of hypercubic smearing on these gauge configurations, and the resulting smeared configurations are then used for all aspects of the subsequent calculation. For the valence quarks, we use the Wilson-clover action with physical quark masses. We consider several methods for extracting information on the PDF. We first extract the lowest four Mellin moments using the leading-twist operator product expansion approximation. Then, we determine the $$x$$ dependence of the PDF through a deep neural network within the pseudo-PDF approach and additionally through the framework of large-momentum effective theory utilizing a hybrid renormalization scheme. This is the first application of the NNLO matching coefficients for the nucleon directly at the physical point.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States); Argonne National Laboratory (ANL), Argonne, IL (United States). Argonne Leadership Computing Facility (ALCF); Argonne National Laboratory (ANL), Argonne, IL (United States). Laboratory Computing Resource Center (LCRC)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); National Science Foundation (NSF); USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)
• Grant/Contract Number: AC02-06CH11357; SC0012704; PHY-1847893; 2138259; 2138286; 2138307; 2137603; 2138296; 2020-0020
• OSTI ID: 1971926
• Alternate ID(s): OSTI ID: 1984783; OSTI ID: 1997228
• Report Number(s): BNL-224498-2023-JAAM; 182908; TRN: US2405212
• Journal Information: Physical Review. D., Vol. 107, Issue 7; ISSN 2470-0010
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English