TY - RPRT TI - Proton isovector helicity PDF at NNLO and the twist-3 moment $\tilde{d}$ 2 from lattice QCD at physical quark masses AU - Gao, Xiang [Brookhaven National Laboratory (BNL), Upton, NY (United States)] AU - Hanlon, Andrew D. [Kent State Univ., Kent, OH (United States)] (ORCID:0000000187868053) AU - Mukherjee, Swagato [Brookhaven National Laboratory (BNL), Upton, NY (United States)] (ORCID:0000000238241008) AU - Petreczky, Peter [Brookhaven National Laboratory (BNL), Upton, NY (United States)] (ORCID:0000000302852066) AU - Shu, Hai-Tao [Central China Normal University, Wuhan (China)] (ORCID:0000000171974281) AU - Yao, Fei [Brookhaven National Laboratory (BNL), Upton, NY (United States)] (ORCID:0000000272270996) AU - Zhang, Rui [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)] (ORCID:0000000295747398) AU - Zhao, Yong [Argonne National Laboratory (ANL), Lemont, IL (United States)] (ORCID:0000000226886415) PY - 2026 DO - 10.1103/kb88-xmzh UR - https://www.osti.gov/biblio/3377367 ID - 3377367 ER -