String-based axial and helicity-flip GPDs: a comparison to lattice QCD

Abstract

We construct an analytic, string based representation of the nucleon's axial and helicity flip conformal moments of generalized parton distributions that holds for any skewness and for both the quark and gluon channels. The starting point is the Mellin Barnes resummation of the conformal partial wave expansion, where the moments are parametrized by open (Reggeon) and closed string (Pomeron) trajectories with slopes determined by experimental form factors and meson/glueball spectroscopy. The forward limits are fixed by the empirical unpolarized and polarized parton distributions. Polynomiality, crossing symmetry and support are satisfied by construction. After NLO DGLAP ERBL evolution to $μ=2$ GeV our analytic framework (i) reproduces some of the currently available lattice moments of $\mathbb{E}$ and $\widetilde{\mathbb{H}}$ in the non singlet sector, (ii) predicts sea quark and gluon polarized moments that will be testable by forthcoming simulations and experiments at Jefferson Lab and the future EIC, and (iii) yields axial and helicity flip GPDs in $x$ space in reasonable agreement with lattice QCD.

Figures (8)

• Figure 1: Non‑singlet helicity–flip conformal moments $\mathbb{E}_{u-d}$ (top 5-blocks) and $\mathbb{E}_{u+d}$ (bottom 5-blocks) at $\mu=2$ GeV for conformal spins $j=1,\dots,5$ (panels ordered left–to–right, top–to–bottom). Blue band: our string‑based prediction. The lattice data are from LHPC LHPC:2007blg, and Ref. Bhattacharya:2023ays.
• Figure 2: Non‑singlet polarized conformal moments $\widetilde{\mathbb{H}}_{u-d}$ (top block) and $\widetilde{\mathbb{H}}_{u+d}$ (bottom block) evolved to $\mu=2$ GeV. Symbols: lattice data of Ref. Bhattacharya:2024wtg and LHPC LHPC:2007blg.
• Figure 3: Predictions for singlet polarized conformal moments at $\mu=2$ GeV. Upper row: sea‑quark singlet $\widetilde{\mathbb{H}}_{\Sigma}(j,t)$. Lower row: pseudovector gluon $\widetilde{\mathbb{H}}_{g}(j,t)$. Conformal spins $j=1,2,3$ are ordered left–to–right. No lattice data are yet available.
• Figure 4: (a) Evolved non-singlet isovector axial gpd at a resolution of $\mu = 2$ GeV compared to Alexandrou:2020zbe and (b) non-singlet isovector gpd $E$ compared to Alexandrou:2020zbe (green, turquoize), Holligan:2023jqh (orange) at $\mu=2$ GeV and Lin:2020rxa (purple) at $\mu=3$ GeV. The dashed lines separate the erbl region (inner) from the dglap region (outer).
• Figure 5: (a) Evolved non-singlet isovector axial gpd at a resolution of $\mu = 2$ GeV compared to Alexandrou:2020zbe and (b) non-singlet isovector gpd $E$ compared to Alexandrou:2020zbe (green, turquoize), Holligan:2023jqh (orange) at $\mu=2$ GeV and Lin:2020rxa (purple) at $\mu=3$ GeV. The dashed lines separate the erbl region (inner) from the dglap region (outer).