Complete twist-three LaMET matching for GPDs

Complete the LaMET matching for twist-three GPDs by incorporating the mixing with three-parton quark–gluon correlators and by determining the perturbative zero-mode contribution proportional to \(\delta(y/x)\) that probes the quasi-GPD at infinite momentum fraction.

Background

The first lattice calculation of axial twist-three GPDs used only a two-parton one-loop kernel borrowed from the forward twist-three distribution gTg_T, omitting the intrinsic mixing with three-parton quark–gluon correlators. In addition, the matching kernel contains a zero-mode term proportional to δ(y/x)\delta(y/x), whose support probes the quasi-GPD at ∣x∣→∞|x|\to\infty, outside the range accessible to the lattice calculation. These omissions prevent a complete twist-three extraction.

References

The matching, however, involves two major unresolved issues. First, the calculation employed only the two-parton one-loop kernel derived for the forward twist-three distribution $g_T$, while the mixing with three-parton quark--gluon correlators, which is intrinsic to twist-three factorization, was not included. Second, the matching kernel contains a perturbative zero-mode term proportional to $\delta(y/x)$. In the large-momentum expansion, the delta function probes the quasi-GPD at $\lvert x\rvert\to\infty$, which cannot be determined from the lattice calculation, and this contribution was therefore omitted.

— Generalized parton distributions: Theory meets experiment  (2609.19544 - Guo et al., 17 Sep 2026) in Section 4.2.2, “The LaMET route to x-dependent GPDs,” subsection on nucleon results