Leading-twist gluon transverse momentum dependent distributions from large-momentum effective theory

TL;DR

This paper tackles the perturbative determination of all leading-twist gluon TMDPDFs and their LaMET-based quasi-distributions. By formulating the gluon-gluon correlator as a matrix in gluon\\otimes hadron spin space using circular polarizations and a frame with equal transverse momentum components, the authors compute the one-loop light-cone TMDPDFs and their quasi-counterparts. They find nonzero one-loop results for \(f_{1T}^{\\perp g}, h_{1}^{\\perp g}, h_{1T}^{g}, h_{1T}^{\\perp g}\), while \(g_{1T}^{g}\) and \(h_{1L}^{\\perp g}\) vanish, and demonstrate a universal one-loop matching coefficient across several distributions despite differing IR kernels. These results establish the essential perturbative inputs for lattice QCD extractions of the full gluon 3D nucleon tomography via LaMET, with potential extensions to higher order and practical lattice implementation.

Abstract

We present the perturbative calculation of the leading-twist gluon transverse momentum dependent distribution functions (TMDPDFs) at one-loop level within large-momentum effective theory. By employing the basis of circular polarizations, we generalize the gluon-gluon correlator to a matrix $Φ_{ΛΛ^\prime}^{ij}(x,\bm{k}_T^2;S)$ in the gluon $\otimes$ hadron spin space. Incorporating the transverse momentum of external states, we derive the leading-twist gluon TMDPDFs and quasi-TMDPDFs at one-loop level. Our calculations reveal nonzero distributions for the gluon TMDPDFs $f_{1T}^{\perp g}(x,\bm{k}_T^2)$, $h_{1}^{\perp g}(x,\bm{k}_T^2)$, $h_{1T}^{g}(x,\bm{k}_T^2)$, and $h_{1T}^{\perp g}(x,\bm{k}_T^2)$. These findings enable future lattice QCD simulations to extract these gluon TMDPDFs, which will facilitate a complete determination of nucleon tomography.

Figures (2)

• Figure 1: One-loop Feynman diagrams contributing to the gluon TMDPDFs without interactions with the Wilson line.
• Figure 2: One-loop Feynman diagrams contributing to the gluon TMDPDFs involving interactions with the Wilson line.