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

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 $\Phi_{\Lambda \Lambda^\prime}^{ij}(x,\bm{k}_T^2;S)$ 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.