Looking at the gluon moment of the nucleon with dynamical twisted mass fermions
Constantia Alexandrou, Vincent Drach, Kyriakos Hadjiyiannakou, Karl Jansen, Bartosz Kostrzewa, Christian Wiese
TL;DR
This work addresses the lattice QCD determination of the gluon momentum fraction $\langle x \rangle_g$ in the nucleon, governed by the momentum sum rule $\sum_q \langle x \rangle_q + \langle x \rangle_g = 1$. It compares two strategies: (i) a Feynman-Hellmann approach that perturbs the gauge action and relates $\partial E_N/\partial \lambda$ to $\langle x \rangle_g$, and (ii) a direct extraction from a zero-momentum gluon three-point function using a gluon operator $O_{\bc\nu}$ with smearing. Preliminary FH results on $24^3\times48$ lattices show a linear $\lambda$-dependence with a slope linking to $\langle x \rangle_g$ but large uncertainties, while the direct method on $32^3\times64$ lattices with five-step HYP-smearing yields a non-zero signal with roughly 10% relative error, indicating a viable path with higher statistics. The study also outlines critical renormalization considerations for the singlet gluon operator and plans to extend to physical pion mass ensembles and other hadrons, moving toward a full determination of the gluon contribution to nucleon momentum and spin.
Abstract
To understand the structure of hadrons it is important to know the PDF of their constituents, the quarks and gluons. In our work we aim to compute the first moment of the gluon PDF $\langle x \rangle_g$ for the nucleon. We follow two possible approaches in order to extract the gluon moment: the Feynman-Hellmann theorem and a direct method with smearing of the gluon operator. We present preliminary results computed on $24^3 \times 48$ lattices for the case where the Feynman-Hellman theorem is used and $32^3 \times 64$ lattices for the direct method, employing $N_f=2+1+1$ maximally twisted mass fermions.