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To understand the structure of hadrons it is important to know the PDF oftheir constituents, the quarks and gluons. In our work we aim to compute thefirst moment of the gluon PDF $\langle x \rangle_g$ for the nucleon. We followtwo possible approaches in order to extract the gluon moment: theFeynman-Hellmann theorem and a direct method with smearing of the gluonoperator. We present preliminary results computed on $24^3 \times 48$ latticesfor 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 massfermions.

Looking at the gluon moment of the nucleon with dynamical twisted mass fermions