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We present preliminary results on the leading-twisttransverse-momentum-dependent (TMD) gluon linearity function, which is directlyconnected to nucleon transverse-spin asymmetries originating from the densityof linearly-polarized gluons. The function is calculated in a spectator-modelframework for the parent proton and for the $f$-type gauge-link structure. Ourwork represents a further step toward the definition of a complete set of gluonTMD distributions at twist-2 that can be used to access the gluon dynamicsinside nucleons and nuclei at new-generation colliders.

Toward twist-2 $T$-odd transverse-momentum-dependent gluon distributions: the $f$-type linearity function