Linear polarization of gluons and Higgs plus jet production at the LHC

We show that the production of a Higgs boson in association with a jet in proton-proton collisions is sensitive to the linear polarization of gluons inside unpolarized protons. We present the analytical expressions, at leading order in perturbative QCD, for various transverse momentum dependent observables, which can be measured at the LHC. Since there are no experimental constraints on the linearly polarized gluon distribution, its effects are studied by adopting two different models. In particular, we find that the $\cos 2\varphi$ azimuthal asymmetry is a very promising observable because it could give access to the sign of this new distribution.