  Infrared renormalons in Quantum Chromodynamics are associated with
non-perturbative corrections to short distance observables. Linear renormalons,
i.e. such that the associated non-perturbative corrections scale like one
inverse power of the hard scale, can affect at a non-negligible level even the
very high-energy phenomena studied at the Large Hadron Collider. Using an
Abelian model, we study the presence of linear renormalons in the transverse
momentum distribution of a neutral vector boson $Z$ produced in hadronic
collisions. We consider a process where the $Z$ transverse momentum is balanced
by a sizable recoil against a coloured final state particle. One may worry that
such a colour configuration, not being azimuthally symmetric, could generate
unbalanced soft radiation, associated in turn with linear infrared renormalons
affecting the transverse momentum distribution of the vector boson. We
performed a numerical calculation of the renormalon effects for this process in
the so-called large $b_0$ limit. We found no evidence of linear renormalons in
the transverse momentum distribution of the $Z$ in the large
transverse-momentum region, irrespective of rapidity cuts.
