  The phenomenon of magnification bias can induce a non-negligible angular
correlation between two samples of galaxies with nonoverlapping redshift
distributions. This signal is particularly clear when background submillimeter
galaxies are used, and has been shown to constitute an independent cosmological
probe. This work extends prior studies on the submillimeter galaxy
magnification bias to the massive neutrino scenario, with the aim being to
assess its sensitivity as a cosmological observable to the sum of neutrino
masses. The measurements of the angular cross-correlation function between
moderate redshift GAMA galaxies and high-redshift submillimeter H-ATLAS
galaxies are fit to the weak lensing prediction down to the arcmin scale. The
signal is interpreted under the halo model, which is modified to accommodate
massive neutrinos. We discuss the impact of the choice of cosmological
parametrization on the sensitivity to neutrino masses. The currently available
data on the magnification bias affecting submillimeter galaxies are sensitive
to neutrino masses when a cosmological parametrization in terms of the
primordial amplitude of the power spectrum $(A_s$) is chosen over the local
root mean square of smoothed linear density perturbations $(\sigma_8$). A clear
upper limit on the sum of neutrino masses can be derived if the value of $A_s$
is either fixed or assigned a narrow Gaussian prior, a behavior that is robust
against changes to the chosen value.
