  Blazars have been suggested as possible neutrino sources long before the
recent IceCube discovery of high-energy neutrinos. We re-examine this
possibility within a new framework built upon the blazar simplified view and a
self-consistent modelling of neutrino emission from individual sources. The
former is a recently proposed paradigm that explains the diverse statistical
properties of blazars adopting minimal assumptions on blazars' physical and
geometrical properties. This view, tested through detailed Monte Carlo
simulations, reproduces the main features of radio, X-ray, and gamma-ray blazar
surveys and also the extragalactic gamma-ray background at energies > 10 GeV.
Here we add a hadronic component for neutrino production and estimate the
neutrino emission from BL Lacs as a class, "calibrated" by fitting the spectral
energy distributions of a preselected sample of BL Lac objects and their
(putative) neutrino spectra. Unlike all previous papers on this topic, the
neutrino background is then derived by summing up at a given energy the fluxes
of each BL Lac in the simulation, all characterised by their own redshift,
synchrotron peak energy, gamma-ray flux, etc. Our main result is that BL Lacs
as a class can explain the neutrino background seen by IceCube above ~ 0.5 PeV
while they only contribute ~ 10% at lower energies, leaving room to some other
population(s)/physical mechanism. However, one cannot also exclude the
possibility that individual BL Lacs still make a contribution at the ~ 20%
level to the IceCube low-energy events. Our scenario makes specific predictions
testable in the next few years.
