  We consider implications of the IceCube excess for hadronuclear (pp)
scenarios of neutrino sources such as galaxy clusters/groups and star-forming
galaxies. Since the observed neutrino flux is comparable to the diffuse
gamma-ray background flux obtained by Fermi, we place new, strong upper limits
on the source spectral index, {\Gamma}<2.1-2.2. In addition, the new IceCube
data imply that these sources contribute at least 30%-40% of the diffuse
gamma-ray background in the 100 GeV range and even ~100% for softer spectra.
Our results, which are insensitive to details of the pp source models, are one
of the first strong examples of the multimessenger approach combining the
measured neutrino and gamma-ray fluxes. The pp origin of the IceCube excess can
further be tested by constraining {\Gamma} with sub-PeV neutrino observations,
by unveiling the sub-TeV diffuse gamma-ray background and by observing such pp
sources with TeV gamma-ray detectors. We also discuss specific pp source models
with a multi-PeV neutrino break/cutoff, which are consistent with the current
IceCube data.
