We consider implications of the IceCube signal 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 \lesssim 2.1 \mbox { - - } 2.2 .
In addition , the new IceCube data imply that these sources contribute at least 30 % \mbox { - - } 40 % of the diffuse \gamma -ray background in the 100 GeV range and even \sim 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 signal 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 .