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The recent discovery of a diffuse cosmic neutrino flux extending up to PeVenergies raises the question of which astrophysical sources generate thissignal. One class of extragalactic sources which may produce such high-energyneutrinos are blazars. We present a likelihood analysis searching forcumulative neutrino emission from blazars in the 2nd Fermi-LAT AGN catalogue(2LAC) using an IceCube neutrino dataset 2009-12 which was optimised for thedetection of individual sources. In contrast to previous searches with IceCube,the populations investigated contain up to hundreds of sources, the largest onebeing the entire blazar sample in the 2LAC catalogue. No significant excess isobserved and upper limits for the cumulative flux from these populations areobtained. These constrain the maximum contribution of the 2LAC blazars to theobserved astrophysical neutrino flux to be $27 \%$ or less between around 10TeV and 2 PeV, assuming equipartition of flavours at Earth and a singlepower-law spectrum with a spectral index of $-2.5$. We can still exclude thatthe 2LAC blazars (and sub-populations) emit more than $50 \%$ of the observedneutrinos up to a spectral index as hard as $-2.2$ in the same energy range.Our result takes into account that the neutrino source count distribution isunknown, and it does not assume strict proportionality of the neutrino flux tothe measured 2LAC $\gamma$-ray signal for each source. Additionally, weconstrain recent models for neutrino emission by blazars.

The contribution of Fermi-2LAC blazars to the diffuse TeV-PeV neutrino flux