Incompatibility of constraints set by MAGIC ICAT telescope on NGC 1068 neutrinos flux with observation by IceCube Data from the MAGIC ICAT telescope, when used to provide constraints on the neutrino flux from NGC1068, predicts maximal event rate of neutrino detection to be about 0.07 per year. As described in the paper https://arxiv.org/pdf/1906.10954.pdf, to derive the constraints on the Cosmic Ray proton population of star formation and of AGN wind origin, comparison was done between the
gamma-ray spectra predicted by the starburst and AGN wind models with the spectrum measured in the HE (0.1-100 GeV) band
and with the upper limits derived in the VHE (0.1-100 TeV) band. Below are some assumptions that were made to derive the constraints, if I understand correctly are -

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*For AGN jet models to be in agreement with observed gamma ray flux and upper limits, a maximum Lorentz factor of jet leptons, $\gamma_{max} = 10^6$ was assumed in order to produce a sharp cutoff close to 100 GeV.

*In both the starburst and AGN wind models, protons were assumed to be accelerated by diffusive shocks.

*Kroupa initial mass function was assumed, yielding kinetic energy luminosity, $L_{kin}^{SF} = 1.4\times 10^{43} erg s^{-1}$
In order to fit the theoretical model based on these assumptions to fit with the observed data, some constraints were imposed, which are summarised below (Hope I didn't miss anything important) -

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*The acceleration efficiency of protons emitted in gamma rays, $\eta$ was constraint to values between 0.1-0.3. This factor determines the fraction of the Cosmic Ray energy input provided by star formation and Active Galactic Nuclei.

*Efficiency of converting proton kinetic energy into gamma, $F_{cal}$ was constrained to values between 0.3-0.6.

But, these constraints are not compatible with the IceCube measurements https://arxiv.org/pdf/2211.09972.pdf, which registered the neutrino event rate of $79_{+22}^{-20}$ over a period of 3186 days or $9.05_{-2.29}^{+2.52}$ per year . This is about two orders of magnitude more than the upper limit set by constraints in the paper mentioned above.
What can be the source of such discrepancy? I've been trying to figure out where did the the assumption go wrong to cause such big discrepancy, when the assumptions seem quite reasonable?
 A: The gamma and neutrino observations are not incompatible, they just can't both be explained by the specific production models assumed in the MAGIC paper. It is not too hard to create models that are consistent with both the MAGIC and IceCube data.
Gamma ray fluxes can be suppressed relative to neutrinos if the high-energy neutrino source is embedded in an environment that is more opaque to GeV–TeV gamma rays than assumed in the earlier models. See, for example, Murase's paper from a few weeks ago on "The Hidden Hearts of Neutrino Active Galaxies". In order to explain the the shape of the observed gamma energy spectrum, however, a two-zone model works better, with high-energy neutrinos being produced in an inner gamma-opaque AGN corona, while the observed gammas mostly come from an outer starburst region, as described in another very recent paper on "Solving the Multimessenger Puzzle of the AGN-starburst Composite Galaxy NGC 1068".
Measurements of sub-GeV gamma fluxes by proposed experiments such as AMEGO-X or e-ASTROGAM would be very helpful, since they could give information on any cascades of initial higher energy gammas produced by the neutrino source.
