TeV γ-ray fluxes from the long campaigns on Mrk 421 as constraints on the emission of TeV-PeV neutrinos and UHECRs

Recently, The Telescope Array Collaboration reported the arrival of 72 ultra-high-energy cosmic rays with some of them possibly related to the direction of Markarian 421. The IceCube Collaboration reported the detection of 37 extraterrestrial neutrinos in the TeV-PeV energy range collected during three consecutive years. In particular, no neutrino track events were associated with this source. In this paper, we consider the proton-photon interactions to correlate the TeV γ-ray fluxes reported by long campaigns with the neutrino and ultra-high-energy cosmic ray observations around this blazar. Considering the results reported by The IceCube and Telescope Array Collaborations, we found that only from ∼25% to 70% of TeV fluxes described with a power law function with exponential cutoff can come from the proton-photon interactions.