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Since its mission, Fermi Collaboration reported the highest flux observedduring July - September 2012 for the BL Lac Markarian 421 (Mrk 421). Theintegrated flux was eight times greater than the average flux reported in thesecond Fermi catalog. During April 2013, Mrk 421 exhibited the highest TeV$\gamma$-ray and optical fluxes recorded. The Telescope Array (TA)collaboration reported the arrival of 72 ultra-high-energy cosmic rays(UHECRs), two in temporal and positional coincidence with the flaring activityobserved in 2012 and one with the flaring activity in 2013. The IceCubecollaboration has reported around 100 neutrino events in the High-EnergyStarting Events (HESE) catalog. Although no neutrino track-like event has beenassociated with this source, a neutrino shower-like event (IC31) is in temporaland positional coincidence with the flare in 2012. Describing the broadbandspectral energy distribution during the flaring activities exhibited in 2012and 2013 with one- and two-zone lepto-hadronic scenarios and one-zone SSCmodel, we study a possible correlation between the neutrino event IC31 and thethree UHECRs. We estimate the number of neutrino and UHECR events generatedfrom the proposed models, and show that while the neutrino events are low toassociate the event IC31 with Mrk 421, the number of UHECRs are similar tothose reported by TA collaboration.

The unprecedented flaring activities around Mrk 421 in 2012 and 2013: The test for neutrino and UHECR event connection