The relentless variability of Mrk 421 from the TeV to the radio

The origin of the gamma-ray emission blazar Mrk 421 is still a matter debate. We used 5.5 years unbiased observing campaign data, obtained using FACT telescope and Fermi LAT detector at TeV GeV energies, longest densest so far, together with contemporaneous multi-wavelength observations, to characterise variability constrain underlying physical mechanisms. studied correlated light curves by ten different instruments found two significant results. X-ray are very well lag <0.6 days. radio (15 Ghz band) widely strongly correlated. Variations curve lead those in radio. Lepto-hadronic purely hadronic models frame shock acceleration predict proton or cooling timescales that ruled out short delays observed 421. Instead observations match predictions leptonic models.