We report on a multi-band variability and correlation study of the TeV blazar Mrk 421 during an exceptional flaring activity observed from 2013 April 11 to 2013 April 19. The study uses, among others, data from GASP-WEBT, Swift, NuSTAR, Fermi-LAT, VERITAS, and MAGIC. The large blazar activity, and the 43 hours of simultaneous NuSTAR and MAGIC/VERITAS observations, permitted variability studies on 15 minute time bins, and over three X-ray bands (3-7 keV, 7-30 keV and 30-80 keV) and three very-high-energy (>0.1 TeV, hereafter VHE) gamma-ray bands (0.2-0.4 TeV, 0.4-0.8 TeV and >0.8 TeV). We detected substantial flux variations on multi-hour and sub-hour timescales in all the X-ray and VHE gamma-ray bands. The characteristics of the sub-hour flux variations are essentially energy-independent, while the multi-hour flux variations can have a strong dependence on the energy of the X-ray and the VHE gamma rays. The three VHE bands and the three X-ray bands are positively correlated with no time-lag, but the strength and the characteristics of the correlation changes substantially over time and across energy bands. Our findings favour multi-zone scenarios for explaining the achromatic/chromatic variability of the fast/slow components of the light curves, as well as the changes in the flux-flux correlation on day-long timescales. We interpret these results within a magnetic reconnection scenario, where the multi-hour flux variations are dominated by the combined emission from various plasmoids of different sizes and velocities, while the sub-hour flux variations are dominated by the emission from a single small plasmoid moving across the magnetic reconnection layer.
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