  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.
