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Multi-wavelength campaigns have been carried out to study the correlationbetween the very high energy (VHE) $\gamma$-ray and the X-ray emissions inblazars but, no conclusive results have been achieved yet. In this paper, weadd Milagro data to the existing VHE $\gamma$-ray data from HEGRA-CT1 andWhipple and test the consistency and robustness of the reported correlationbetween VHE $\gamma$-ray and X-ray fluxes in Mrk 421. We found that at monthlytime scale the correlation is robust, consistent between instruments anddescribed as a linear function. Furthermore, most of the fluxes on shorter timescales are consistent with the correlation within 3 $\sigma_A$ even, where$\sigma_A$ is an estimated intrinsic scatter. However, a break-down of thecorrelation becomes clearly evident at high states of activity with fluxes $\rm\gtrsim 2.5\times 10^{-10}\, cm^{-2}s^{-1}$ at energies above 400 GeVindependently of the time scale, observational period or instrument, even forsingle flares, the X-ray and VHE $\gamma$-ray emissions lie on the correlationuntil the VHE $\gamma$-ray flux reaches values higher than the one mentionedabove. We have interpreted our results within the one-zone synchrotronself-Compton model. We found that describing a single and unique$\gamma$-ray/X-ray correlation strongly narrows the range of possible values ofthe magnetic field $B$ when a constant value of the spectral index along thecorrelation is assumed.

Reconcilement of VHE $\gamma$-ray/X-ray correlation studies in Mrk 421 and break-down at high fluxes