Title: Signature of Particle Diffusion on the X-ray Spectra of the blazar Mkn 421

Abstract: The curvature in blazar spectrum has the potential to understand the particle dynamics in jets. We performed a detailed analysis of simultaneous Swift-XRT (0.3-10 keV) and NuSTAR (3-79 keV)} observations of Mkn 421. Our analysis of NuSTAR observations alone reveals that, during periods of low flux, the hard X-ray spectra are best represented by a steep power-law with photon index reaching $\sim$ 3. However, the spectrum exhibits significant curvature during its high flux states. To investigate this, we explore plausible diffusion processes facilitating shock acceleration in the emission region that can contribute to the observed spectral curvature. Particularly, such processes can cause gradual fall of the photon spectrum at high energies which can be represented by a sub-exponential function. The parameter that decides this spectral change can be used to characterise the energy dependence of the diffusive process. Our results suggest that the X-ray spectra of Mkn 421 are consistent with a scenario where particle acceleration is mediated through Bohm-type diffusion and the spectra beyond the synchrotron peak is modulated by the radiative loss process.