  The radiative loss interpretation for the broken power-law spectra of blazars
is often questioned since the difference between the indices does not support
this inference. Using the blazar Mkn 421 as a case study, we performed a
detailed analysis of its characteristic photon energy where the spectral index
changes significantly. We used the observations of the source by Swift-XRT from
2008 to 2019 to identify the characteristic photon energy and the corresponding
spectral indices. The spectra in the energy range 0.3-10.0 keV can be well
fitted by a log parabola as well as a smooth broken power-law. From the smooth
broken power-law spectral fit we show that the spectral indices before and
after the characteristic photon energy are strongly anti-correlated. Further,
the spectral curvature measured at the characteristic photon energy indicates
an anti-correlation with the low energy spectral index while the high energy
spectral index shows a positive correlation. These findings are at variance
with a simple radiative loss interpretation for the characteristic photon
energy, and alternative scenarios are thus discussed. Though these scenarios
are in principle capable of reproducing the correlation results, they deviate
significantly from the observed properties.
