have different order of magnitude for different sets and combinations of the coefficients (it is implied, of course, that the quantities with the same dimensionality are being compared), and it turns out that there still exists at least one relatively loosely constrained parameter of dimensions of mass. Considering the CPT-odd fermion Lagrangian term $ -{\overline}{\psi} \gamma^{5} \gamma^{\mu} b_{\mu} \psi $, one may argue [@Andrianov_Giacconi_Soldati] that the upper bound on the timelike component of $ b_{\mu} $ may be $ | b^{0} | < 10^{-2} \, \text{eV} $, while for the spacelike components one has $ | {\bf b} | < 10^{-18} \, \text{eV} $ or even stronger, and the remaining tensor coefficients are also estimated to be smaller than the upper bound on $ b^{0} $ [@sme_reviews]. This makes it reasonable to study the effects caused by the non-zero parameter $ b^{0} $ in the first place since it could actually be the greatest one among the others (with the same dimensions). One of the aims of our investigation is to examine the consequences of this situation for the synchrotron radiation and to place bounds on $ b^{0} $ possibly more stringent than those available in the literature.

At the 