Bremsstrahlung approximation for inclusive processes

The inclusive reaction $a+b\longrightarrow c+\dots$, where $a$ and $b$ are scalar “nucleons” of the field $\psi$ and $c$ is the detected meson $A$, is considered in the quantum field model $\mathscr L_{\operatorname{int}}=-ig\psi^*\overset\leftrightarrow\partial_\mu\psi A^\mu$. The cross section of this reaction in the pionization region is found in the bremsstrahlung approximation. It is shown that the simple model of bremsstrahlung production of secondary particles cannot pretend to describe inclusive processes in the central region $(x\sim 0)$.