[Color online] Left: the $\pi^0$ peak position as a function of the transverse momentum for several values of nonlinearity parameters ($d$, $e$), with default values for $a$, $b$ and $c$. Right: the deviation from a constant value of the $\pi^0$ peak position expressed in $\chi^2/NDF$ as a function of the nonlinearity parameters ($d$, $e$).