Invariant mass distributions of $\pi^+\pi^-\pi^0$ candidates shown in the vicinity of the nominal $\omega$ mass in exemplary \pt intervals. Each panel displays a different $\pi^0$ reconstruction method, which is indicated in the respective panel and described in the text. A third-order polynomial is used to describe the background, which is subtracted from the distribution and the obtained signal is fitted with a Gaussian with two exponential tails. The integration range used to obtain the raw yields via bin-by-bin counting is indicated by vertical gray lines.