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.

Correction factors applied to the raw $\omega$ yields according to Eq. $\ref{eq:xsection}$ for the five $\pi^0$ reconstruction methods, as indicated in the legend. The factors include the reconstruction efficiency $\epsilon_{\text{rec}}$ and the geometrical acceptance $A$ of the involved detectors.

Ratios of the $\omega$ production cross section obtained using five different $\pi^0$ reconstruction methods with respect to a Levy--Tsallis fit of the combined measurement. The fit parameters are given in Table $\ref{tab:fitparameters}$ together with the reduced $\chi^2$ of the converged fit. The statistical and systematic uncertainties of the individual measurements are given in Table $\ref{tab:syst}$ and are represented by vertical bars and boxes, respectively.

Invariant cross section of $p+p\rightarrow\omega+X$ production at midrapidity in pp collisions at $\sqrt{s}=\SI{13}{TeV}$ compared to theoretical predictions. The cross section is parametrized using a Levy--Tsallis function (dashed grey line), where the fit parameters are given in Table $\ref{tab:fitparameters}$. The systematic uncertainty of the measurement is denoted by boxes, excluding the normalization uncertainty of 1.58\%, which is shown separately as a grey box in the bottom panel of the figure To account for the finite width of each \pt-interval, the data points are shifted according to the underlying spectrum, as described by the fit The red line represents the theoretical prediction obtained using the PYTHIA8.2  event generator with the Monash 2013 tune . The width of the line indicates the statistical uncertainty of the prediction. The blue dashed line shows a NLO calculation  incorporating $\omega$ fragmentation based on a broken SU(3) model, where all scales are chosen to be $\mu=\pt$ and the blue shaded band denotes the scale uncertainty The bottom panel shows the ratio of the data, as well as the theoretical predictions to the Levy--Tsallis parametrization.

Ratio of $\omega/\pi^0$ production as a function of transverse momentum for pp collisions at $\sqrt{s}=\SI{13}{TeV}$. The data is compared to various measurements at lower collision energies ranging from $\sqrt{s}=62$ to \SI{7000}{GeV} . The data is confronted with various theoretical calculations, which are given in the legend and described in the text. In addition, the ratio obtained from \mt-scaling of the measured $\pi^0$ meson cross section is shown.