Measurements of ${\rm Y}$ States Production in $\mathit{\text{p+p}}$ Collisions at $\sqrt{s}=500\mathrm{G}\mathrm{e}\mathrm{V}$ with STAR: Cross Sections, Ratios, and Multiplicity Dependence

We report measurements of ${\rm Y}(1S)$, ${\rm Y}(2S)$ and ${\rm Y}(3S)$ production in $\mathit{\text{p+p}}$ collisions at $\sqrt{s}=500\mathrm{G}\mathrm{e}\mathrm{V}$ by the STAR experiment in year 2011, corresponding to an integrated luminosity ${\mathcal{L}}_{int}=13\mathrm{p}{\mathrm{b}}^{-1}$. The results provide precise cross sections, transverse momentum ($p_T$) and rapidity ($y$) spectra, as well as cross section ratios for $p_{\mathrm{T}}<10\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}$ and $\mathrm{\mid }y\mathrm{\mid }<1$. The dependence of the ${\rm Y}$ yield on charged particle multiplicity has also been measured, offering new insights into the mechanisms of quarkonium production. The data are compared to various theoretical models: the Color Evaporation Model (CEM) accurately describes the ${\rm Y}(1S)$ production, while the Color Glass Condensate + Non-relativistic Quantum Chromodynamics (CGC+NRQCD) model overestimates the data, particularly at low $p_T$. Conversely, the Color Singlet Model (CSM) underestimates the rapidity dependence. These discrepancies highlight the need for further development in understanding the production dynamics of heavy quarkonia in high-energy hadronic collisions. The trend in the multiplicity dependence is consistent with CGC/Saturation and String Percolation models or ${\rm Y}$ production happening in multiple parton interactions modeled by PYTHIA8.