$f_0(980)$ production from $K\bar{K}$ coalescence in pp collisions at $\sqrt{s}=5.02$ TeV within UrQMD
We investigate the production of the scalar meson $f_0(980)$ in proton--proton collisions at $\sqrt{s}=5.02$~TeV using the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport model supplemented with a $K\bar{K}$ coalescence afterburner. After conservatively tuning the UrQMD string-fragmentation parameters, the model reproduces the bulk charged-kaon production in the low-to-intermediate transverse-momentum region, providing the kaon phase-space distribution used as input for the coalescence calculation. In the present implementation, both charged and neutral kaon--antikaon pairs are considered, and each accepted $K\bar{K}$ pair is assigned to the isoscalar $f_0(980)$ and isovector $a_0(980)$ channels with an equal Monte Carlo probability. Using the updated integration analysis, we find that $Δp=0.4$~GeV/$c$ gives the best directly simulated agreement with the ALICE $p_T$ spectrum and integrated yield, while a linear interpolation between the neighboring points at $Δp=0.3$ and $0.4$~GeV/$c$ yields an interpolated optimum of $Δp^{\ast}\approx0.365$~GeV/$c$. Within this constrained hadronic coalescence framework, the measured $f_0(980)$ production is reasonably described, and the results are consistent with interpreting the $f_0(980)$ as a late-stage $K\bar{K}$ molecular configuration formed near kinetic freeze-out in small collision systems.