Constraining the $f_0(980)$ Structure and Formation Dynamics via Anisotropy-Response Scaling

Abstract

A species-resolved anisotropy-response scaling framework is used to investigate the structure and formation dynamics of the $f_0(980)$ in relativistic nuclear collisions. Published measurements in high-multiplicity p+Pb collisions at $\sqrt{s_{NN}}=8.16$~TeV exhibit broad scaling closure under a single-meson response construction, with a small effective final-state response, $\zeta_{f_0}\simeq0.04$, whereas a symmetric ${\rm K\bar K}$ constituent-response construction gives substantially poorer closure. An explicitly molecular ${\rm K\bar K}$ calculation also exhibits single-meson-like scaling but gives a substantially larger effective final-state response, $\zeta_{f_0}\simeq0.16$. Thus, single-meson scaling alone is not a unique structural discriminator. The combined response construction and $\zeta_{f_0}$ constraints characterize the measured $f_0(980)$ by a single-meson-like anisotropy response with weak final-state sensitivity, distinctly different from the molecular benchmark. These results establish anisotropy-response scaling as a new experimental probe of $f_0(980)$ formation dynamics and motivate systematic tests across collision systems and beam energies.