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Probing the structure of $f_{0}(980)$ from the elliptic flow in p-Pb collisions at the LHC

Yili Wang, Wenbin Zhao, Che Ming Ko, Fengkun Guo, Ju-Jun Xie, Huichao Song

TL;DR

The paper tackles the question of the $f_0(980)$'s internal structure by testing whether it is a $K\bar{K}$ molecular state through its elliptic flow $v_2$ in $p$-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV. It employs a realistic $K+\bar{K}\to f_0(980)$ coalescence framework with a Gaussian Wigner function whose width is tied to the RMS radius, using kaon phase-space distributions from the Hydro-Coal-Frag model and UrQMD for hadronic evolution. The results reproduce CMS $v_2(p_T)$ and are compatible with ALICE $p_T$ spectra for $f_0(980)$ with radii in the 1–1.5 fm range, and they predict a breakdown of simple NC scaling due to unequal-momentum coalescence, unless an unrealistically large radius is assumed. This supports the $K\bar{K}$ molecular picture and demonstrates the necessity of realistic coalescence calculations to interpret flow data for light exotic hadrons, providing a pathway to study their structure in heavy-ion and light-ion collisions.

Abstract

The $f_{0}(980)$ is a light scalar meson whose internal structure remains under debate and investigation. Assuming that the $f_0(980)$ is a $K\bar K$ molecule that can only survive at the kinetic freeze-out of the evolving bulk matter, we implement the coalescence model to study its transverse momentum ($p_T$) spectra and elliptic flow ($v_2$) in high-multiplicity p-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV. Using the well-tuned kaon phase-space distributions from the Hydro-Coal-Frag model, our $K\bar{K}$ coalescence calculations with reasonable values for the $f_0(980)$ radius successfully reproduce the elliptic flow measured by CMS over the range $0 < p_{T} < 12$ GeV and also agree with the $p_T$-spectra from ALICE. These results in heavy ion collisions are consistent with the $K\bar K$ molecular picture of the $f_0(980)$. We also find that the number-of-constituent scaling of $v_2$ for the $f_0(980)$ is violated in p-Pb collisions at the LHC because most $f_0(980)$ are produced from the coalescence of kaons that have different momenta. Our study demonstrates the necessity of realistic coalescence model calculations and also explains why the CMS interpretation of the $f_0(980)$ as an ordinary $q\bar q$ meson is no longer valid by interpreting the measured $v_2$ with a simple scaling formula based on the assumption of equal momentum coalescence. The investigation also provides a novel way to explore the internal structure of light exotic hadrons that can be abundantly produced in relativistic heavy and/or light ion collisions.

Probing the structure of $f_{0}(980)$ from the elliptic flow in p-Pb collisions at the LHC

TL;DR

The paper tackles the question of the 's internal structure by testing whether it is a molecular state through its elliptic flow in -Pb collisions at TeV. It employs a realistic coalescence framework with a Gaussian Wigner function whose width is tied to the RMS radius, using kaon phase-space distributions from the Hydro-Coal-Frag model and UrQMD for hadronic evolution. The results reproduce CMS and are compatible with ALICE spectra for with radii in the 1–1.5 fm range, and they predict a breakdown of simple NC scaling due to unequal-momentum coalescence, unless an unrealistically large radius is assumed. This supports the molecular picture and demonstrates the necessity of realistic coalescence calculations to interpret flow data for light exotic hadrons, providing a pathway to study their structure in heavy-ion and light-ion collisions.

Abstract

The is a light scalar meson whose internal structure remains under debate and investigation. Assuming that the is a molecule that can only survive at the kinetic freeze-out of the evolving bulk matter, we implement the coalescence model to study its transverse momentum () spectra and elliptic flow () in high-multiplicity p-Pb collisions at TeV. Using the well-tuned kaon phase-space distributions from the Hydro-Coal-Frag model, our coalescence calculations with reasonable values for the radius successfully reproduce the elliptic flow measured by CMS over the range GeV and also agree with the -spectra from ALICE. These results in heavy ion collisions are consistent with the molecular picture of the . We also find that the number-of-constituent scaling of for the is violated in p-Pb collisions at the LHC because most are produced from the coalescence of kaons that have different momenta. Our study demonstrates the necessity of realistic coalescence model calculations and also explains why the CMS interpretation of the as an ordinary meson is no longer valid by interpreting the measured with a simple scaling formula based on the assumption of equal momentum coalescence. The investigation also provides a novel way to explore the internal structure of light exotic hadrons that can be abundantly produced in relativistic heavy and/or light ion collisions.

Paper Structure

This paper contains 4 sections, 4 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Results and Discussion
  4. Summary

Figures (3)

  • Figure 1: (Color online) The $p_T$-spectra of $f_0(980)$ in 0--20% p-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV, calculated from the coalescence model with different RMS radius by using the phase-space distributions of kaons generated from the Hydro-Coal-Frag hybrid model. Also plotted are the $p_T$-spectra of kaons. The data are taken from the ALICE Collaboration ALICE:2016deiALICE:2023cxn.
  • Figure 2: (Color online) Scaled differential elliptic flow $v_2(p_T)$ of kaons (with $n = 1$) from the Hydro-Coal-Frag model and $f_0(980)$ (with $n = 2$) from the coalescence model in 0--20% p + Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV. The kaon data are taken from the ALICE Collaboration ALICE:2013snk and the $f_0(980)$ data are taken from the CMS Collaboration CMS:2023rev.
  • Figure 3: (Color online) Scaling behavior for the elliptic flow between kaons ($n = 1$) and $f_0(980)$ ($n = 2$) in 0--20% p - Pb collisions, calculated from the Hydro-Coal-Frag model for kaons and from the coalescence model with different RMS radii for the $f_0(980)$. The data are from the ALICE and CMS Collaborations ALICE:2013snkCMS:2023rev.