Elliptic anisotropy measurement of the f0(980) hadron in proton-lead collisions and evidence for its quark-antiquark composition

Abstract

Despite the f₀(980) hadron having been discovered half a century ago, the question about its quark content has not been settled: it might be an ordinary quark-antiquark ( $q\overline{q}$ ) meson, a tetraquark ( $q\overline{q}q\overline{q}$ ) exotic state, a kaon-antikaon ( $K\overline{K}$ ) molecule, or a quark-antiquark-gluon ( $q\overline{q}g$ ) hybrid. This paper reports strong evidence that the f₀(980) state is an ordinary $q\overline{q}$ meson, inferred from the scaling of elliptic anisotropies (v₂) with the number of constituent quarks (n_q), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f₀(980) state is reconstructed via its dominant decay channel f₀(980) → π⁺π^-, in proton-lead collisions recorded by the CMS experiment at the LHC, and its v₂ is measured as a function of transverse momentum (p_T). It is found that the n_q = 2 ( $q\overline{q}$ state) hypothesis is favored over n_q = 4 ( $q\overline{q}q\overline{q}$ or $K\overline{K}$ states) by 7.7, 6.3, or 3.1 standard deviations in the p_T < 10, 8, or 6 GeV/c ranges, respectively, and over n_q = 3 ( $q\overline{q}g$ hybrid state) by 3.5 standard deviations in the p_T < 8 GeV/c range. This result represents the first determination of the quark content of the f₀(980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates.

Fig. 1. Coalescence hadronization.

This picture illustrates the formation of hadrons in heavy-ion collisions in the coalescence model. Hadrons tend to form when the constituent quarks have similar positions and momenta. [Detector image reprinted from ref. , under a CC BY SA 4.0 license].

Fig. 2. Elliptic anisotropy results.

The nonflow-effect-subtracted elliptic anisotropy $v_2^{\mathrm{sub}}$ of the f₀(980) is shown as a function of p_T within ∣y∣ ≲ 2.4 in high-multiplicity pPb collisions. The error bars show statistical uncertainties while the shaded areas represent systematic uncertainties.

Fig. 3. NCQ scaling of elliptic anisotropy.

The $v_2^{\mathrm{sub}}/n_{\mathrm{q}}$ of the f₀(980) state (for the n_q = 2 and 4 hypotheses) as a function of KE_T/n_q, compared with those of ${\mathrm{K}}_{\mathrm{S}}^0$, Λ, Ξ⁻, and Ω strange hadrons in high-multiplicity pPb collisions. The error bars show statistical uncertainties while the shaded areas represent systematic uncertainties. The red curve is the NCQ scaling parameterization of the data for ${\mathrm{K}}_{\mathrm{S}}^0$, Λ, Ξ⁻, and Ω hadrons given by Eq. (3).

Fig. 4. Exclusion significance from n_q = 4.

The log-likelihood ratio distributions for the n_q = 2 and 4 hypotheses from pseudo-experiments, together with the measured value for the f₀(980) state in the 0 < p_T < 10 GeV/c range.

Fig. 5. Invariant mass fit.

The invariant mass spectrum of opposite-sign pion pairs after the combinatorial background subtraction, for the pair transverse momentum 4 < p_T < 6 GeV/c and the azimuthal angle 0 < ϕ–ψ₂ < π/12, in high-multiplicity pPb collisions. The solid blue curve is the fit result within the fit range marked with vertical blue dashed lines; the orange dashed curve represents the residual background. The solid red curve represents the f₀(980) signal, while the dashed dark-violet and light-green curves correspond to the background contributions from the ρ (770)⁰ and f₂ (1270) resonances, respectively. The ratio between data and the fit result is shown in the lower panel, with the error bars representing statistical uncertainties only. The low-mass region exhibits a nontrivial turn-on behavior and is not included in the fit.

Fig. 6. Elliptic anisotropy before the nonflow effect subtraction.

a The f₀(980) yield in the 4 < p_T < 6 GeV/c range as a function of ϕ–ψ₂ in high-multiplicity pPb collisions. Error bars show statistical uncertainties. The red curve is a fit to Eq. (1) with only the n = 2 term, from which the elliptic anisotropy v₂ parameter is extracted. b The elliptic anisotropy v₂ of the f₀(980) state is shown before the nonflow effect subtraction as a function of p_T within rapidity ∣y∣ ≲ 2.4 in high-multiplicity pPb collisions. The error bars show statistical uncertainties while the shaded areas represent systematic uncertainties.

Fig. 7. NCQ scaling of elliptic anisotropy in p_T/n_q.

The $v_2^{\mathrm{sub}}/n_{\mathrm{q}}$ of the f₀(980) state (for the n_q = 2 and 4 hypotheses) as a function of p_T/n_q is compared with those of the ${\mathrm{K}}_{\mathrm{S}}^0$, Λ, Ξ⁻, and Ω strange hadrons in high-multiplicity pPb collisions. Error bars show the statistical uncertainties while the shaded areas represent systematic uncertainties. The red curve is the NCQ scaling parameterization of the data for the ${\mathrm{K}}_{\mathrm{S}}^0$, Λ, Ξ⁻, and Ω hadrons.

Fig. 8. The χ² scan.

The χ² of the f₀(980) elliptic flow data with respect to the NCQ scaling parameterization, scanned in steps of n_q. The three curves correspond to using f₀(980) data for p_T < 6, 8, and 10 GeV/c, respectively.

Fig. 9. Exclusion significances.

Same as Fig. 4 but using ${\text{f}}_0\left(980\right)v_2^{\mathrm{sub}}$ data within the restricted ranges p_T < 8 GeV/c (a) and p_T < 6 GeV/c (b). c The expected log-likelihood ratio distributions for n_q = 2 vs. 3 hypotheses from the pseudo-experiments and the observed value for the f₀(980) in data in the p_T < 8 GeV/c range to extract the exclusion significance for n_q = 3.