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| Elliptic anisotropy measurement of the f$_0$(980) hadron in proton-lead collisions and evidence for its quark-antiquark composition | ||
| CMS Collaboration | ||
| 28 December 2023 | ||
| Nature Commun. 16 (2025) 1, 7990 | ||
| Abstract: Despite the f$_0$(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 ($ \mathrm{q}\overline{\mathrm{q}} $) meson, a tetraquark ($ \mathrm{q}\overline{\mathrm{q}}\mathrm{q}\overline{\mathrm{q}} $) exotic state, a kaon-antikaon ($ \mathrm{K}\overline{\mathrm{K}} $) molecule, or a quark-antiquark-gluon ($ \mathrm{q}\overline{\mathrm{q}}\mathrm{g} $) hybrid. This paper reports strong evidence that the f$_0$(980) state is an ordinary $ \mathrm{q}\overline{\mathrm{q}} $ meson, inferred from the scaling of elliptic anisotropies ($ v_{2} $) with the number of constituent quarks ($ n_{\mathrm{q}} $), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f$_0$(980) state is reconstructed via its dominant decay channel $ \mathrm{f}_0(980) \to \pi^{+}\pi^{-} $, in proton-lead collisions recorded by the CMS experiment at the LHC, and its $ v_{2} $ is measured as a function of transverse momentum ($ p_{\mathrm{T}} $). It is found that the $ n_{\mathrm{q}} = $ 2 ($ \mathrm{q}\overline{\mathrm{q}} $ state) hypothesis is favored over $ n_{\mathrm{q}} = $ 4 ($ \mathrm{q} \overline{\mathrm{q}} \mathrm{q} \overline{\mathrm{q}} $ or $ \mathrm{K}\overline{\mathrm{K}} $ states) by 7.7, 6.3, or 3.1 standard deviations in the $ p_{\mathrm{T}} < $ 10, 8, or 6 GeV/$c$ ranges, respectively, and over $ n_{\mathrm{q}}= $ 3 ($ \mathrm{q}\overline{\mathrm{q}}\mathrm{g} $ hybrid state) by 3.5 standard deviations in the $ p_{\mathrm{T}} < $ 8 GeV/$c$range. This result represents the first determination of the quark content of the f$_0$(980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates. | ||
| Links: e-print arXiv:2312.17092 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 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 [43], under a \hrefhttps://creativecommons.org/licenses/by-sa/4.0/CC BY SA 4.0 license.] |
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Figure 2:
Elliptic anisotropy results. The nonflow-effect-subtracted elliptic anisotropy $ v_2^{\text{sub}} $ of the f$_0$(980) is shown as a function of $ p_{\mathrm{T}} $ within $ |y| \lesssim $ 2.4 in high-multiplicity pPb collisions. The error bars show statistical uncertainties while the shaded areas represent systematic uncertainties. |
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Figure 3:
NCQ scaling of elliptic anisotropy. The $ v_2^{\text{sub}}/n_{\mathrm{q}} $ of the f$_0$(980) state (for the $ n_{\mathrm{q}}= $ 2 and 4 hypotheses) as a function of $ KE_{\text T}/n_{\mathrm{q}} $, compared with those of $ \mathrm{K^0_S} $, $ \Lambda $, $ \Xi^{-} $, and $ \Omega $ strange hadrons [53] 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^0_S} $, $ \Lambda $, $ \Xi^{-} $, and $ \Omega $ hadrons given by Eq. (2). |
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Figure 4:
Exclusion significance from $ n_{\mathrm{q}}= $ 4. The log-likelihood ratio distributions for the $ n_{\mathrm{q}}= $ 2 and 4 hypotheses from pseudo-experiments, together with the measured value for the f$_0$(980) state in the 0 $ < p_{\mathrm{T}} < 10 GeV/$c$range. |
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Figure 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_{\mathrm{T}} < $ 6 GeV/$c$and the azimuthal angle 0 $ < \phi-\psi_{2} < \pi/ $12, in high-multiplicity pPb collisions. The solid blue curve is the fit result within the fit range marked with vertical blue dashed lines; the orange dashed curve represents the residual background. The solid red curve represents the f$_0$(980) signal, while the dashed dark-violet and light-green curves correspond to the background contributions from the $ \rho$(770)$^0 $ and f$_2$(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. |
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Figure 6:
Elliptic anisotropy before the nonflow effect subtraction. a: The f$_0$(980) yield in the 4 $ < p_{\mathrm{T}} < $ 6 GeV/$c$range as a function of $ \phi-\psi_{2} $ 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 $ v_{2} $ parameter is extracted. b: The elliptic anisotropy $ v_{2} $ of the f$_0$(980) state is shown before the nonflow effect subtraction as a function of $ p_{\mathrm{T}} $ within rapidity $ |y| \lesssim $ 2.4 in high-multiplicity pPb collisions. The error bars show statistical uncertainties while the shaded areas represent systematic uncertainties. |
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Figure 7:
NCQ scaling of elliptic anisotropy in $ p_{\mathrm{T}}/n_{\mathrm{q}} $. The $ v_2^{\text{sub}}/n_{\mathrm{q}} $ of the f$_0$(980) state (for the $ n_{\mathrm{q}}= $ 2 and 4 hypotheses) as a function of $ p_{\mathrm{T}}/n_{\mathrm{q}} $ is compared with those of the $ \mathrm{K^0_S} $, $ \Lambda $, $ \Xi^{-} $, and $ \Omega $ strange hadrons \protect [53] 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^0_S} $, $ \Lambda $, $ \Xi^{-} $, and $ \Omega $ hadrons. |
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Figure 8:
{The $ \chi^2 $ scan.} The $ \chi^2 $ of the f$_0$(980) elliptic flow data with respect to the NCQ scaling parameterization, scanned in steps of $ n_\mathrm{q} $. The three curves correspond to using f$_0$(980) data for $ p_{\mathrm{T}} < $ 6, 8, and 10 GeV/$c$, respectively. |
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Figure 9:
Exclusion significances. a, b: same as Fig. 4 but using f$_0$(980) $v_2^{\text{sub}} $ data within the restricted ranges $ p_{\mathrm{T}} < $ 8 GeV/$c$ (a) and $ p_{\mathrm{T}} < $ 6 GeV/$c$ (b). c: The expected log-likelihood ratio distributions for $ n_{\mathrm{q}}= $ 2 vs. 3 hypotheses from the pseudo-experiments and the observed value for the f$_0$(980) in data in the $ p_{\mathrm{T}} < $ 8 GeV/$c$range to extract the exclusion significance for $ n_{\mathrm{q}}= $ 3. |
| Tables | |
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Table 1:
Sources and magnitudes of the uncertainties in the extracted $ n_{\mathrm{q}} $ of the f$_0$(980) state in the range $ p_{\mathrm{T}} < $ 10 GeV/$c$. |
| Summary |
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