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| CMS-HIN-20-002 ; CERN-EP-2023-294 | ||
| 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 | ||
| Submitted to Nature Physics | ||
| 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}\bar{\mathrm{q}} $) meson, a tetraquark ($ \mathrm{q}\bar{\mathrm{q}}\mathrm{q}\bar{\mathrm{q}} $) exotic state, a kaon-antikaon ($ \mathrm{K}\overline{\mathrm{K}} $) molecule, or a quark-antiquark-gluon ($ \mathrm{q}\bar{\mathrm{q}}\mathrm{g} $) hybrid. This paper reports strong evidence that the f$_0$(980) state is an ordinary $ \mathrm{q}\bar{\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}\bar{\mathrm{q}} $ state) hypothesis is favored over $ n_{\mathrm{q}} = $ 4 ($ \mathrm{q} \bar{\mathrm{q}} \mathrm{q} \bar{\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}\bar{\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 ; 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. |
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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 $ \mathrm{p}\mathrm{Pb} $ 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 [50] in high-multiplicity $ \mathrm{p}\mathrm{Pb} $ 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. \eqrefequ:ncq. |
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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 $ \mathrm{p}\mathrm{Pb} $ 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:
Extraction of the elliptic anisotropy $ v_{2} $ parameter. 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 $ \mathrm{p}\mathrm{Pb} $ collisions. Error bars show statistical uncertainties. The red curve is a fit to Eq. (1) with only the $ n= $ 2 term. |
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Figure 7:
Elliptic anisotropy before the nonflow effect subtraction. The elliptic anisotropy $ v_{2} $ of the f$_0$(980) state is shown as a function of $ p_{\mathrm{T}} $ within rapidity $ |y| \lesssim $ 2.4 in high-multiplicity $ \mathrm{p}\mathrm{Pb} $ collisions. The error bars show statistical uncertainties while the shaded areas represent systematic uncertainties. |
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Figure 8:
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 [50] in high-multiplicity $ \mathrm{p}\mathrm{Pb} $ 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 9:
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 10:
Exclusion significances for $ n_{\mathrm{q}}= $ 4.} Same as Fig. 4 but using $ \mathrm{f}_0(980) v_2^{\text{sub}} $ data within the restricted ranges $ p_{\mathrm{T}} < $ 8 GeV/$c$ (upper) and $ p_{\mathrm{T}} < $ 6 GeV/$c$ (lower). |
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Figure 10-a:
Exclusion significances for $ n_{\mathrm{q}}= $ 4.} Same as Fig. 4 but using $ \mathrm{f}_0(980) v_2^{\text{sub}} $ data within the restricted ranges $ p_{\mathrm{T}} < $ 8 GeV/$c$ (upper) and $ p_{\mathrm{T}} < $ 6 GeV/$c$ (lower). |
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Figure 10-b:
Exclusion significances for $ n_{\mathrm{q}}= $ 4.} Same as Fig. 4 but using $ \mathrm{f}_0(980) v_2^{\text{sub}} $ data within the restricted ranges $ p_{\mathrm{T}} < $ 8 GeV/$c$ (upper) and $ p_{\mathrm{T}} < $ 6 GeV/$c$ (lower). |
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Figure 11:
Exclusion significance for $ n_{\mathrm{q}}= $ 3.} 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. |
| 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 |
| The f$_0$(980) state is observed in the $ \pi^{+}\pi^{-} $ invariant mass distribution of high-multiplicity proton-lead collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 8.16 TeV, using data collected by the CMS experiment in 2016 and corresponding to an integrated luminosity of 186$\,\text{nb}^{-1}$. The elliptic flow anisotropy $ v_{2} $ of the f$_0$(980) state is measured as a function of $ p_{\mathrm{T}} $ up to 10 GeV/$c$, with respect to the second-order harmonic plane reconstructed from forward/backward energy flow. After subtracting the nonflow contamination, evaluated from $ \mathrm{K^0_S} $ measurements, we obtain the corrected $ v_2^{\text{sub}} $ observable. By comparing the $ \mathrm{f}_0(980) v_2^{\text{sub}} $ to those of $ \mathrm{K^0_S} $, $ \Lambda $, $ \Xi^{-} $, and $ \Omega $ under the number-of-constituent-quarks scaling hypothesis, we rule out the hypotheses that the f$_0$(980) is a tetraquark state or a $ {\mathrm{K}\overline{\mathrm{K}}} $ molecule, in favor of an ordinary $ \mathrm{q}\bar{\mathrm{q}} $ meson hypothesis, at 7.7 standard deviations (6.3 or 3.1 standard deviations, respectively, if only a restricted range of $ p_{\mathrm{T}} < $ 8 or 6 GeV/$c$ is considered). The f$_0$(980) data in the $ p_{\mathrm{T}} < $ 8 GeV/$c$ range are found to disfavor a quark-antiquark-gluon hybrid state at 3.5 standard deviations. The number of constituent quarks of the f$_0$(980) state, as extracted from a fit to the $ v_2^{\text{sub}} $ data, is consistent with the value of 2, characteristic of an ordinary meson. Consequently, we find strong evidence that the f$_0$(980) hadron is a normal quark-antiquark state. We believe that the results reported in this paper present a clear solution to a half-a-century-old puzzle. The experimental determination of the quark content of the f$_0$(980) state with high confidence, using this novel approach, is expected to stimulate further experimental investigations as well as theoretical studies. It paves the way for studies of other exotic hadron candidates using the collective flow scaling approach in high-multiplicity proton-nucleus and heavy ion collisions. |
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