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CMS-PAS-HIN-20-002
Elliptic anisotropy measurement of the f0(980) hadron in proton-lead collisions and evidence of its quark-antiquark composition by CMS
Abstract: Despite its discovery half a century ago, the question about the quark content of the f0(980) hadron has not been settled, whether its being an ordinary quark-antiquark meson, a tetraquark exotic state, a kaon-antikaon molecule, or a quark-antiquark-gluon hybrid. In this note, evidence that the f0(980) hadron is an ordinary quark-antiquark meson is reported, by employing the number-of-constituent-quark (NCQ) scaling of elliptic flow anisotropies (v2), empirically established by conventional hadrons up to transverse momentum (pT) of about 10 GeV/c in relativistic heavy ion collisions. The f0(980) is reconstructed via the invariant mass of its main decay channel f0(980)π+π in proton-lead collisions recorded by the CMS experiment at the LHC. The f0(980) yield is measured relative to the second-order symmetry plane as reconstructed from the energy deposited in the forward/backward region of the CMS detector, and its v2 parameter is extracted as a function of pT. It is found that the f0(980) explanation as an ordinary quark-antiquark state is preferred over a tetraquark or K¯K molecule hypothesis at 7.7, 6.3, or 3.1 standard deviations in the pT< 10, 8, or 6 GeV/c ranges, respectively. The quark-antiquark hypothesis is also preferred by 3.5 standard deviations over the pT< 8 GeV/c range for nq= 3, characteristic of a quark-antiquark-gluon hybrid state. The first determination of the f0(980) state quark content with high confidence using this novel approach advances the study of quantum chromodynamics, the fundamental theory governing the physics of hadrons.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
This picture illustrates the formation of hadrons in heavy ion collisions in the coalescence model. Hadrons are formed only when the constituent quarks have similar positions and momenta.

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Figure 2:
The same-sign combinatorial background subtracted invariant mass spectrum for pair transverse momentum 4 <pT< 6 GeV/c and azimuthal angle 0 <ϕψ2<π/ 12 in high-multiplicity (185 Nofflinetrk< 250) pPb collisions at sNN= 8.16 TeV. The solid blue curve is the fit result where the blue dashed lines indicate the fitting range; the orange dashed curve represents the residual background, and the violet dashed line represents the total background. Solid red curve represent f0(980) signal, while the dashed deep violet and green curves represent the background contributions from ρ(770) and f2(1270), respectively. The ratio between data and fit is shown in the bottom panel. Error bars show statistical uncertainties.

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Figure 3:
The f0(980) yield for 4 <pT< 6 GeV/c as a function of ϕψ2 in high-multiplicity pPb collisions at sNN= 8.16 TeV. 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 4:
The elliptic anisotropy v2 and the nonflow-subtracted vsub2 of the f0(980) as functions of pT within pseudorapidity |η|< 2.4 in high-multiplicity 185 Nofflinetrk< 250 pPb collisions at sNN= 8.16 TeV. Error bars show statistical uncertainties, while the shaded areas represent systematic uncertainties.

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Figure 4-a:
The elliptic anisotropy v2 and the nonflow-subtracted vsub2 of the f0(980) as functions of pT within pseudorapidity |η|< 2.4 in high-multiplicity 185 Nofflinetrk< 250 pPb collisions at sNN= 8.16 TeV. Error bars show statistical uncertainties, while the shaded areas represent systematic uncertainties.

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Figure 4-b:
The elliptic anisotropy v2 and the nonflow-subtracted vsub2 of the f0(980) as functions of pT within pseudorapidity |η|< 2.4 in high-multiplicity 185 Nofflinetrk< 250 pPb collisions at sNN= 8.16 TeV. Error bars show statistical uncertainties, while the shaded areas represent systematic uncertainties.

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Figure 5:
The vsub2/nq of f0(980) (with nq= 2 and 4) as functions of pT/nq (left panel) and ET/nq (right panel), compared with those of other hadrons (K0S, Λ, Ξ, Ω strange hadrons) in high-multiplicity 185 Nofflinetrk< 250 pPb collisions at sNN= 8.16 TeV. Error bars show statistical uncertainties, while the shaded areas represent systematic uncertainties. The red curves are the NCQ scaling parameterizations to the data of the other hadrons.

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Figure 5-a:
The vsub2/nq of f0(980) (with nq= 2 and 4) as functions of pT/nq (left panel) and ET/nq (right panel), compared with those of other hadrons (K0S, Λ, Ξ, Ω strange hadrons) in high-multiplicity 185 Nofflinetrk< 250 pPb collisions at sNN= 8.16 TeV. Error bars show statistical uncertainties, while the shaded areas represent systematic uncertainties. The red curves are the NCQ scaling parameterizations to the data of the other hadrons.

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Figure 5-b:
The vsub2/nq of f0(980) (with nq= 2 and 4) as functions of pT/nq (left panel) and ET/nq (right panel), compared with those of other hadrons (K0S, Λ, Ξ, Ω strange hadrons) in high-multiplicity 185 Nofflinetrk< 250 pPb collisions at sNN= 8.16 TeV. Error bars show statistical uncertainties, while the shaded areas represent systematic uncertainties. The red curves are the NCQ scaling parameterizations to the data of the other hadrons.

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Figure 6:
The log-likelihood ratio distributions for hypotheses nq= 2 and nq= 4 from the pseudoexperiments and the observed value (0 <pT< 10 GeV/c).

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Figure 7:
The χ2 of the f0(980) elliptic flow data from the NCQ-scaling parameterization, scanned in steps of nq.

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Figure 8:
Same as Fig. 6 but using f0(980)vsub2 data within restricted pT ranges of pT< 8 GeV/c (left panel) and pT< 6 GeV/c (right panel).

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Figure 8-a:
Same as Fig. 6 but using f0(980)vsub2 data within restricted pT ranges of pT< 8 GeV/c (left panel) and pT< 6 GeV/c (right panel).

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Figure 8-b:
Same as Fig. 6 but using f0(980)vsub2 data within restricted pT ranges of pT< 8 GeV/c (left panel) and pT< 6 GeV/c (right panel).

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Figure 9:
The log-likelihood ratio distributions for hypotheses nq= 2 and nq= 3 from the pseudoexperiments and the observed value.

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Figure 10:
The χ2 of the f0(980) elliptic flow data from the NCQ-scaling parameterization, scanned in steps of nq. The three curves correspond to using f0(980) data from pT< 6 GeV/c, pT< 8 GeV/c, and pT< 10 GeV/c, respectively.
Tables

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Table 1:
Sources and magnitudes of the uncertainties in the extracted nq of the f0(980) with data from pT< 10 GeV/c.
Summary
In summary, the f0(980) yields are extracted at midrapidity (|η|< 2.4) from the invariant mass spectra of its main π+π decay channel in high-multiplicity pPb collisions at sNN= 8.16 TeV by the CMS experiment at the LHC. The elliptic flow anisotropy v2 of the f0(980) is measured as a function of pT up to 10 GeV/c, with respect to the second-order harmonic plane reconstructed from forward/backward energies. Nonflow contamination is estimated from K0S measurements and is subtracted. By comparing the nonflow-subtracted vsub2 of the f0(980) to those of K0S, Λ, Ξ, and Ω under the NCQ scaling hypothesis, we found evidence that the f0(980) hadron is a normal quark-antiquark state. The f0(980) is 7.7 standard deviations away from being a nq= 4 tetraquark state or K¯K molecule. The significance is 6.3 σ and 3.1 σ respectively, if only the restricted pT range of pT< 8 GeV/c and pT< 6 GeV/c is considered. The f0(980) data in pT< 8 GeV/c are found to be 3.5 σ away from the NCQ scaling with nq= 3, characteristic of a quark-antiquark-gluon hybrid state. The number of constituent quarks nq of the f0(980) is also extracted, and is consistent with the value of 2. Our experimental determination of the quark content of the f0(980) with high confidence under this novel approach is expected to stimulate further experimental investigations as well as theoretical studies. Those future endeavors will likely advance our understanding of QCD and Nature.
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