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| CMS-PAS-HIN-20-002 | ||
| Elliptic anisotropy measurement of the f$_0$(980) hadron in proton-lead collisions and evidence of its quark-antiquark composition by CMS | ||
| CMS Collaboration | ||
| 2 September 2023 | ||
| Abstract: Despite its discovery half a century ago, the question about the quark content of the $ \rm{f}_0(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 $ \rm{f}_0(980) $ hadron is an ordinary quark-antiquark meson is reported, by employing the number-of-constituent-quark (NCQ) scaling of elliptic flow anisotropies ($ v_2 $), empirically established by conventional hadrons up to transverse momentum ($ p_{\rm {T}} $) of about 10 GeV/$ c $ in relativistic heavy ion collisions. The $ \rm{f}_0(980) $ is reconstructed via the invariant mass of its main decay channel $ {\rm{f}_0(980)} \to \pi ^ + \pi ^ - $ in proton-lead collisions recorded by the CMS experiment at the LHC. The $ \rm{f}_0(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 $ v_2 $ parameter is extracted as a function of $ p_{\rm {T}} $. It is found that the $ \rm{f}_0(980) $ explanation as an ordinary quark-antiquark state is preferred over a tetraquark or $ {\rm{K}\overline{K}} $ molecule hypothesis at 7.7, 6.3, or 3.1 standard deviations in the $ p_{\rm {T}} < $ 10, 8, or 6 $ \rm{GeV/c} $ ranges, respectively. The quark-antiquark hypothesis is also preferred by 3.5 standard deviations over the $ p_{\rm {T}} < $ 8 GeV/$c$ range for $ n_{\rm{q}}= $ 3, characteristic of a quark-antiquark-gluon hybrid state. The first determination of the $ \rm{f}_0(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. | ||
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Links:
CDS record (PDF) ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, Submitted to NP. The superseded preliminary plots can be found here. |
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| 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 $ < p_{\mathrm{T}} < $ 6 GeV/$ c $ and azimuthal angle 0 $ < \phi-\psi_2 < \pi/ $ 12 in high-multiplicity (185 $ \leq N_{\rm trk}^{\rm offline} < $ 250) pPb collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}= $ 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 $ \rm{f}_0(980)$ signal, while the dashed deep violet and green curves represent the background contributions from $ \rho(770) $ and $ \mathrm{f}_2(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 $ \rm{f}_0(980)$ yield for 4 $ < p_{\mathrm{T}} < $ 6 GeV/$ c $ as a function of $ \phi-\psi_2 $ in high-multiplicity pPb collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}= $ 8.16 TeV. Error bars show statistical uncertainties. The red curve is a fit to Eq. (1) with only the $ n= $ 2 term. |
png pdf |
Figure 4:
The elliptic anisotropy $ v_2 $ and the nonflow-subtracted $ v_2^{\rm sub} $ of the $ \rm{f}_0(980)$ as functions of $ p_{\mathrm{T}} $ within pseudorapidity $ |\eta| < $ 2.4 in high-multiplicity 185 $ \leq N_{\rm trk }^{\rm offline} < $ 250 pPb collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}= $ 8.16 TeV. Error bars show statistical uncertainties, while the shaded areas represent systematic uncertainties. |
png pdf |
Figure 4-a:
The elliptic anisotropy $ v_2 $ and the nonflow-subtracted $ v_2^{\rm sub} $ of the $ \rm{f}_0(980)$ as functions of $ p_{\mathrm{T}} $ within pseudorapidity $ |\eta| < $ 2.4 in high-multiplicity 185 $ \leq N_{\rm trk }^{\rm offline} < $ 250 pPb collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}= $ 8.16 TeV. Error bars show statistical uncertainties, while the shaded areas represent systematic uncertainties. |
png pdf |
Figure 4-b:
The elliptic anisotropy $ v_2 $ and the nonflow-subtracted $ v_2^{\rm sub} $ of the $ \rm{f}_0(980)$ as functions of $ p_{\mathrm{T}} $ within pseudorapidity $ |\eta| < $ 2.4 in high-multiplicity 185 $ \leq N_{\rm trk }^{\rm offline} < $ 250 pPb collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}= $ 8.16 TeV. Error bars show statistical uncertainties, while the shaded areas represent systematic uncertainties. |
png pdf |
Figure 5:
The $ v_2^{\rm sub}/n_\mathrm{q} $ of $ \rm{f}_0(980)$ (with $ n_\mathrm{q}= $ 2 and 4) as functions of $ p_{\mathrm{T}}/n_\mathrm{q} $ (left panel) and $ E_{\mathrm{T}}/n_\mathrm{q} $ (right panel), compared with those of other hadrons ($ \mathrm{K^0_S} $, $ \Lambda $, $ \Xi^{-} $, $ \Omega ^- $ strange hadrons) in high-multiplicity 185 $ \leq N_{\rm trk }^{\rm offline} < $ 250 pPb collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}= $ 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. |
png pdf |
Figure 5-a:
The $ v_2^{\rm sub}/n_\mathrm{q} $ of $ \rm{f}_0(980)$ (with $ n_\mathrm{q}= $ 2 and 4) as functions of $ p_{\mathrm{T}}/n_\mathrm{q} $ (left panel) and $ E_{\mathrm{T}}/n_\mathrm{q} $ (right panel), compared with those of other hadrons ($ \mathrm{K^0_S} $, $ \Lambda $, $ \Xi^{-} $, $ \Omega ^- $ strange hadrons) in high-multiplicity 185 $ \leq N_{\rm trk }^{\rm offline} < $ 250 pPb collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}= $ 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. |
png pdf |
Figure 5-b:
The $ v_2^{\rm sub}/n_\mathrm{q} $ of $ \rm{f}_0(980)$ (with $ n_\mathrm{q}= $ 2 and 4) as functions of $ p_{\mathrm{T}}/n_\mathrm{q} $ (left panel) and $ E_{\mathrm{T}}/n_\mathrm{q} $ (right panel), compared with those of other hadrons ($ \mathrm{K^0_S} $, $ \Lambda $, $ \Xi^{-} $, $ \Omega ^- $ strange hadrons) in high-multiplicity 185 $ \leq N_{\rm trk }^{\rm offline} < $ 250 pPb collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}= $ 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. |
png pdf |
Figure 6:
The log-likelihood ratio distributions for hypotheses $ n_\mathrm{q}= $ 2 and $ n_\mathrm{q}= $ 4 from the pseudoexperiments and the observed value (0 $ < p_{\mathrm{T}} < $ 10 GeV/c). |
png pdf |
Figure 7:
The $ \chi^2 $ of the $ \rm{f}_0(980)$ elliptic flow data from the NCQ-scaling parameterization, scanned in steps of $ n_\mathrm{q} $. |
png pdf |
Figure 8:
Same as Fig. 6 but using $ \rm{f}_0(980)v_2^{\rm sub} $ data within restricted $ p_{\mathrm{T}} $ ranges of $ p_{\mathrm{T}} < $ 8 GeV/$ c $ (left panel) and $ p_{\mathrm{T}} < $ 6 GeV/$ c $ (right panel). |
png pdf |
Figure 8-a:
Same as Fig. 6 but using $ \rm{f}_0(980)v_2^{\rm sub} $ data within restricted $ p_{\mathrm{T}} $ ranges of $ p_{\mathrm{T}} < $ 8 GeV/$ c $ (left panel) and $ p_{\mathrm{T}} < $ 6 GeV/$ c $ (right panel). |
png pdf |
Figure 8-b:
Same as Fig. 6 but using $ \rm{f}_0(980)v_2^{\rm sub} $ data within restricted $ p_{\mathrm{T}} $ ranges of $ p_{\mathrm{T}} < $ 8 GeV/$ c $ (left panel) and $ p_{\mathrm{T}} < $ 6 GeV/$ c $ (right panel). |
png pdf |
Figure 9:
The log-likelihood ratio distributions for hypotheses $ n_\mathrm{q}= $ 2 and $ n_\mathrm{q}= $ 3 from the pseudoexperiments and the observed value. |
png pdf |
Figure 10:
The $ \chi^2 $ of the $ \rm{f}_0(980)$ elliptic flow data from the NCQ-scaling parameterization, scanned in steps of $ n_\mathrm{q} $. The three curves correspond to using $ \rm{f}_0(980)$ data from $ p_{\mathrm{T}} < $ 6 GeV/$ c $, $ p_{\mathrm{T}} < $ 8 GeV/$ c $, and $ p_{\mathrm{T}} < $ 10 GeV/$ c $, respectively. |
| Tables | |
png pdf |
Table 1:
Sources and magnitudes of the uncertainties in the extracted $ n_\mathrm{q} $ of the $ \rm{f}_0(980)$ with data from $ p_{\mathrm{T}} < $ 10 GeV/$ c $. |
| Summary |
| In summary, the $ \rm{f}_0(980)$ yields are extracted at midrapidity ($ |\eta| < $ 2.4) from the invariant mass spectra of its main $ \pi^+\pi^- $ decay channel in high-multiplicity pPb collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}= $ 8.16 TeV by the CMS experiment at the LHC. The elliptic flow anisotropy $ v_2 $ of the $ \rm{f}_0(980)$ 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 energies. Nonflow contamination is estimated from $ \mathrm{K^0_S} $ measurements and is subtracted. By comparing the nonflow-subtracted $ v_2^{\rm sub} $ of the $ \rm{f}_0(980)$ to those of $ \mathrm{K^0_S} $, $ \Lambda $, $ \Xi^{-} $, and $ \Omega $ under the NCQ scaling hypothesis, we found evidence that the $ \rm{f}_0(980)$ hadron is a normal quark-antiquark state. The $ \rm{f}_0(980)$ is 7.7 standard deviations away from being a $ n_\mathrm{q}= $ 4 tetraquark state or $ {\mathrm{K}\overline{\mathrm{K}}} $ molecule. The significance is 6.3 $ \sigma $ and 3.1 $ \sigma $ respectively, if only the restricted $ p_{\mathrm{T}} $ range of $ p_{\mathrm{T}} < $ 8 GeV/c and $ p_{\mathrm{T}} < $ 6 GeV/$c$ is considered. The $ \rm{f}_0(980)$ data in $ p_{\mathrm{T}} < $ 8 GeV/$ c $ are found to be 3.5 $ \sigma $ away from the NCQ scaling with $ n_\mathrm{q}= $ 3, characteristic of a quark-antiquark-gluon hybrid state. The number of constituent quarks $ n_\mathrm{q} $ of the $ \rm{f}_0(980)$ is also extracted, and is consistent with the value of 2. Our experimental determination of the quark content of the $ \rm{f}_0(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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