CMS-HIN-20-002

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
Accepted for publication in 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 ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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).
png pdf	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).
png pdf	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).
png pdf	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
png pdf	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.

References
1	M. Gell-Mann	A schematic model of baryons and mesons	PL 8 (1964) 214
2	G. Zweig	An SU $_3$ model for strong interaction symmetry and its breaking; Version 2	Developments in the Quark Theory of Hadrons. Vol. 1. 1964-1978 link
3	R. L. Jaffe	Perhaps a stable dihyperon	PRL 38 (1977) 195
4	R. L. Jaffe	Exotica	Phys. Rept. 409 (2005) 1	hep-ph/0409065
5	Belle Collaboration	Observation of a narrow charmonium-like state in exclusive $B^\pm \to K^\pm \pi^+ \pi^- J/\psi$ decays	PRL 91 (2003) 262001	hep-ex/0309032
6	LHCb Collaboration	Observation of an exotic narrow doubly charmed tetraquark	Nature Phys. 18 (2022) 751	2109.01038
7	A. Esposito, A. Pilloni, and A. D. Polosa	Multiquark resonances	Phys. Rept. 668 (2017) 1	1611.07920
8	S. L. Olsen, T. Skwarnicki, and D. Zieminska	Nonstandard heavy mesons and baryons: experimental evidence	Rev. Mod. Phys. 90 (2018) 015003	1708.04012
9	S. D. Protopopescu et al.	$\pi\pi$ partial wave analysis from reactions $\pi^+ p \to \pi^+ \pi^- \Delta^{++}$ and $\pi^+ p \to K^+ K^- \Delta^{++}$ at 7.1 GeVc	PRD 7 (1973) 1279
10	B. Hyams et al.	$\pi\pi$ phase shift analysis from 600 to 1900 MeV	NPB 64 (1973) 134
11	G. Grayer et al.	High statistics study of the reaction $\pi^- p \to \pi^-\pi^+ n$ : apparatus, method of analysis, and general features of results at 17 GeVc	NPB 75 (1974) 189
12	R. L. Jaffe	Multi-quark hadrons. 1. phenomenology of ( $Q^2{\bar Q}^2$ ) mesons	PRD 15 (1977) 267
13	J. D. Weinstein and N. Isgur	$\mathrm{K}\overline{\mathrm{K}}$ molecules	PRD 41 (1990) 2236
14	C. Amsler and N. A. Tornqvist	Mesons beyond the naive quark model	Phys. Rept. 389 (2004) 61
15	D. V. Bugg	Four sorts of meson	Phys. Rept. 397 (2004) 257	hep-ex/0412045
16	E. Klempt and A. Zaitsev	Glueballs, hybrids, multiquarks. experimental facts versus QCD inspired concepts	Phys. Rept. 454 (2007) 1	0708.4016
17	A. Deandrea et al.	The $\mathrm{s}\overline{\mathrm{s}}$ and $\mathrm{K}\overline{\mathrm{K}}$ nature of f $_0$ (980) in $\mathrm{D}_{s}$ decays	PLB 502 (2001) 79	hep-ph/0012120
18	Particle Data Group Collaboration	Review of Particle Physics	PTEP 2022 (2022) 083C01
19	CMS Collaboration	Evidence for \HepParticleResonanceX3872 in Pb-Pb collisions and studies of its prompt production at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=$ 5.02 TeV	PRL 128 (2022) 032001	CMS-HIN-19-005 2102.13048
20	S. T. Butler and C. A. Pearson	Deuterons from high-energy proton bombardment of matter	PR 129 (1963) 836
21	C. B. Dover, U. W. Heinz, E. Schnedermann, and J. Zimanyi	Relativistic coalescence model for high-energy nuclear collisions	Phys. Rev. C 44 (1991) 1636
22	R. J. Fries, V. Greco, and P. Sorensen	Coalescence models for hadron formation from quark gluon plasma	Ann. Rev. Nucl. Part. Sci. 58 (2008) 177	0807.4939
23	R. C. Hwa and C. B. Yang	Scaling behavior at high $p_{\mathrm{T}}$ and the p/ $\pi$ ratio	Phys. Rev. C 67 (2003) 034902	nucl-th/0211010
24	R. J. Fries, B. Muller, C. Nonaka, and S. A. Bass	Hadronization in heavy ion collisions: recombination and fragmentation of partons	PRL 90 (2003) 202303	nucl-th/0301087
25	V. Greco, C. M. Ko, and P. Levai	Parton coalescence and the antiproton/pion anomaly at RHIC	PRL 90 (2003) 202302	nucl-th/0301093
26	J.-Y. Ollitrault	Anisotropy as a signature of transverse collective flow	PRD 46 (1992) 229
27	CMS Collaboration	Observation of long-range near-side angular correlations in proton-proton collisions at the LHC	JHEP 09 (2010) 091	CMS-QCD-10-002 1009.4122
28	ATLAS Collaboration	Observation of long-range elliptic azimuthal anisotropies in $\sqrt{s}=$ 13 and 2.76 TeV pp collisions with the ATLAS detector	PRL 116 (2016) 172301	1509.04776
29	CMS Collaboration	Measurement of long-range near-side two-particle angular correlations in pp collisions at $\sqrt{s} =$ 13 TeV	PRL 116 (2016) 172302	CMS-FSQ-15-002 1510.03068
30	CMS Collaboration	Evidence for collectivity in pp collisions at the LHC	PLB 765 (2017) 193	CMS-HIN-16-010 1606.06198
31	CMS Collaboration	Observation of long-range near-side angular correlations in proton-lead collisions at the LHC	PLB 718 (2013) 795	CMS-HIN-12-015 1210.5482
32	ALICE Collaboration	Long-range angular correlations on the near and away side in $\mathrm{p}\mathrm{Pb}$ collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=$ 5.02 TeV	PLB 719 (2013) 29	1212.2001
33	ATLAS Collaboration	Observation of associated near-side and away-side long-range correlations in $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=$ 5.02 TeV proton-lead collisions with the ATLAS detector	PRL 110 (2013) 182302	1212.5198
34	CMS Collaboration	Multiplicity and transverse momentum dependence of two- and four-particle correlations in $\mathrm{p}\mathrm{Pb}$ and PbPb collisions	PLB 724 (2013) 213	CMS-HIN-13-002 1305.0609
35	ATLAS Collaboration	Measurement of long-range pseudorapidity correlations and azimuthal harmonics in $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=$ 5.02 TeV proton-lead collisions with the ATLAS detector	Phys. Rev. C 90 (2014) 044906	1409.1792
36	CMS Collaboration	Long-range two-particle correlations of strange hadrons with charged particles in $\mathrm{p}\mathrm{Pb}$ and PbPb collisions at LHC energies	PLB 742 (2015) 200	CMS-HIN-14-002 1409.3392
37	CMS Collaboration	Evidence for collective multiparticle correlations in $\mathrm{p}\mathrm{Pb}$ collisions	PRL 115 (2015) 012301	CMS-HIN-14-006 1502.05382
38	LHCb Collaboration	Measurements of long-range near-side angular correlations in $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=$ 5 TeV proton-lead collisions in the forward region	PLB 762 (2016) 473	1512.00439
39	A. Gu, T. Edmonds, J. Zhao, and F. Wang	Elliptical flow coalescence to identify the f $_0$ (980) content	Phys. Rev. C 101 (2020) 024908	1902.07152
40	A. M. Poskanzer and S. A. Voloshin	Methods for analyzing anisotropic flow in relativistic nuclear collisions	Phys. Rev. C 58 (1998) 1671	nucl-ex/9805001
41	D. Molnar and S. A. Voloshin	Elliptic flow at large transverse momenta from quark coalescence	PRL 91 (2003) 092301	nucl-th/0302014
42	L. Maiani, A. D. Polosa, V. Riquer, and C. A. Salgado	Counting valence quarks at RHIC and LHC	PLB 645 (2007)	hep-ph/0606217
43	ExHIC Collaboration	Multi-quark hadrons from heavy ion collisions	PRL 106 (2011) 212001	1011.0852
44	A. Gu and F. Wang	Transverse momentum spectra of f $_0$ (980) from coalescence model	PLB 848 (2024) 138399	2306.08584
45	ALICE Collaboration	Observation of abnormal suppression of f $_0$ (980) production in $\mathrm{p}\mathrm{Pb}$ collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 5.02 TeV		2311.11786
46	STAR Collaboration	Particle type dependence of azimuthal anisotropy and nuclear modification of particle production in Au + Au collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 200 GeV	PRL 92 (2004) 052302	nucl-ex/0306007
47	PHENIX Collaboration	Scaling properties of azimuthal anisotropy in Au+Au and Cu+Cu collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 200 GeV	PRL 98 (2007) 162301	nucl-ex/0608033
48	ALICE Collaboration	Elliptic flow of identified hadrons in Pb-Pb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=$ 2.76 TeV	JHEP 06 (2015) 190	1405.4632
49	ALICE Collaboration	Anisotropic flow of identified particles in Pb-Pb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=$ 5.02 TeV	JHEP 09 (2018) 006	1805.04390
50	CMS Collaboration	Elliptic flow of charm and strange hadrons in high-multiplicity $\mathrm{p}\mathrm{Pb}$ collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV	PRL 121 (2018) 082301	CMS-HIN-17-003 1804.09767
51	CMS Collaboration	HEPData record for this analysis	link
52	CMS Collaboration	Description and performance of track and primary-vertex reconstruction with the CMS tracker	JINST 9 (2014) P10009	CMS-TRK-11-001 1405.6569
53	CMS Collaboration	Strategies and performance of the CMS silicon tracker alignment during LHC Run 2	NIM A 1037 (2022) 166795	CMS-TRK-20-001 2111.08757
54	CMS Collaboration	Performance of the CMS Level-1 trigger in proton-proton collisions at $\sqrt{s} =$ 13 TeV	JINST 15 (2020) P10017	CMS-TRG-17-001 2006.10165
55	CMS Collaboration	The CMS trigger system	JINST 12 (2017) P01020	CMS-TRG-12-001 1609.02366
56	CMS Collaboration	The CMS experiment at the CERN LHC	JINST 3 (2008) S08004
57	CMS Collaboration	Development of the CMS detector for the CERN LHC Run 3	Accepted by JINST, 2023	CMS-PRF-21-001 2309.05466
58	CMS Collaboration	Observation of correlated azimuthal anisotropy Fourier harmonics in $pp$ and $p+Pb$ collisions at the LHC	PRL 120 (2018) 092301	CMS-HIN-16-022 1709.09189
59	V. Weisskopf and E. P. Wigner	Berechnung der nat\"urlichen linienbreite auf grund der Diracschen lichttheorie	Z. Phys. 63 (1930) 54
60	CMSnoop	Coulomb wave functions	\hrefM.~H. Hull and G.~Breit, , . Springer Berlin Heidelberg, Berlin, Heidelberg, 1959 link
61	STAR Collaboration	$\rho^0$ production and possible modification in Au+Au and p+p collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 200 GeV	PRL 92 (2004) 092301	nucl-ex/0307023
62	STAR Collaboration	NCQ scaling of f $_0$ (980) elliptic flow in 200 GeV Au+Au collisions by STAR and its constituent quark content	Eur. Phys. J. Web Conf. 259 (2022) 10013	2202.01618
63	M. Gyulassy and X.-N. Wang	HIJING 1.0: A Monte Carlo program for parton and particle production in high-energy hadronic and nuclear collisions	Comput. Phys. Commun. 83 (1994) 307	nucl-th/9502021
64	GEANT4 Collaboration	GEANT 4---a simulation toolkit	NIM A 506 (2003) 250
65	P. T. Matthews and A. Salam	Relativistic theory of unstable particles. II	PR 115 (1959) 1079
66	R. A. Kycia and S. Jadach	Relativistic Voigt profile for unstable particles in high energy physics	J. Math. Anal. Appl. 463 (2018) 1040	1711.09304