Abstract
Using 15.6 fb−1 of e+e− collision data collected at twenty-four center-of-mass energies from 4.0 to 4.6 GeV with the BESIII detector, the helicity amplitudes of the process e+e− → π+π−ω are analyzed for the first time. Born cross section measurements of two-body intermediate resonance states with statistical significance greater than 5σ are presented, such as f0(500), f0(980), f2(1270), f0(1370), b1(1235)±, and ρ(1450)±. In addition, evidence of a resonance state in e+e− → π+π−ω production is found. The mass of this state obtained by line shape fitting is about 4.2 GeV/c2, which is consistent with the production of ψ(4160) or Y(4220).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Particle Data Group, Review of Particle Physics, Prog. Theor. Exp. Phys. 2020 (2020) 083C01.
Belle collaboration, Observation of a narrow charmonium-like state in exclusive B± → K±π+π−J/ψ decays, Phys. Rev. Lett. 91 (2003) 262001 [hep-ex/0309032] [INSPIRE].
BaBar collaboration, Observation of a broad structure in the π+π−J/ψ mass spectrum around 4.26 GeV/c2, Phys. Rev. Lett. 95 (2005) 142001 [hep-ex/0506081] [INSPIRE].
BESIII collaboration, Observation of a Charged Charmoniumlike Structure in e+e− → π+π−J/ψ at \( \sqrt{s} \) = 4.26 GeV, Phys. Rev. Lett. 110 (2013) 252001 [arXiv:1303.5949] [INSPIRE].
Belle collaboration, Study of e+e− → π+π−J/ψ and Observation of a Charged Charmoniumlike State at Belle, Phys. Rev. Lett. 110 (2013) 252002 [Erratum ibid. 111 (2013) 019901] [arXiv:1304.0121] [INSPIRE].
CLEO collaboration, Confirmation of the Y(4260) resonance production in ISR, Phys. Rev. D 74 (2006) 091104 [hep-ex/0611021] [INSPIRE].
Belle collaboration, Measurement of e+e− → π+π−J/ψ cross-section via initial state radiation at Belle, Phys. Rev. Lett. 99 (2007) 182004 [arXiv:0707.2541] [INSPIRE].
BESIII collaboration, Precise measurement of the e+e− → π+π−J/ψ cross section at center-of-mass energies from 3.77 to 4.60 GeV, Phys. Rev. Lett. 118 (2017) 092001 [arXiv:1611.01317] [INSPIRE].
BESIII collaboration, Study of e+e− → ωχcJ at center-of-mass energies from 4.21 to 4.42 GeV, Phys. Rev. Lett. 114 (2015) 092003 [arXiv:1410.6538] [INSPIRE].
BESIII collaboration, Evidence of Two Resonant Structures in e+e− → π+π−hc, Phys. Rev. Lett. 118 (2017) 092002 [arXiv:1610.07044] [INSPIRE].
BESIII collaboration, Measurement of e+e− → π+π−ψ(3686) from 4.008 to 4.600 GeV and observation of a charged structure in the π±ψ(3686) mass spectrum, Phys. Rev. D 96 (2017) 032004 [Erratum ibid. 99 (2019) 019903] [arXiv:1703.08787] [INSPIRE].
BESIII collaboration, Evidence of a resonant structure in the e+e− → π+D0D*− cross section between 4.05 and 4.60 GeV, Phys. Rev. Lett. 122 (2019) 102002 [arXiv:1808.02847] [INSPIRE].
BaBar collaboration, Evidence of a broad structure at an invariant mass of 4.32 GeV/c2 in the reaction e+e− → π+π−ψ2S measured at BaBar, Phys. Rev. Lett. 98 (2007) 212001 [hep-ex/0610057] [INSPIRE].
H.-X. Chen, W. Chen, X. Liu and S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rep. 639 (2016) 1 [arXiv:1601.02092] [INSPIRE].
Y.-R. Liu et al., Pentaquark and Tetraquark states, Prog. Part. Nucl. Phys. 107 (2019) 237 [arXiv:1903.11976] [INSPIRE].
L. Maiani, V. Riquer, F. Piccinini and A.D. Polosa, Four quark interpretation of Y(4260), Phys. Rev. D 72 (2005) 031502 [hep-ph/0507062] [INSPIRE].
A. Ali et al., A new look at the Y tetraquarks and Ωc baryons in the diquark model, Eur. Phys. J. C 78 (2018) 29 [arXiv:1708.04650] [INSPIRE].
S.J. Brodsky, D.S. Hwang and R.F. Lebed, Dynamical Picture for the Formation and Decay of the Exotic XYZ Mesons, Phys. Rev. Lett. 113 (2014) 112001 [arXiv:1406.7281] [INSPIRE].
J.-R. Zhang and M.-Q. Huang, The P-wave [cs][\( \overline{c}\overline{s} \)] tetraquark state: Y(4260) or Y(4660)?, Phys. Rev. D 83 (2011) 036005 [arXiv:1011.2818] [INSPIRE].
J.-R. Zhang and M.-Q. Huang, Could Yb(10890) be the P-wave [bq][\( \overline{b}\overline{q} \)] tetraquark state?, JHEP 11 (2010) 057 [arXiv:1011.2815] [INSPIRE].
Z.-G. Wang, Tetraquark state candidates: Y(4260), Y(4360), Y(4660) and Zc(4020/4025), Eur. Phys. J. C 76 (2016) 387 [arXiv:1601.05541] [INSPIRE].
N. Brambilla et al., Heavy Quarkonium: Progress, Puzzles, and Opportunities, Eur. Phys. J. C 71 (2011) 1534 [arXiv:1010.5827] [INSPIRE].
S.-L. Zhu, The Possible interpretations of Y(4260), Phys. Lett. B 625 (2005) 212 [hep-ph/0507025] [INSPIRE].
F.E. Close and P.R. Page, Gluonic charmonium resonances at BaBar and BELLE?, Phys. Lett. B 628 (2005) 215 [hep-ph/0507199] [INSPIRE].
L. Liu et al., Excited and exotic charmonium spectroscopy from lattice QCD, JHEP 07 (2012) 126 [arXiv:1204.5425] [INSPIRE].
E. Braaten, C. Langmack and D.H. Smith, Born-Oppenheimer Approximation for the XYZ Mesons, Phys. Rev. D 90 (2014) 014044 [arXiv:1402.0438] [INSPIRE].
X. Li and M.B. Voloshin, Y(4260) and Y(4360) as mixed hadrocharmonium, Mod. Phys. Lett. A 29 (2014) 1450060 [arXiv:1309.1681] [INSPIRE].
M.B. Voloshin, Charmonium, Prog. Part. Nucl. Phys. 61 (2008) 455 [arXiv:0711.4556] [INSPIRE].
F.-K. Guo, C. Hanhart and U.-G. Meissner, Evidence that the Y(4660) is a f0(980)ψ′ bound state, Phys. Lett. B 665 (2008) 26 [arXiv:0803.1392] [INSPIRE].
Z.-G. Wang and X.-H. Zhang, Analysis of Y(4660) and related bound states with QCD sum rules, Commun. Theor. Phys. 54 (2010) 323 [arXiv:0905.3784] [INSPIRE].
Q. Wang, C. Hanhart and Q. Zhao, Decoding the riddle of Y(4260) and Zc(3900), Phys. Rev. Lett. 111 (2013) 132003 [arXiv:1303.6355] [INSPIRE].
M. Cleven et al., Y(4260) as the first S-wave open charm vector molecular state?, Phys. Rev. D 90 (2014) 074039 [arXiv:1310.2190] [INSPIRE].
Q. Wang et al., Y(4260): hadronic molecule versus hadro-charmonium interpretation, Phys. Rev. D 89 (2014) 034001 [arXiv:1309.4303] [INSPIRE].
Z.-G. Wang, Analysis of the Y(4220) and Y(4390) as molecular states with QCD sum rules, Chin. Phys. C 41 (2017) 083103 [arXiv:1611.03250] [INSPIRE].
D.-Y. Chen, J. He and X. Liu, Nonresonant explanation for the Y(4260) structure observed in the e+e− → J/ψπ+π− process, Phys. Rev. D 83 (2011) 054021 [arXiv:1012.5362] [INSPIRE].
D.-Y. Chen, X. Liu, X.-Q. Li and H.-W. Ke, Unified Fano-like interference picture for charmoniumlike states Y(4008), Y(4260) and Y(4360), Phys. Rev. D 93 (2016) 014011 [arXiv:1512.04157] [INSPIRE].
A. Martinez Torres, K.P. Khemchandani, D. Gamermann and E. Oset, The Y(4260) as a J/\( \psi K\overline{K} \) system, Phys. Rev. D 80 (2009) 094012 [arXiv:0906.5333] [INSPIRE].
X.-H. Liu and G. Li, Exploring the threshold behavior and implications on the nature of Y(4260) and Zc(3900), Phys. Rev. D 88 (2013) 014013 [arXiv:1306.1384] [INSPIRE].
C.-F. Qiao, One explanation for the exotic state Y(4260), Phys. Lett. B 639 (2006) 263 [hep-ph/0510228] [INSPIRE].
DASP collaboration, Total Cross-section for Hadron Production by e+e− Annihilation at Center-of-mass Energies Between 3.6 and 5.2 GeV, Phys. Lett. B 76 (1978) 361.
BES collaboration, Determination of the ψ(3770), ψ(4040), ψ(4160) and ψ(4415) resonance parameters, Phys. Lett. B 660 (2008) 315 [eConf C070805 (2007) 02] [arXiv:0705.4500] [INSPIRE].
X.H. Mo, C.Z. Yuan and P. Wang, On the leptonic partial widths of the excited ψ states, Phys. Rev. D 82 (2010) 077501 [arXiv:1007.0084] [INSPIRE].
LHCb collaboration, Observation of a resonance in B+ → K+μ+μ− decays at low recoil, Phys. Rev. Lett. 111 (2013) 112003 [arXiv:1307.7595] [INSPIRE].
BESIII collaboration, Measurements of e+e− → \( {K}_S^0 \)K±π∓π0 and \( {K}_S^0 \)K±π∓η at center-of-mass energies from 3.90 to 4.60GeV, Phys. Rev. D 99 (2019) 012003 [arXiv:1810.09395] [INSPIRE].
BESIII collaboration, Precision measurements of σB(e+e− → \( {K}_S^0 \)K±π∓) at center-of-mass energies between 3.8 and 4.6 GeV, Phys. Rev. D 99 (2019) 072005 [arXiv:1808.08733] [INSPIRE].
BESIII collaboration, Study of e+e− → 2(\( p\overline{p} \)) at center-of-mass energies between 4.0 and 4.6 GeV, Phys. Rev. D 103 (2021) 052003 [arXiv:2012.11079] [INSPIRE].
BESIII collaboration, Cross sections for the reactions e+e− → K+K−π+π−(π0), K+K−K+K−(π0), π+π−π+π−(π0), \( p\overline{p} \)π+π−(π0) in the energy region between 3.773 and 4.600 GeV, Phys. Rev. D 104 (2021) 112009 [arXiv:2109.12751] [INSPIRE].
BESIII collaboration, Design and Construction of the BESIII Detector, Nucl. Instrum. Meth. A 614 (2010) 345 [arXiv:0911.4960] [INSPIRE].
C.H. Yu et al., BEPCII Performance and Beam Dynamics Studies on Luminosity, in proceedings of the 7th International Particle Accelerator Conference (IPAC 2016), Busan, Republic of Korea, 8–13 May 2016, pp. 1014–1018 [https://doi.org/10.18429/JACoW-IPAC2016-TUYA01] [INSPIRE].
K.-X. Huang et al., Method for detector description transformation to Unity and application in BESIII, Nucl. Sci. Tech. 33 (2022) 142 [arXiv:2206.10117] [INSPIRE].
X. Li et al., Study of MRPC technology for BESIII endcap-TOF upgrade, Radiat. Detect. Technol. Meth. 1 (2017) 13.
Y.-X. Guo et al., The study of time calibration for upgraded end cap TOF of BESIII, Radiat. Detect. Technol. Meth. 1 (2017) 15.
P. Cao et al., Design and construction of the new BESIII endcap Time-of-Flight system with MRPC Technology, Nucl. Instrum. Meth. A 953 (2020) 163053.
BESIII collaboration, Measurement of the center-of-mass energies at BESIII via the di-muon process, Chin. Phys. C 40 (2016) 063001 [arXiv:1510.08654] [INSPIRE].
BESIII collaboration, Measurement of integrated luminosities at BESIII for data samples at center-of-mass energies between 4.0 and 4.6 GeV, Chin. Phys. C 46 (2022) 113002 [arXiv:2203.03133] [INSPIRE].
BESIII collaboration, Precision measurement of the integrated luminosity of the data taken by BESIII at center of mass energies between 3.810 GeV and 4.600 GeV, Chin. Phys. C 39 (2015) 093001 [arXiv:1503.03408] [INSPIRE].
Z.Y. Deng et al., Object-Oriented BESIII Detector Simulation System, Chin. Phys. C 30 (2006) 371 http://cpc.ihep.ac.cn/article/id/283d17c0-e8fa-4ad7-bfe3-92095466def1.
GEANT4 collaboration, GEANT4 — a simulation toolkit, Nucl. Instrum. Meth. A 506 (2003) 250.
Y.-T. Liang et al., A uniform geometry description for simulation, reconstruction and visualization in the BESIII experiment, Nucl. Instrum. Meth. A 603 (2009) 325 [INSPIRE].
Y. Zheng-Yun, L. Yu-Tie and M. Ya-Jun, A method for detector description exchange among ROOT GEANT4 and GEANT3, Chin. Phys. C 32 (2008) 572.
S. Jadach et al., The Precision Monte Carlo event generator KK for two fermion final states in e+e− collisions, Comput. Phys. Commun. 130 (2000) 260 [hep-ph/9912214].
S. Jadach, B.F.L. Ward and Z. Was, Coherent exclusive exponentiation for precision Monte Carlo calculations, Phys. Rev. D 63 (2001) 113009 [hep-ph/0006359] [INSPIRE].
R.-G. Ping, Event generators at BESIII, Chin. Phys. C 32 (2008) 599 [INSPIRE].
D.J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum. Meth. A 462 (2001) 152 [INSPIRE].
BESIII collaboration, Cross section measurements of e+e− → ωχc0 form \( \sqrt{s} \) = 4.178 to 4.278 GeV, Phys. Rev. D 99 (2019) 091103 [arXiv:1903.02359] [INSPIRE].
LHCb collaboration, Observation of J/ψp Resonances Consistent with Pentaquark States in \( {\Lambda}_b^0 \) → J/ψK−p Decays, Phys. Rev. Lett. 115 (2015) 072001 [arXiv:1507.03414] [INSPIRE].
Belle collaboration, Experimental constraints on the spin and parity of the Z(4430)+, Phys. Rev. D 88 (2013) 074026 [arXiv:1306.4894] [INSPIRE].
H. Chen and R.-G. Ping, Coherent helicity amplitude for sequential decays, Phys. Rev. D 95 (2017) 076010 [arXiv:1704.05184] [INSPIRE].
S.U. Chung, A General formulation of covariant helicity coupling amplitudes, Phys. Rev. D 57 (1998) 431 [INSPIRE].
S.U. Chung, Helicity coupling amplitudes in tensor formalism, Phys. Rev. D 48 (1993) 1225 [Erratum ibid. 56 (1997) 4419] [INSPIRE].
S.U. Chung and J.M. Friedrich, Covariant helicity-coupling amplitudes: A New formulation, Phys. Rev. D 78 (2008) 074027 [arXiv:0711.3143] [INSPIRE].
F. James and M. Roos, Minuit: A System for Function Minimization and Analysis of the Parameter Errors and Correlations, Comput. Phys. Commun. 10 (1975) 343 [INSPIRE].
BESII collaboration, The sigma pole in J/ψ → ωπ+π−, Phys. Lett. B 598 (2004) 149 [hep-ex/0406038].
BESII collaboration, Production of sigma in ψ(2S) → π+π−J/ψ, Phys. Lett. B 645 (2007) 19 [hep-ex/0610023].
V.P. Druzhinin, S.I. Eidelman, S.I. Serednyakov and E.P. Solodov, Hadron Production via e+e− Collisions with Initial State Radiation, Rev. Mod. Phys. 83 (2011) 1545 [arXiv:1105.4975] [INSPIRE].
E.A. Kuraev and V.S. Fadin, On Radiative Corrections to e+e− Single Photon Annihilation at High-Energy, Sov. J. Nucl. Phys. 41 (1985) 466 [hep-ph/9502298].
R.-G. Ping et al., Tuning and validation of hadronic event generator for R value measurements in the tau-charm region, Chin. Phys. C 40 (2016) 113002 [arXiv:1605.09208] [INSPIRE].
S. Eidelman and F. Jegerlehner, Hadronic contributions to g − 2 of the leptons and to the effective fine structure constant alpha α(\( {M}_Z^2 \)), Z. Phys. C 67 (1995) 585 [hep-ph/9502298] [INSPIRE].
F. Jegerlehner, Precision measurements of σhadronic for αeff(E) at ILC energies and (g − 2)μ, Nucl. Phys. B 162 (2006) 22 [hep-ph/0608329].
F. Jegerlehner, The Running fine structure constant αE via the Adler function, Nucl. Phys. B Proc. Suppl. 181–182 (2008) 135 [arXiv:0807.4206] [INSPIRE].
F. Jegerlehner, Theoretical precision in estimates of the hadronic contributions to (g − 2)μ and αQED(MZ), Nucl. Phys. B Proc. Suppl. 126 (2004) 325 [hep-ph/0310234].
F. Jegerlehner, Hadronic vacuum polarization effects in αem(MZ), in proceedings of the Mini-Workshop on Electroweak Precision Data and the Higgs Mass, Zeuthen, Germany, 28 February–1 March 2003, pp. 97–112 [hep-ph/0308117] [INSPIRE].
BaBar collaboration, The e+e− → 2(π+π−)π0, 2(π+π−)η, K+K−π+π−π0 and K+K−π+π−η Cross Sections Measured with Initial-State Radiation, Phys. Rev. D 76 (2007) 092005 [Erratum ibid. 77 (2008) 119902] [arXiv:0708.2461] [INSPIRE].
BESIII collaboration, Measurements of the branching fractions of ηc → K+K−π0, \( {K}_s^0 \)K±π∓,2(π+π−π0), and \( p\overline{p} \), Phys. Rev. D 100 (2019) 012003 [arXiv:1903.05375] [INSPIRE].
BESIII collaboration, Search for hadronic transition χcJ → ηcπ+π− and observation of χcJ → \( K\overline{K} \)πππ, Phys. Rev. D 87 (2013) 012002 [arXiv:1208.4805] [INSPIRE].
B.P. Roe, Probability and Statistics in Experimental Physics, second edition, Springer, New York, NY, U.S.A. (2001) [https://doi.org/10.1007/978-1-4684-9296-5].
X.H. Mo, Unbiased χ2 Estimator for Linear Function Fit Involving Correlated Data, High Energy Phys. Nuclear Phys. 31 (2007) 745 https://s3.cern.ch/inspire-prod-files-1/16cc7aad6b62745311929a4a1f8f62a0.
Acknowledgments
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key R&D Program of China under Contracts Nos. 2020YFA0406300, 2020YFA0406400; National Natural Science Foundation of China (NSFC) under Contracts Nos. 11975118, 12175244, 11875262, 11635010, 11735014, 11835012, 11935015, 11935016, 11935018, 11961141012, 12022510, 12025502, 12035009, 12035013, 12192260, 12192261, 12192262, 12192263, 12192264, 12192265, 12061131003; the Science and Technology Innovation Program of Hunan Province under Contract No. 2020RC3054; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contract No. U1832207; the CAS Center for Excellence in Particle Physics (CCEPP); 100 Talents Program of CAS; The Institute of Nuclear and Particle Physics (INPAC) and Shanghai Key Laboratory for Particle Physics and Cosmology; ERC under Contract No. 758462; European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement under Contract No. 894790; German Research Foundation DFG under Contracts Nos. 443159800, Collaborative Research Center CRC 1044, GRK 2149; Istituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Science and Technology fund; National Science Research and Innovation Fund (NSRF) via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation under Contract No. B16F640076; STFC (United Kingdom); Suranaree University of Technology (SUT), Thailand Science Research and Innovation (TSRI), and National Science Research and Innovation Fund (NSRF) under Contract No. 160355; The Royal Society, U.K. under Contracts Nos. DH140054, DH160214; The Swedish Research Council; U.S. Department of Energy under Contract No. DE-FG02-05ER41374.
Author information
Authors and Affiliations
Consortia
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2303.09718
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
The BESIII collaboration., Ablikim, M., Achasov, M.N. et al. Study of the e+e− → π+π−ω process at center-of-mass energies between 4.0 and 4.6 GeV. J. High Energ. Phys. 2023, 159 (2023). https://doi.org/10.1007/JHEP08(2023)159
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)159