A coherent study of e+e−→ωπ0, ωπ+π−, and ωη

Yan Wu; Qinsong Zhou; Wenbiao Yan; Guangshun Huang

doi:10.52396/JUSTC-2023-0086

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Open Access JUSTC Physics 08 June 2023

A coherent study of e⁺e⁻→ωπ⁰, ωπ⁺π⁻, and ωη

Yan Wu^{1, 2},
Qinsong Zhou^{3, 4},
Wenbiao Yan^{1, 2

,},
Guangshun Huang^{1, 2}

1.
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
2.
State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei 230026, China
3.
School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
4.
Research Center for Hadron and CSR Physics, Lanzhou University & Institute of Modern Physics of CAS, Lanzhou 730000, China

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https://doi.org/10.52396/JUSTC-2023-0086

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Author Bio:
Yan Wu is currently pursuing his master degree in Department of Modern Physics at University of Science and Technology of China. His primary research is related with experimental high energy physics at BESIII

Qinsong Zhou is currently pursuing his Ph.D. degree in School of Physical Science and Technology at Lanzhou University. His primary research is related with theoretical high energy physics. He has published several papers at Physical Review C, Physical Review D, and The European Physical Journal C
Corresponding author: E-mail: wenbiao@ustc.edu.cn
Received Date: 10 May 2023
Accepted Date: 28 May 2023

Available Online: 08 June 2023

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Abstract

Abstract

In this work, a combined analysis is performed on the processes of $e^+e^-\to\omega\pi^0\pi^0$, $e^+e^-\to\omega\pi^+\pi^-$, and $e^+e^-\to\omega\eta$ to study possible $\omega$ excited states at approximately 2.2 GeV. The resonance parameters are extracted by simultaneous fits of the Born cross section line shapes of these processes. In the fit with one resonance, the mass and width are fitted to be $(2207\pm14)$ MeV$/c^2$ and $(104\pm16)$ MeV, respectively. The result is consistent with previous measurements. In the fit with two resonances, the mass and width for the first resonance are fitted to be $(2160\pm36)$ MeV$/c^2$ (solution I), $(2154\pm12)$ MeV$/c^2$ (solution II) and $(141\pm74)$ MeV (solution I), $(152\pm77)$ MeV (solution II), respectively. The mass and width for the second resonance are fitted to be $(2298\pm19)$ MeV$/c^2$ (solution I), $(2309\pm6)$ MeV$/c^2$ (solution II) and $(106\pm77)$ MeV (solution I), $(99\pm23)$ MeV (solution II), respectively. The result is consistent with the theoretical prediction of $\omega(4S)$ and $\omega(3D)$. The intermediate subprocesses in $e^+e^-\to\omega\pi^+\pi^-$ are analyzed using the resonance parameters of the previous fits in this work. In the fit with one resonance, the fitting result of $\varGamma^{e^+e^-}_{{\rm{R}}}B_{{\rm{R}}}$ is partially consistent with the previous result. In the fit with two resonances, the fitting result of $\varGamma^{e^+e^-}_{{\rm{R}}}B_{{\rm{R}}}$ is of the same order of magnitude as the theoretical prediction. This work may provide useful information for studying the light flavor vector meson family.

Graphical abstract

Simultaneous fit of ${{e}^{+}}{{e}^{-}}\to \omega {{\pi }^{0}}{{\pi }^{0}} $, $\omega {{\pi }^{+}}{{\pi }^{-}} $, and ωη with one resonance.

Abstract

In this work, a combined analysis is performed on the processes of $e^+e^-\to\omega\pi^0\pi^0$, $e^+e^-\to\omega\pi^+\pi^-$, and $e^+e^-\to\omega\eta$ to study possible $\omega$ excited states at approximately 2.2 GeV. The resonance parameters are extracted by simultaneous fits of the Born cross section line shapes of these processes. In the fit with one resonance, the mass and width are fitted to be $(2207\pm14)$ MeV$/c^2$ and $(104\pm16)$ MeV, respectively. The result is consistent with previous measurements. In the fit with two resonances, the mass and width for the first resonance are fitted to be $(2160\pm36)$ MeV$/c^2$ (solution I), $(2154\pm12)$ MeV$/c^2$ (solution II) and $(141\pm74)$ MeV (solution I), $(152\pm77)$ MeV (solution II), respectively. The mass and width for the second resonance are fitted to be $(2298\pm19)$ MeV$/c^2$ (solution I), $(2309\pm6)$ MeV$/c^2$ (solution II) and $(106\pm77)$ MeV (solution I), $(99\pm23)$ MeV (solution II), respectively. The result is consistent with the theoretical prediction of $\omega(4S)$ and $\omega(3D)$. The intermediate subprocesses in $e^+e^-\to\omega\pi^+\pi^-$ are analyzed using the resonance parameters of the previous fits in this work. In the fit with one resonance, the fitting result of $\varGamma^{e^+e^-}_{{\rm{R}}}B_{{\rm{R}}}$ is partially consistent with the previous result. In the fit with two resonances, the fitting result of $\varGamma^{e^+e^-}_{{\rm{R}}}B_{{\rm{R}}}$ is of the same order of magnitude as the theoretical prediction. This work may provide useful information for studying the light flavor vector meson family.

Public Summary

We perform a combined analysis on e⁺e⁻→ωπ⁰π⁰, e⁺e⁻→ωπ⁺π⁻, and e⁺e⁻→ωη to study possible ω excited states around 2.2 GeV.
In the fit with one resonance, the mass and width are consistent with previous measurements.
In the fit with two resonances, the masses and widths are consistent with theoretical predictions.
The fitting result of $ \varGamma _\text{R}^{{{e}^{+}}{{e}^{-}}}{{B}_\text{R}} $ is partially consistent with experimental result and theoretical prediction.

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References(24)

References

[1]	Wang J Z, Chen D Y, Liu X, et al. Costructing J/ψ family with updated data of charmoniumlike Y states. Phys. Rev. D, 2019, 99 (11): 114003. doi: 10.1103/PhysRevD.99.114003
[2]	Wang J Z, Qian R Q, Liu X, et al. Are the Y states around 4.6 GeV from e⁺e^– annihilation higher charmonia? Physical Review D, 2020, 101: 034001. doi: 10.1103/PhysRevD.101.034001
[3]	Wang J Z, Sun Z F, Liu X, et al. Higher bottomonium zoo. The European Physical Journal C, 2018, 78 (11): 915. doi: 10.1140/epjc/s10052-018-6372-1
[4]	Pang C Q, Wang J Z, Liu X, et al. A systematic study of mass spectra and strong decay of strange mesons. The European Physical Journal C, 2017, 77 (12): 861. doi: 10.1140/epjc/s10052-017-5434-0
[5]	Song Q T, Chen D Y, Liu X, et al. Charmed-strange mesons revisited: Mass spectra and strong decays. Physical Review D, 2015, 91: 054031. doi: 10.1103/PhysRevD.91.054031
[6]	Song Q T, Chen D Y, Liu X, et al. Higher radial and orbital excitations in the charmed meson family. Physical Review D, 2015, 92: 074011. doi: 10.1103/PhysRevD.92.074011
[7]	Wang J Z, Chen D Y, Song Q T, et al. Revealing the inner structure of the newly observed D₂(3000). Physical Review D,* 2016, 94: 094044. doi: 10.1103/PhysRevD.94.094044
[8]	Particle Data Group, R. L. Workman R L, Burkert V D, et al. Review of particle physics. Progress of Theoretical and Experimental Physics, 2022, 8: 083C01. doi: 10.1093/ptep/ptac097
[9]	Pang C Q, Wang Y R, Hu J F, et al. Study of the ω meson family and newly observed ω-like state X(2240). Physical Review D, 2020, 101: 074022. doi: 10.1103/PhysRevD.101.074022
[10]	Barnes T, Close F E, Page P R, et al. Higher quarkonia. Physical Review D, 1997, 55: 4157–4188. doi: 10.1103/PhysRevD.55.4157
[11]	Ebert D, Faustov R N, Galkin V O. Masses of light mesons in the relativistic quark model. Modern Physics Letters A, 2005, 20: 1887–1893. doi: 10.1142/S021773230501813X
[12]	Ebert D, Faustov R N, Galkin V O. Mass spectra and Regge trajectories of light mesons in the relativistic quark model. Physical Review D, 2009, 79: 114029. doi: 10.1103/PhysRevD.79.114029
[13]	Wang X, Sun Z F, Chen D Y, et al. Nonstrange partner of strangeonium-like state Y(2175). Physical Review D, 2012, 85: 074024. doi: 10.1103/PhysRevD.85.074024
[14]	Anisovich A V, Baker C A, Batty C J, et al. I=0, C=−1 mesons from 1940 to 2410 MeV. Physics Letters B, 2002, 542: 19–28. doi: 10.1016/S0370-2693(02)02303-1
[15]	Bugg D V. Partial wave analysis of p¯p→Λ¯Λ. The European Physical Journal C-Particles and Fields, 2004, 36: 161–168. doi: https://doi.org/10.1140/epjc/s2004-01955-5
[16]	Omega Photon Collaboration, Atkinson M, Axon T J, et al. Photon diffractive dissociation to ρρπ and ρπππ states. Zeitschrift für Physik C Particles and Fields, 1988, 38: 535–541. doi: https://doi.org/10.1007/BF01624357
[17]	Aubert B, Bona M, Boutigny D, et al. The e ⁺ e^- → 2(π ⁺ π^-) π⁰, 2(π⁺ π^-) eta, K⁺ K^- π⁺ π^- π⁰ and K ⁺ K ^- π ⁺ π ^- η cross sections measured with initial-state radiation. Physical Review D, 2007, 76: 092005. doi: 10.1103/PhysRevD.76.092005
[18]	Lees J P, Poireau V, Tisserand V, et al. Study of the reactions e ⁺ e⁻ → π ⁺ π ⁻ π⁰ π⁰ π⁰and π⁺ π⁻ π⁰ π⁰η at center-of-mass energies from threshold to 4.35 GeV using initial-state radiation. Physical Review D, 2018, 98: 112015. doi: 10.1103/PhysRevD.98.112015
[19]	Lees J P, Poireau V, Tisserand V, et al. Resonances in e⁺ e⁻ annihilation near 2.2 GeV. Physical Review D, 2020, 101: 012011. doi: 10.1103/PhysRevD.101.012011
[20]	The BESIII collaboration, Ablikim M, Achasov M N, et al. Measurement of e ⁺ e ⁻→ωπ ⁺ π ⁻ cross section at $ \sqrt{s}$ = 2.000 to 3.080 GeV. Journal of High Energy Physics, 2023, 1: 111. doi: https://doi.org/10.1007/JHEP01(2023)111
[21]	M. Ablikim, Achasov M N, Adlarson P, et al. Measurement of the e ⁺ e ⁻ → ωπ⁰ π⁰ cross section at center-of-mass energies from 2.0 to 3.08 GeV. Physical Review D, 2022, 105: 032005. doi: 10.1103/PhysRevD.105.032005
[22]	Ablikim M, Achasov M N, Adlarson P, et al. Observation of a resonant structure in e⁺e⁻→ωη and another in e⁺e⁻ → ωπ⁰ at center-of-mass energies between 2.00 GeV and 3.08 GeV. Physics Letters B, 2021, 813: 136059. doi: 10.1016/j.physletb.2020.136059
[23]	Zhou Q S, Wang J Z, Liu X. Role of the ω(4S) and ω(3D) states in mediating the e ⁺ e ⁻ →ωη and ωπ⁰ π⁰ processes. Physical Review D, 2022, 106: 034010. doi: 10.1103/PhysRevD.106.034010
[24]	Wang J Z, Wang L M, Liu X, et al. Deciphering the light vector meson contribution to the cross sections of e ⁺e^– annihilations into the open-strange channels through a combined analysis. Physical Review D, 2021, 104: 054045. doi: 10.1103/PhysRevD.104.054045

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Figure 1. A comparison of resonance parameters of these reported ω states with masses around 2.2 GeV^[14–22].

Figure 2. Solution I of the simultaneous fit of $e^+e^-\to\omega\pi^0\pi^0$, $\omega\pi^+\pi^-$, and $\omega\eta$ with one resonance. Black dots with error bars are from experimental data, and the error bars include both statistical and systematic uncertainties. The blue solid curve represents the total fit. The red dashed curve represents the contribution of resonant part. The green dashed curve presents the contribution of non-resonant part. The pink curve represents the interference between the two parts.

Figure 3. Solution II of the simultaneous fit of $e^+e^-\to\omega\pi^0\pi^0$, $\omega\pi^+\pi^-$, and $\omega\eta$ with one resonance. The symbols’ descriptions are consistent with Fig. 2.

Figure 4. Solution I of the simultaneous fit of $e^+e^-\to\omega\pi^0\pi^0$, $\omega\pi^+\pi^-$, and $\omega\eta$ with two resonances. Black dots with error bars are from experimental data, and the error bars include both statistical and systematic uncertainties. The blue solid curve represents the total fit. The red dashed curve represents the contribution of $\omega(4S)$. The cyan dashed curve represents the contribution of $\omega(3D)$. The green dashed curve presents the contribution of non-resonant part. The pink curve represents the interference between the resonant and non-resonant parts.

Figure 5. Solution II of the simultaneous fit of $e^+e^-\to\omega\pi^0\pi^0$, $\omega\pi^+\pi^-$ and $\omega\eta$ with two resonances. The symbols’ descriptions are consistent with Fig. 4.

Figure 6. Solution I of the simultaneous fit of the intermediate modes in $e^+e^-\to\omega\pi^+\pi^-$ with one resonance. The symbol descriptions are consistent with Fig. 2.

Figure 7. Solution II of the simultaneous fit of the intermediate modes in $e^+e^-\to\omega\pi^+\pi^-$ with one resonance. The symbol description is consistent with Fig. 2.

Figure 8. Solution I of the simultaneous fit of the intermediate modes in $e^+e^-\to\omega\pi^+\pi^-$ with two resonances. The symbols’ descriptions are consistent with Fig. 4

Figure 9. Solution II of the simultaneous fit of the intermediate modes in $e^+e^-\to\omega\pi^+\pi^-$ with two resonances. The symbols’ descriptions are consistent with Fig. 4.

[1]	Wang J Z, Chen D Y, Liu X, et al. Costructing J/ψ family with updated data of charmoniumlike Y states. Phys. Rev. D, 2019, 99 (11): 114003. doi: 10.1103/PhysRevD.99.114003
[2]	Wang J Z, Qian R Q, Liu X, et al. Are the Y states around 4.6 GeV from e⁺e^– annihilation higher charmonia? Physical Review D, 2020, 101: 034001. doi: 10.1103/PhysRevD.101.034001
[3]	Wang J Z, Sun Z F, Liu X, et al. Higher bottomonium zoo. The European Physical Journal C, 2018, 78 (11): 915. doi: 10.1140/epjc/s10052-018-6372-1
[4]	Pang C Q, Wang J Z, Liu X, et al. A systematic study of mass spectra and strong decay of strange mesons. The European Physical Journal C, 2017, 77 (12): 861. doi: 10.1140/epjc/s10052-017-5434-0
[5]	Song Q T, Chen D Y, Liu X, et al. Charmed-strange mesons revisited: Mass spectra and strong decays. Physical Review D, 2015, 91: 054031. doi: 10.1103/PhysRevD.91.054031
[6]	Song Q T, Chen D Y, Liu X, et al. Higher radial and orbital excitations in the charmed meson family. Physical Review D, 2015, 92: 074011. doi: 10.1103/PhysRevD.92.074011
[7]	Wang J Z, Chen D Y, Song Q T, et al. Revealing the inner structure of the newly observed D₂(3000). Physical Review D,* 2016, 94: 094044. doi: 10.1103/PhysRevD.94.094044
[8]	Particle Data Group, R. L. Workman R L, Burkert V D, et al. Review of particle physics. Progress of Theoretical and Experimental Physics, 2022, 8: 083C01. doi: 10.1093/ptep/ptac097
[9]	Pang C Q, Wang Y R, Hu J F, et al. Study of the ω meson family and newly observed ω-like state X(2240). Physical Review D, 2020, 101: 074022. doi: 10.1103/PhysRevD.101.074022
[10]	Barnes T, Close F E, Page P R, et al. Higher quarkonia. Physical Review D, 1997, 55: 4157–4188. doi: 10.1103/PhysRevD.55.4157
[11]	Ebert D, Faustov R N, Galkin V O. Masses of light mesons in the relativistic quark model. Modern Physics Letters A, 2005, 20: 1887–1893. doi: 10.1142/S021773230501813X
[12]	Ebert D, Faustov R N, Galkin V O. Mass spectra and Regge trajectories of light mesons in the relativistic quark model. Physical Review D, 2009, 79: 114029. doi: 10.1103/PhysRevD.79.114029
[13]	Wang X, Sun Z F, Chen D Y, et al. Nonstrange partner of strangeonium-like state Y(2175). Physical Review D, 2012, 85: 074024. doi: 10.1103/PhysRevD.85.074024
[14]	Anisovich A V, Baker C A, Batty C J, et al. I=0, C=−1 mesons from 1940 to 2410 MeV. Physics Letters B, 2002, 542: 19–28. doi: 10.1016/S0370-2693(02)02303-1
[15]	Bugg D V. Partial wave analysis of p¯p→Λ¯Λ. The European Physical Journal C-Particles and Fields, 2004, 36: 161–168. doi: https://doi.org/10.1140/epjc/s2004-01955-5
[16]	Omega Photon Collaboration, Atkinson M, Axon T J, et al. Photon diffractive dissociation to ρρπ and ρπππ states. Zeitschrift für Physik C Particles and Fields, 1988, 38: 535–541. doi: https://doi.org/10.1007/BF01624357
[17]	Aubert B, Bona M, Boutigny D, et al. The e ⁺ e^- → 2(π ⁺ π^-) π⁰, 2(π⁺ π^-) eta, K⁺ K^- π⁺ π^- π⁰ and K ⁺ K ^- π ⁺ π ^- η cross sections measured with initial-state radiation. Physical Review D, 2007, 76: 092005. doi: 10.1103/PhysRevD.76.092005
[18]	Lees J P, Poireau V, Tisserand V, et al. Study of the reactions e ⁺ e⁻ → π ⁺ π ⁻ π⁰ π⁰ π⁰and π⁺ π⁻ π⁰ π⁰η at center-of-mass energies from threshold to 4.35 GeV using initial-state radiation. Physical Review D, 2018, 98: 112015. doi: 10.1103/PhysRevD.98.112015
[19]	Lees J P, Poireau V, Tisserand V, et al. Resonances in e⁺ e⁻ annihilation near 2.2 GeV. Physical Review D, 2020, 101: 012011. doi: 10.1103/PhysRevD.101.012011
[20]	The BESIII collaboration, Ablikim M, Achasov M N, et al. Measurement of e ⁺ e ⁻→ωπ ⁺ π ⁻ cross section at $ \sqrt{s}$ = 2.000 to 3.080 GeV. Journal of High Energy Physics, 2023, 1: 111. doi: https://doi.org/10.1007/JHEP01(2023)111
[21]	M. Ablikim, Achasov M N, Adlarson P, et al. Measurement of the e ⁺ e ⁻ → ωπ⁰ π⁰ cross section at center-of-mass energies from 2.0 to 3.08 GeV. Physical Review D, 2022, 105: 032005. doi: 10.1103/PhysRevD.105.032005
[22]	Ablikim M, Achasov M N, Adlarson P, et al. Observation of a resonant structure in e⁺e⁻→ωη and another in e⁺e⁻ → ωπ⁰ at center-of-mass energies between 2.00 GeV and 3.08 GeV. Physics Letters B, 2021, 813: 136059. doi: 10.1016/j.physletb.2020.136059
[23]	Zhou Q S, Wang J Z, Liu X. Role of the ω(4S) and ω(3D) states in mediating the e ⁺ e ⁻ →ωη and ωπ⁰ π⁰ processes. Physical Review D, 2022, 106: 034010. doi: 10.1103/PhysRevD.106.034010
[24]	Wang J Z, Wang L M, Liu X, et al. Deciphering the light vector meson contribution to the cross sections of e ⁺e^– annihilations into the open-strange channels through a combined analysis. Physical Review D, 2021, 104: 054045. doi: 10.1103/PhysRevD.104.054045

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A coherent study of e⁺e⁻→ωπ⁰, ωπ⁺π⁻, and ωη