Abstract:Motivated by the large cross section of e + e − → ηJ/ψ process measured by the BESIII and Belle Collaborations recently, we evaluate this process at O(α 4 s ) accuracy in the framework of nonrelativistic QCD. We find that the cross section at the center-of-mass energy √ s = 4.009 GeV is 34.6pb, which is consistent with the BESIII data. The comparison with the Belle data in the region from 4.0 GeV to 5.3 GeV is also presented. Concerning the η and η ′ mixing and the potential gluonium component of η ′ , we also… Show more
“…The Gegenbauer momenta are adopted as a q,s 2 (1GeV ) = 0.44 ± 0.22 [26]. For η , we have a g 2 (1GeV ) = 0.1 and sin 2 φ G = 0.26 [21]. The decay constant of η c is about 498 MeV [23].…”
Section: Phenomenological Discussionmentioning
confidence: 99%
“…This kind of production mechanism is blind to quark charges, so the amplitude is identical to the production of |qq and |ss . Two gluons transitions to η and η are also investigated in electroproduction e + e − → J/ψ + η(η ) [21].…”
Section: Factorization Formulae a Nrqcd Ldmes And Covariant Projmentioning
Motivated by recent measurements of the radiative decay rates of the P -wave spin singlet charmonium hc to the light meson η or η by the BESIII Collaboration, we investigate the decay rates of these channels at order αα 4 s . The photon is radiated mainly from charm quark pairs in the lowest order Feynman diagrams, since the diagrams where a photon radiated from light quarks are suppressed by αs or the relative charm quark velocity v, due to Charge parity conservation. The form factors of two gluons to η or η are employed, which are the major mechanism for η and η productions. η(η ) is treated as a light cone object when we consider that the parent charmonium mass is much heavier than that of the final light meson. We obtain the branching ratio B(hc → γη ) = (1.94in the nonrelativistic QCD approach, which is in agreement with the BESIII measurement. The prediction of the branching ratio of hc → γη is also within the range of experimental error after including the larger uncertainty of the total decay width Γ hc . The applications of these formulae to the radiative decays to η(η ) of the P -wave spin singlet bottomonium h b (nP ) are presented. These studies will shed some light on the η − η mixing effects, the flavor SU(3) symmetry breaking, as well as the nonperturbative dynamics of charmonium and bottomonium.
“…The Gegenbauer momenta are adopted as a q,s 2 (1GeV ) = 0.44 ± 0.22 [26]. For η , we have a g 2 (1GeV ) = 0.1 and sin 2 φ G = 0.26 [21]. The decay constant of η c is about 498 MeV [23].…”
Section: Phenomenological Discussionmentioning
confidence: 99%
“…This kind of production mechanism is blind to quark charges, so the amplitude is identical to the production of |qq and |ss . Two gluons transitions to η and η are also investigated in electroproduction e + e − → J/ψ + η(η ) [21].…”
Section: Factorization Formulae a Nrqcd Ldmes And Covariant Projmentioning
Motivated by recent measurements of the radiative decay rates of the P -wave spin singlet charmonium hc to the light meson η or η by the BESIII Collaboration, we investigate the decay rates of these channels at order αα 4 s . The photon is radiated mainly from charm quark pairs in the lowest order Feynman diagrams, since the diagrams where a photon radiated from light quarks are suppressed by αs or the relative charm quark velocity v, due to Charge parity conservation. The form factors of two gluons to η or η are employed, which are the major mechanism for η and η productions. η(η ) is treated as a light cone object when we consider that the parent charmonium mass is much heavier than that of the final light meson. We obtain the branching ratio B(hc → γη ) = (1.94in the nonrelativistic QCD approach, which is in agreement with the BESIII measurement. The prediction of the branching ratio of hc → γη is also within the range of experimental error after including the larger uncertainty of the total decay width Γ hc . The applications of these formulae to the radiative decays to η(η ) of the P -wave spin singlet bottomonium h b (nP ) are presented. These studies will shed some light on the η − η mixing effects, the flavor SU(3) symmetry breaking, as well as the nonperturbative dynamics of charmonium and bottomonium.
“…Treating η and η ′ with the Light-Cone approach and J/ψ with non-relativistic QCD, and together with the contribution of the resonance decays, the authors of Ref. [13] can reproduce the measured e + e − → ηJ/ψ line shape and predict the production cross section of the analogous process e + e − → η ′ J/ψ at c.m. energies √ s from 4.3 to 5.3 GeV.…”
mentioning
confidence: 99%
“…To check the theoretical predictions [13] and to search for potential η ′ J/ψ transitions from charmonium and charmonium-like states, we measure the process e + e − → η ′ J/ψ with the data taken at BESIII. The CLEO-c experiment searched for this process with data at c.m.…”
The process e + e − → η ′ J/ψ is observed for the first time with a statistical significance of 8.6σ at center-of-mass energy √ s = 4.226 GeV and 7.3σ at √ s = 4.258 GeV using data samples collected with the BESIII detector. The Born cross sections are measured to be (3.7 ± 0.7 ± 0.3) and (3.9 ± 0.8 ± 0.3) pb at √ s = 4.226 and 4.258 GeV, respectively, where the first errors are statistical and the second systematic. Upper limits at the 90% confidence level of the Born cross sections are also reported at other 12 energy points.
“…So the LDMEs for the X(3940) and X(4160) can be obtained correspondingly. For the LDMEs of ψ(nS), we can obtain the value from the measured electric widths [4,40,41], i.e.…”
In this paper, we study double charmonia production in Upsilon peaks, especially, a S-wave charmonium ηc and a P-wave charmonium hc( 1 P1), or a S-wave charmonium J/ψ and the X(3940) and X(4160) within the nonrelativistic QCD (NRQCD) approach which is a powerful tool to realize the factorization of double charmonia production in electron-positron annihilation. The J P C = 1 −− state Υ(nS) can provide an ideal laboratory for studying the properties of double-heavy quarkonium and also can separate the perturbative and nonperturbative parts due to the large heavy quark mass compared with the typical hadron scale ΛQCD. Explanation of the X(3940) and X(4160) as the 3 1 S0 and 4 1 S0 states, respectively, are compatible with the observed upper limits for the branching fractions of Υ(1S, 2S) → J/ψ + X, where X = X(3940), X(4160) by the Belle Collaboration. The branching fractions of Υ(1S, 2S, 3S) → ηc + hc( 1 P1) are predicted to be around 10 −6 , which shall be tested in Belle-II experiments.
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