Electro-weak production of pseudovector C-even heavy quarkonia in electron-positron collisions on Belle II and BES III

It is shown that the molecular model for the X{3872) state contradicts the new experimental data as well as the old ones. It is suggested to study the \chi_{c1} and \chi_{b1} states in the e+e-\to\chi_{c1}/\chi_{b1} reactions.


OUTLINE
The X(3872) = χ c1 (3872) meson [1], a patriarch of the XYZ spectroscopy, was appointed to be the D 0D * 0 + c.c. molecule with a radius greater than 3 fermi from the very beginning despite the fact that X(3872) = χ c1 (3872) is produced in hard processes with a radius less than one fermi as intensively as the compact charmonium ψ(2S ). Even the landmark result of the LHCb Collaboration [2] BR(X → γψ(2S )) BR(X → γJ/ψ) = 2.46 ± 0.7 , directly pointing to the charmonium nature of X(3872), did not stop the molecular lobby.
We reviewed the scenario in detail where X(3872) resonance is the cc = χ c1 (2P) charmonium which "sits on" the D 0D * 0 threshold. We explained all known data on X(3872) and suggested clear program of verification of our scenario [3][4][5].
We predicted the significant number of decay channels via two gluons: X(3872) → gluon gluon → light hadrons, the same as in the case χ c1 (1P) → gluon gluon → light hadrons. It means that two virtual gluons can produced the X(3872) resonance here ψ(m k ): . The BES III Collaboration found the X(3872) resonance in the reaction e + e − → γX(3872) at center-of-mass energies for 4.009 to 4.420 GeV [6] e + e − →  Recently the BES III Collaboration found the X(3872) resonance in the reaction e + e − → γX(3872) at center-of-mass energies for 4.15 to 4.3 GeV [7] e + e − → ψ(4160) see Fig. 1 and see Fig. 2.
The giant colourless molecule does not connected with gluons! Its colourless constituents D 0 ,D * 0 do not connected with gluons also! So The BES III Collaboration closes the molecular model of the X(3872) resonance.
As for the tetraquark model, the two-gluon production of the X(3872) resonance is possible e + e − → γ gluon gluon → γqqcc → γX(3872), q = u, d. But, such a process is described by nonplanar diagrams, which are depressed always. So the BES III collaboration puts in a difficult position the tetraquark model of the X(3872) resonance.
Thus the BES III collaboration confirms the cc charmonium model of the X(3872) resonance .
It is often thought that violations of isotopic invariance in the decays X(3872) → π + π − J/ψ and X(3872) → π 0 χ c1 (1P) are crucial for the X(3872) nature. However, this is a misunderstanding. These are the problems of the second row.
As for the isotopic symmetry violation via m d − m u , it can be considerable also, for example, the ρ 0 − ω and η − π 0 transitions are of the order (m d − m u ) × 1 GeV order [8].

OUTLOOK
In this energy region the weak interaction grows with energy increase ∝ G F E 2 , here G F = 10 −5 m −2 p is the Fermi constant. 1 It is interesting to note that else in Ref. [9] there was shown that the ω do not produced virtually in the X(3872) → ωJ/ψ decay. One can see only the left tail of ω far off the resonance. Let us add that a background can interfere with this tail constructively or destructively. But the molecular lobby hard discusses the strong isotopic breaking in the above decays.   . Diagram of the process e + e − → γ * γ * → χ c1 /χ b1 G F E 2 = 1.4 × 10 −4 for χ c1 (1P) and G F E 2 = 1.7 × 10 −4 for χ c1 (3872). That is, G F E 2 ∼ α 2 in the BES III energy region.
Note that the above estimations were became under the assumption that the resonance widths are not small compared to the energy resolution.