Exotics at Our Home

I. Light Scalars as Four-quark States II. Isotensor Tensor Tensor E(1500-1600) State III. X(3872) State as Charmonium \chi_{c1}(2P) IV. Two-gluon Annihilation of Charmonium \chi_{c2}(2P) There are considered problems of the exotic states, in which the author with his collaborators has made clear physical predictions, considerable part of wich is supported by experement already


I. INTRODUCTION
I would like to discuss the exotic phenomena that I know not by hearsay. That is, the exotic phenomena, which we analyzed, explained and made the new predictions, the considerable part of which is confirmed already by experiment, and other ones wait the experimental checking.

II. LIGHT SCALARS AS FOUR-QUARK STATES
The a 0 (980) and f 0 (980) mesons are well-established parts of the proposed light scalar meson nonet [1]. From the beginning, the a 0 (980) and f 0 (980) mesons became one of the central problems of nonperturbative QCD, as they are important for understanding the way chiral symmetry is realized in the low-energy region and, consequently, for understanding confinement. Many experimental and theoretical papers have been devoted to this subject.
There is much evidence that supports the four-quark model of light scalar mesons [2,3].
As a result the practically model-independent prediction of the qq model g 2 f 2 γγ : g 2 a 2 γγ = 25 : 9 agrees with experiment rather well. As to the ideal qq model prediction g 2 f 0 γγ : g 2 a 0 γγ = 25 : 9, it is excluded by experiment.
It was shown in Ref. [10] that the production of a 0 0 (980) and f 0 (980) in φ → a 0 0 γ → ηπ 0 γ and φ → f 0 γ → π 0 π 0 γ decays is caused by the four-quark transitions, resulting in strong restrictions on the large-N C expansion of the decay amplitudes. The analysis showed that these constraints give new evidence in favor of the four-quark nature of the a 0 (980) and f 0 (980) mesons.
In Refs. [17,18] it was shown that the description of the φ → K + K − → γa 0 0 (980)/f 0 (980) decays requires virtual momenta of K(K) greater than 2 GeV, while in the case of loose molecules with a binding energy about 20 MeV, they would have to be about 100 MeV.
Besides, it should be noted that the production of scalar mesons in the pion-nucleon collisions with large momentum transfers also points to their compactness [19].
It was also shown in Refs. [20,21] that the linear S L (2) × S R (2) σ model [22] reflects all of the main features of low-energy ππ → ππ and γγ → ππ reactions up to energy 0.8 GeV and agrees with the four-quark nature of the σ meson. This allowed for the development of a phenomenological model with the right analytical properties in the complex s plane that took into account the linear σ model, the σ(600) − f 0 (980) mixing and the background [23].
This background has a left cut inspired by crossing symmetry, and the resulting amplitude agrees with results obtained using the chiral expansion, dispersion relations, and the Roy equation [24], and with the four-quark nature of the σ(600) and f 0 (980) mesons as well.
This model well describes the experimental data on ππ → ππ scattering up to 1.2 GeV.
It is shown in Ref. [26] that the recent data on the K 0 S K + correlation in Pb-Pb interactions Ref. [27] agree with the data on the γγ → ηπ 0 and φ → ηπ 0 γ reactions and support the four-quark model of the a 0 (980) meson. It is shown that the data does not contradict the validity of the Gaussian assumption.
In Refs. [28,29] it was suggested the program of studying light scalars in semileptonic D and B decays, which are the unique probe of the qq constituent pair in the light scalars. We studied production of scalars σ(600) and f 0 (980) in the D + s → ss e + ν → π + π − e + ν decays, the conclusion was that the fraction of the ss constituent components in σ(600) and f 0 (980) is small. Unfortunately, at the moment the CLEO statistics [30] is rather poor, and thus new high-statistics data are highly desirable.
It was noted in Refs. [28,29] that no less interesting is the study of semileptonic decays of D 0 and D + mesons -D + → dd e + ν → [σ(600) + f 0 (980)]e + ν → π + π − e + ν, D 0 → dū e + ν → a − 0 e + ν → π − ηe + ν and D + → dd e + ν → a 0 0 e + ν → π 0 ηe + ν (or the charged-conjugated ones) which had not been investigated. It is very tempting to study light scalar mesons in semileptonic decays of B mesons [29]: Recently BESIII Collaboration measured the decays D 0 → dū e + ν → a − 0 e + ν → π − ηe + ν and D + → dd e + ν → a 0 0 e + ν → π 0 ηe + ν for the first time [31]. In Ref. [32] we discuss the Ref. [28] program in light of these measurements taking into account contribution of a ′ 0 meson with mass about 1400 MeV. A variant when a − 0 (980) has no qq constituent component at all is presented in Figure 1, that is, a − 0 (980) is produced as a result of mixing The first measurement of BESIII is the important step for the investigation of light scalar mesons nature, but for the present the statistics is not adequate for the conclusions.
We explained the strong boost near the threshold in the γγ → ρ 0 ρ 0 reaction by the production of the isotensor tensor and isoscalar tensor resonances, then the destructive interference of their contributions in the γγ → ρ + ρ − reaction follows from isotopic symmetry! Experiment backed up this prediction, JADE 1983, ARGUS 1991, see Figure 2 and Refs. [33,34].
We believe that the Belle data will support the above picture.
We [35] hope that JEFLAB will find the charged components of the isotensor tensor state E ± in the mass spectra of the ρ ± ρ 0 states in the reactions γN → ρ ± ρ 0 N(∆).
But, the bounding energy is small, ǫ B < ∼ 1 MeV. That is, the radius of the molecule is large, r X(3872) > ∼ 5 = 5 · 10 −13 cm. As for the charmonium, its radius is less one fermi, r χ c1 (2P ) < ∼ fermi = 10 −13 cm. That is, the molecule volume is 125 ÷ 1000 times as large as the charmonium volume, This means a probability of production of a giant molecule in hard processes, at small distances, is suppressed in comparison with a probability of production of heavy a charmonium by a factor ∼ V χ c1 (2P ) /V X(3872) .
In addition, [1,39,41,43] The extended molecule is produced in hard processes as intensively as the compact charmonium. It's miracle!
We explain the shift of the mass of the X(3872) resonance with respect to the prediction of a potential model for the mass of the χ c1 (2P ) charmonium by the contribution of the virtual D * D + c.c. intermediate states into the self energy of the X(3872) resonance [38,39].
This allows us to estimate the coupling constant of the X(7872) resonance with the D * 0D0 channel, the branching ratio of the X(3872) → D * 0D0 + c.c. decay, and the branching ratio of the X(3872) decay into all non-D * 0D0 + c.c. states [37][38][39].
We [38,39] predict that the hadron channels of the decays of χ c1 (2P ) via two gluon ( X(3872) → gluon gluon → hadrons) should be the same as in the χ c1 (1P ) case, that is, there should be a few tens of such channels. The discovery of these decays would be the strong (if not decisive) confirmation of our scenario.
As for BR(X → ωJ/ψ) ∼ BR(X → ρJ/ψ), this could be a result of dynamics. In our scenario the ωJ/ψ state is produced via the three gluons.
As for the ρJ/ψ state, it is produced both via the one photon, and via the three gluons (via the contribution ∼ m u − m d ).
It is well known that the physics of charmonium (cc) and bottomonium (bb) is similar.
Let us compare the already known features of X(3872) with the ones of Υ b1 (2P ).
If the three-gluon mechanism (its part ∼ m u − m d ) dominates in the X(3872) → ρJ/ψ decay then one should expect We believe that discovery of a significant number of unknown decays of X(3872) into non-D * 0D0 + c.c. states via two gluons and discovery of the χ b1 (2P ) → ρΥ(1S) decay could decide destiny of X(3872).
Once more, we discuss the scenario where the χ c1 (2P ) charmonium sits on the D * 0D0 threshold but not a mixing of the giant D * D molecule and the compact χ c1 (2P ) charmonium. Note that the mixing of such states requests the special justification. That is, it is necessary to show that the transition of the giant molecule into the compact charmonium is considerable at insignificant overlapping of their wave functions. Such a transition ∼ V χ c1 (2P ) /V X(3872) and a branching ratio of a decay via such a transition Note that now the X(3872) state is named in Ref. [1] as χ c1 (3872).
We [44] expect that BR(χ c2 (2P ) → gluon gluon) > ∼ 2% if the Particle Data Group as well as the BaBar and Belle collaborations have correctly identified the state.
In reality, this branching ratio corresponds to the one for χ c2 (2P ) decaying into light hadrons. The hadron channels of the two-gluon decays of χ c2 (2P ) should be the same as in the χ c2 (1P ) case, that is, there should be a few tens of such channels.
The ratio of the two-photon and two-gluon widths of the charmonium decays does not depend on the wave function in the nonrelativistic potential model of charmonium [45]. It allows to find the low limit of BR(χ c2 (2P ) → gluon gluon). The comparison with the wellknown data about χ c2 (1P ) allows us to conclude that BR(χ c2 (2P ) → 2g) ≈ (6.5 ± 2.0)% is very likely.
The confirmation of the χ c2 (2P ) state can be tested by BESIII, for example, through the process e + e − → ψ(4040) → γχ c2 (2P ). The search for two-gluon decays of the χ c2 (2P ) state is feasible for BESIII as well as other super factories such as BaBar and Belle.

VI. ACKNOWLEDGMENTS
I am grateful to Organizers of QUARKS-2018 for the kind Invitation.
The work was supported by the program of fundamental scientific researches of the SB