How learn the branching ratio X(3872) \to D*^0 \bar D^0 + c.c.

Enfant terrible of charmonium spectroscopy, the resonance X(3872), generated a stream of interpretations and ushered in a new exotic XYZ spectroscopy. In the meantime, many (if not all) characteristics of X(3872) are rather ambiguous. We construct spectra of decays of the resonance X(3872) with good analytical and unitary properties which allows to define the branching ratio of the \(X(3872) \to D*^0 \bar D^0 + c.c.\) decay studying only one more decay, for example, the X(3872) → π⁺π^? J/ψ(1S) decay. We next define the range of values of the coupling constant of the X(3872) resonance with the \(X(3872) \to D*^0 \bar D^0 + c.c.\) system. Finally, we show that our spectra are effective means of selection of models for the resonance X(3872).     

Why <Emphasis Type="Italic">X</Emphasis>(3872) is not a molecule

We discuss the scenario where the X(3872) resonance is the \(c\bar c\) = χ_c1(2P) charmonium which “sits on” the D*⁰\({\bar D^0}\) threshold. 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*\(\bar D\) + c.c. intermediate states into the self energy of the X(3872) resonance. This allows us to estimate the coupling constant of the X(3872) resonance with the D*⁰\({\bar D^0}\) channel, the branching ratio of the X(3872) → D*⁰\({\bar D^0}\) + c.c. decay, and the branching ratio of the X(3872) decay into all non-D*⁰\({\bar D^0}\) + c.c. states. We predict a significant number of unknown decays of X(3872) via two gluon: X(3872) → gluongluon → hadrons. We suggest a physically clear program of experimental researches for verification of our assumption.     

Recent Results on Hadron Spectroscopy at Belle

Recent activities of the Belle experiment in Hadron spectroscopy are presented. The discovery of two charged bottomonium-like particles, ${Z_b^{\pm}(10610)}$ and ${Z_b^{\pm}(10650)}$ in the ${\Upsilon (nS)\pi^{\pm}}$ (n = 1, 2, 3) and h _b (m P)π ^± (m = 1, 2) final states is followed by the observation of the corresponding peaks in the ${B^*\bar{B}^{(*)}}$ final states that favors the molecular interpretation of Z _b . In addition, a neutral partner candidate is explored at 10,610 MeV in the ${\Upsilon (2S)\pi^0}$ mass spectrum projection. We have got no evidence of an X(3872) partner in J/ψ π ^± π ⁰, J/ψ η and ${\chi_{c1,2}\gamma}$ final states while an evidence of the narrow peak at 3,823 MeV/c ² in ${\chi_{c1}\gamma}$ is thought to be ³ D ₂ charmonium (ψ ₂) candidate. The feasibilities of the search for X(3872) partner in the B → J/ψ π ⁰ π ⁰ K decays, the measurement of light flavored baryons production cross section, and the study of K–p interaction in ${\phi p}$ final state are also discussed.     

Effects of final state interactions in B^ + \to D_S^ + \bar K^0 decay

We investigate the effects of final state interactions (FSI) contributions in the nonleptonic two body $B^ + \to D_S^ + \bar K^0$ decay, however the hadronic decay of $B^ + \to D_S^ + \bar K^0$ is analyzed by using “QCD factorization” (QCDF) method and final state interaction (FSI). First, the $B^ + \to D_S^ + \bar K^0$ decay is calculated via QCDF method and only the annihilation graphs exist in that method. Hence, the FSI must be seriously considered to solve the $B^ + \to D_S^ + \bar K^0$ decay and the D ⁰π⁺(D ⁰*ρ⁺), D ⁺π⁰(D ⁺*ρ⁰) and D ⁺η _c (D ⁺*J/ψ) via the exchange of K ^+(*), K ^0(*) and D _s ^+(*) mesones are chosen for the intermediate states. To estimate the intermediate states amplitudes, the QCDF method is again used. These amplitudes are used in the absorptive part of the diagrams. The experimental branching ratio of $B^ + \to D_S^ + \bar K^0$ decay is less than 8 × 10^?4 and the predicted branching ratio is 0.23 × 10^?9 in the absence of FSI effects and it becomes 6.74 × 10^?4 when FSI contributions are taken into account.     

The Λ c (2940)+ as a D*N Molecule in a Constituent Quark Model and a Possible Λ b (6248)

The Λ _c (2940)⁺ is studied in a constituent quark model. The model describes the deuteron as an NN bound state and the X(3872) as a DD* molecule. We studied the meson baryon sector and found a D*N bound state consistent with the data available for the Λ _c (2940)⁺. The existence of this bound state in this picture implies the existence of a ${\bar B^* N}$ partner that we predict as a Λ _b (6248). Different decay channels for this state are also studied.     

Strong decays of χcJ(2P) and χcJ(3P)

In the framework of the chiral quark model, the mass spectrum of χ _cJ (J = 0, 1, 2, n = 1, 2, 3) is studied with the Gaussian expansion method. Using the wave functions obtained in the study of mass spectrum, the open charm two-body strong decay widths of these states are calculated by using the ³ P ₀ model. The results show that the masses of χ _cJ (1P) and χ _c2(2P) are consistent with the experimental data. But the strong decay width of χ _c2(2P) is three times that of the experimental value. The decay width of χ _c1(2P) is sensitive to its mass. In the quark-antiquark picture, the width is about 385 MeV. However, if the channel coupling effects shift its mass to 3872 MeV, its decay width will be around 1 MeV. The possibility of assigning the state X(3872) as χ _c1(2P) cannot be excluded. To assign X(3915) as χ _c0(2P) is disfavored, due to the unmatching of decay channel. For the χ _cJ (3P) states, no states have been assigned. The possible candidates of χ _c0(3P) are X(4160) and X(4140). Their masses are close to the theoretical ones. The experimental branching ratio of X(4160), $\Gamma (X(4160) \to D\bar D)/\Gamma (X(4160) \to D*\bar D*) < 0.09$ is compatible with that of χ _c0(3P), 0.07. However the broad decay width of X(4160) cannot be explained by the open charm two-body decay. To assign X(4140) as χ _c0(3P) is also possible, due to the compatibility of the total decay width, the further measurement of decay modes of X(4140) are expected to justify the assignment.     

Investigation of N 2 + (C 2Σ u + → X 2Σ g + fluorescence excited through auger decay of the 1s −1π* resonance

A theoretical investigation of N ₂ ⁺ (C ²Σ _u ⁺ → X ²Σ _g ⁺ molecular fluorescence excited through the Auger decay of the 1s ^?1π* resonance is carried out. The fluorescence cross sections are calculated with due regard for the dependence of the matrix element of the C → X dipole transition on the internuclear distance, the interference between channels of excitation via different vibrational levels v _r of the 1s ^?1π* resonance, the rotational structure of the fluorescence band, and the predissociation of the N ₂ ⁺ C ²Σ _u ⁺ v′ ≥3) states. The calculated cross sections are in good agreement with the experimental results of recent measurements. The results of the calculations have demonstrated that the observed dependence of the cross section of the (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″) fluorescence on the excitation energy and the fluorescence wavelength for a group of bands with equal values of the difference Δv = v′ ? v″ is associated with transitions between the vibrational levels of the electronic states involved in the excitation and subsequent cascade decay of the 1s ^?1π* resonance: N₂ (v ₀ = 0) → N*₂(1s ^?1π*(v _r)) ? N ₂ ⁺ : (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″).     

Charmonium 2007: New experimental results

The most important experimental results in charmonium physics in the energy region above the threshold for open-charm production that were obtained in recent years are surveyed. The first measurements of the exclusive cross sections for e ⁺ e ^? → D \(\bar D\), D \(\bar D\)*, and D* \(\bar D\)* processes are discussed along with the discovered decay ψ(4415) → \(\bar D_2^* \)(2460). The properties of charmonium-like states, including the group of states Y (4260), Y (4325), and Y (4660) with quantum numbers of J ^PC = 1^??; the X(3940) and X(4160) states discovered in the process of double charmonium production in e ⁺ e ^? annihilation; and the X(3872), Y(3940), and Z ^±(4430) states found in B-meson decays, are presented.     

Pionic deuterium

The strong-interaction shift ε _1s ^πD and broadening Γ _1s ^πD in pionic deuterium have been determined in a high statistics study of the πD(3p-1s) X-ray transition using a high-resolution crystal spectrometer. The pionic deuterium shift will provide constraints for the pion-nucleon isospin scattering lengths extracted from measurements of shift and broadening in pionic hydrogen. The hadronic broadening is related to pion absorption and production at threshold. The results are ε _1s ^πD = (?2356 ± 31) meV (repulsive) and Γ _1s ^πD meV yielding for the complex πD scattering length a _πD = [?(24.99±0.33)+i(6.22 _?0.26 ^+0.12 )] × 10^?3 m _π ^?1 . From the imaginary part, the threshold parameter for pion production is obtained to be α = (251 _?11 ⁺⁵ ) μb. This allows, in addition, and by using results from pion absorption in ³He at threshold, the determination of the effective couplings g ₀ and g ₁ for s-wave pion absorption on isoscalar and isovector NN pairs.     

The Charmonium-Molecule Hybrid Structure of the X(3872)

In order to understand the structure of the X(3872) the effects of the ${{\rm c\overline{c}}}$ charmonium core state coupling to the ${D^0\overline{D}^{*0}}$ and D ⁺ D ^*? molecule states are studied. The obtained structure of the X(3872) is about 9 % of ${{\rm c}\overline{{\rm c}}}$ charmonium, 75 % of the isoscalar ${D\overline{D}}$ molecule and 16 % of the isovector ${D\overline{D}}$ molecule which explains observed properties of the X(3872) well.     

Measurement of the masses and lifetimes of the charmed mesonsD 0,D + andD s +

We present the final results on the measurement of the masses and lifetimes of the mesonsD ⁰,D ⁺ andD _s ⁺ in the NA32 experiment at the CERN SPS, using silicon microstrip detectors and charge-coupled devices for vertex reconstruction. We measure the following lifetimes: \(\tau _{D^0 } = 3.88 \pm _{0.21}^{0.23} \cdot 10^{ - 13} s\) using a sample of 479D°→K ^?π⁺π^?π⁺ and 162D°→K ^?π⁺ decays; \(\tau _{D^ + } = 10.5 \pm _{0.72}^{0.77} \cdot 10^{ - 13} s\) with a sample of 317D ⁺→K ^?π⁺π⁺ decays; \(\tau _{D_s^ + } = 4.69 \pm _{0.86}^{1.02} \cdot 10^{ - 13} s\) with a sample of 54D _s ⁺ →K ⁺ K ^?π⁺ decays. We measure the following masses:m _D ⁰=1864.6±0.3±1.0 MeV,m _D ⁺=1870.0±0.5±1.0 MeV and \(m_{D_s^ + } \) =1967.0±1.0±1.0 MeV.     

A string-breaking model of heavy meson decays

Within QCD, heavy quarkonia are viewed as a quark antiquark pair bound by a narrow chromoelectric flux tube. This flux can create light quark antiquark pairs accounting for the decay into mesons with heavy quantum numbers. This model is shown to be as consistent with current data on charmonium decays intoD-meson pairs and upsilon decay to \(B\bar B\) , as is the physically less appealing³ P ₀ model.     

Final state interaction effects in the B + → D + K 0 decay

The exclusive decay of B ⁺ → D ⁺ K ⁰ is calculated by the QCD factorization method (QCDF) and final state interaction (FSI). First, the B ⁺ → D ⁺ K ⁰ decay is calculated via QCDF method. The result that is found by using the QCDF method is less than the experimental result. So FSI is considered to solve the B ⁺ → D ⁺ K ⁰ decay. For this decay, the D _s ⁺ π⁰, D _s ⁺ *ρ⁰, D _s ⁺ *? via the exchange of \(\bar K^0\) , \(\bar K^{0*} \) , D ^?, and D ^?* mesons are chosen for the intermediate states. The above intermediate states are calculated by using the QCDF method. In the FSI effects, the results of our calculations depend on η as the phenomenological parameter. The range of this parameter is selected from 2 to 2.4. It is found that if η = 2.4 is selected, the numbers of the branching ratio are placed in the experimental range. The experimental branching ratio of this decay is less than 2.9 × 10^?6 and our results calculated by QCDF and FSI are (0.16 ± 0.04) × 10^?6 and (2.8 ± 0.09) × 10^?6, respectively.     

Evidence for a newK * \bar K state at a mass of 1,530 MeV withIJ PC=01++ observed inK − p interactions at 4.2 GeV/c

Evidence is presented for a newK ^* \(\bar K\) +c.c. resonance with a mass of (1,526±6) MeV, a width of (107±15) MeV and quantum numbersIJ ^PC=01⁺⁺. We call itD′ meson. Initially it is observed as aK ^* \(\bar K\) +c.c. enhancement in the reactionsK ^? p→(K _s ⁰ K ^±π^?)Λ at 4.2 GeV/c. The isospin assignmentI=0 comes from its further observation in the reactionsK ^? p→(K _s ⁰ K ^±π^?)Σ ⁰ andK ^? p→(K _s ⁰ K ^±π^?)Σ(1,385)⁰ but not inK ^? p→(K ⁺ K ^?π^?)Σ⁺ orK ^? p→(K _s ⁰ K ^±π^?)Σ(1,385)⁺. A maximum likelihood analysis of the (K \(\bar K\) π) decay Dalitz plots in the reactionsK ^? p→(K _s ⁰ K ^±π^?) determines theJ ^PC of theD′ meson to be 1⁺⁺. A satisfactorySU(3) fit is obtained to a 1⁺⁺ nonet composed of theI-1A ₁, theI=1/2Q _A with theD(1,285) and theD′(1,526) as theI=0 members having a mixing angle close to the magic one.     

Measurement ofD meson production in 200 GeV π−-Be interactions

We have measured the differential and total cross sections ofD meson production in 200 GeV π^?-beryllium interactions, using a sample of 48 fully reconstructed and nearly background-freeD mesons in the decay channelsK ^?π^±,K ^?π^±π^± andK ^?π^?π^±π^±. A single electron trigger has been used to select events containing a pair of charmed particles. A vertex telescope of 6 silison microstrip detectors allowed the reconstruction of tracks of charged secondaries and the reconstruction of primary and decay vertices with high precision. The ratio of branching fractions for \(\mathop {D^0 }\limits^{( - )} \to K^ \mp \pi ^ \pm \) to \(\mathop {D^0 }\limits^{( - )} \to K^ \mp \pi ^ \mp \pi ^ \pm \pi ^ \pm \) , and an upper limit for \(D^0 - \bar D^0 \) mixing are presented.     

Radiative open charm decay of the Y(3940) , Z(3930) , X(4160) resonances

We determine the radiative decay amplitudes for the decay into D^* and $ \bar{{D}}$ $ \gamma$ , or D ^* _s and $ \bar{{D}}_{s}^{}$ $ \gamma$ of some of the charmonium-like states classified as X , Y , Z resonances, plus some other hidden charm states which are dynamically generated from the interaction of vector mesons with charm. The mass distributions as a function of the $ \bar{{D}}$ $ \gamma$ or $ \bar{{D}}_{s}^{}$ $ \gamma$ invariant mass show a peculiar behavior as a consequence of the D ^* $ \bar{{D}}^{*}_{}$ nature of these states. The experimental search of these magnitudes can shed light on the nature of these states.     

Inclusive single and double diffractive dissociations inK + p interactions at 32 GeV/c

We study single and double inclusive diffractive production in a 32 GeV/c K ⁺ p experiment in MIRABELLE at the Serpukhov accelerator. From reactionsK ⁺ p→K ⁺+X ⁺ andK ⁺ p→X ⁺+p we determine the total proton and kaon single diffractive dissociation cross sections \(\sigma (p\xrightarrow{{K^ + }}p_D ) = 0.90 \pm 0.12 mb\) and \(\sigma (K^ + \xrightarrow{p}K_D^ + ) = 0\) . 90±0.17 mb, respectively. In either case the only notable contributions come from dissociations into 1 and 3 charged particles. Kaon dissociation exhibits a pronounced slope-mass correlation. The search for double diffractive production in reactionsK ⁺ p→(K ⁺π^?π⁺)+X ⁺ andK ⁺ p→(pπ ⁺ π ^?)+X ⁺ leads in either case to an estimated total double diffractive cross section σ(K ⁺p→K _D ⁺ p_D) of ?220 μb. The double dissociation differential cross section exhibits a large slope of ?10GeV^?2 in the nearthreshold mass region, rapidly decreasing to ?4 GeV^?2 with increasing excitation mass. At our c.m. energy \((\sqrt s \simeq 8 GeV)\) the ratio σ_{inel dif}/σ_el is 0.85±0.10, the total diffractive cross section σ_dif≡σ_el+σ_{inel dif}=4.41±0.24 mb and the fraction σ_dif(K ⁺ p)/σ_tot(K ⁺ p) is 25±2%. TheK ⁺ andK ^? diffractive excitation mass spectra, differential cross sections and total diffractive cross sections are very similar for both single and double dissociations.     

Study of the decayf 1(1285)→ρ0(770)γ

The decayf ₁(1285)→ρ⁰(770)γ was studied at VES spectrometer of IHEP. Clear signal off ₁(1285) is seen in the effective mass spectrum of the π⁺π^?γ system in the reaction π^?γN→π⁺π^?π^?γN at the momentum $P_{\pi ^ - } = 37 GeV/c$ . The branching fraction of decayf ₁(1285)→ρ⁰(770)γ has been found to be $$BR(f_1 (1285) \to \rho ^0 (770)\gamma ) = (2.8 \pm 0.7(stat) \pm 0.6(syst)) \cdot 10^{ - 2} .$$ The ratio of the helicity amplitudes for ρ⁰ meson in its rest frame was determined by the analysis of angular distributions: $$\rho _{00} /\rho _{11} = 3.9 \pm 0.9(stat) \pm 1.0(syst).$$