Hadro-quarkonia dynamics and Z b states

Dynamics of hadro-quarkonium system is formulated, based on the channel coupling of a light hadron (h) and heavy quarkonium $\left( {Q\bar Q} \right)$ to heavy-light mesons ( $Q_{\bar q}$ , $\bar Q_q$ ). Equations for hadro-quarkonium amplitudes and resonance positions are written explicitly, and numerically calculated for the special case of π?(nS) (n = 1, 2, 3). It is also shown that the recently observed by Belle two peaks Z _b (10610) and Z _b (10650) are in agreement with the proposed theory. It is demonstrated that theory predicts peaks at the BB*, B*B* thresholds in all available π?(nS) channels.     

Possible hadronic molecular states composed of S-wave heavy-light mesons

We perform a systematical study of possible molecular states composed of the S wave heavy light mesons,where the S–D mixing and η-η' mixing are explicitly included.Our calculation indicates that the observed X(3872) could be a loosely shallow molecular state composed of D*+ h.c,while neither Z_c(3900)/Z_c(4020) nor Z_b(10610)/Z_b(10650) is supported to be a molecule.Some observed possible molecular states are predicted,which could be searched for by further experimental measurements.     

Bound state nature of the exotic Z<Subscript>b</Subscript> states

The assumption that the newly observed charged bottomonia states Z _b(10610) and Z _b(10650) are of molecular nature is confronted with the measured invariant-mass distributions for the transitions of the ϒ(5S) to the final states h _b π ⁺ π ⁻ and h _b(2P)π ⁺ π ⁻. It is shown that the assumption that the Z _b(10610) and Z _b(10650) are B [`(B)]*\bar B* + c.c. and B <sup>*</sup> [`(B)]*\bar B* bound states, respectively, with very small binding energies is consistent with the data. The calculation is based on a power counting for bottom meson loops, which is explicitly given up to two-loop in the framework of a nonrelativistic effective-field theory. We also show that if the Z_b states are of molecular nature, then the data should not be analyzed by using a Breit-Wigner parametrization.     

Exotic Mesons with Hidden Bottom Near Thresholds

We discuss exotic meson spectroscopy near open bottom thresholds. Assuming the exotic mesons as ${B^{(\ast)}\bar{B}^{(\ast)}}$ molecular states, we study the interaction among two heavy mesons in terms of the one boson exchange potential model. It is shown that masses of Z _b (10610) and Z _b (10650) are reproduced as ${B^{(\ast)}\bar{B}^{(\ast)}}$ bound and resonance states. Besides, we also show that ${B^{(\ast)}\bar{B}^{(\ast)}}$ molecular states having various exotic quantum numbers can exist around the thresholds. By contrast, there are no ${D^{(\ast)}\bar{D}^{(\ast)}}$ molecular states having exotic quantum numbers.     

Energy scan of cross sections for <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>–</Superscript> annihilation into quarkonia and light hadrons in the Belle experiment

The cross sections of the reactions e⁺e^– → ?(nS)π⁺π^? (n = 1, 2,3) and e⁺e^– → h _b (nP)π⁺π^? (n = 1, 2) are measured as a function of the cms collision energy from their thresholds up to 11.02 GeV using the data of the Belle experiment operating at the KEKB e⁺e^– collider. The peaks of the ?(10 860) and ?(11020) resonances are observed in the cross sections with an insignificant contribution of the continuum. The decay ?(11020) → h _b (nP)π⁺π^? is found to fully proceed through intermediate isovector states Z _b (10610) and Z _b (10650).     

The quasimolecular 1sσ orbital in collision systemsα(Z 1+Z 2)≳1, its excitation and spectroscopy

An analytical formula for the excitation probability of the quasimolecular 1sσ orbital as a function of the impact parameterb is derived for collision systems withα(Z ₁+Z ₂)?1. This formula describes well all existing experimental data for those collision systems except for the heaviest system Pb+Cm (Z ₁+Z ₂=178) at impact parametersb?40 fm. It is discussed in which way energies of the quasimolecular 1sσ orbital can be extracted from experimental 1sσ vacancy production data.     

A tool for spectroscopy of super-heavy quasimolecules (Z 1+Z 2>137) the Bang-Hansteen scaling rule

From 90° line width analysis ofKα₁ lines excited in very heavy ion-atom collisions (Z ₁ +Z ₂>137) mean impact parameters for the ionization probability are derived. The experimental mean impact parameters are shown to obey the Bang-Hansteen scaling rule¯bE(R)=C · ?v correlating the minimum momentum transferE(R)/v and the mean impact parameterb. Theoretical values of the constantC are (0.8±0.1) for 2p _1/2 σ excitation and (1.0±0.1) for 1sσ excitation in the rangeZ ₁+Z ₂=140–160. It is proposed to apply the scaling rule as a spectroscopic tool to study the 1sσ and 2p _1/2 σ levels in superheavy quasimolecules. The need of a sound theoretical base justifying the application of the scaling rule is emphasized.     

Measurement of the semileptonic branching fraction of inclusive b baryon decays to Λ

We present the first measurement of the ratio R _Λl defined as R _Λl = BR(Λ _b → ΛlX)/BR(Λ _b → ΛX) where Λ _b denotes all weakly decaying b baryons and l represents the average of electrons and muons. Using all hadronic Z⁰ decay events collected with the OPAL detector near the Z⁰ resonance, we measure R _Λl = (7.0 ± 1.2 ± 0.7)%. We also measure f(b → Λ _b) · BR(Λ _b → Λ X) = (3.93 ± 0.46 ± 0.37)%, f(b → B) · BR(B → Λ X) = (1.94 ± 0.28 ± 0.24)%, and BR(b → ΛX) = (5.87 ± 0.46 ± 0.48)%. In all cases, the uncertainties shown are statistical and systematic, respectively.     

Comparison of lattice gauge theories with gauge groups Z2 and SU(2)

We study a model of a pure Yang Mills theory with gauge group SU(2) on a lattice in Euclidean space. We compare it with the model obtained by restricting variables to $\text{Z}$₂. An inequality relating expectation values of the Wilson loop integral in the two theories is established. It shows that confinement of static quarks is true in our SU(2) model whenever it holds for the corresponding $\text{Z}$₂-model. The SU(2) model is shown to have high and low temperature phases that are distinguished by a qualitatively different behavior of the 't Hooft disorder parameter.     

Z c (4025) as the hadronic molecule with hidden charm

We have studied the loosely bound $D^{*}\bar{D}^{*}$ system. Our results indicate that the recently observed charged charmonium-like structure Z _c (4025) can be an ideal $D^{*}\bar{D}^{*}$ molecular state. We have also investigated its pionic, dipionic, and radiative decays. We stress that both the scalar isovector molecular partner Z _c0 and three isoscalar partners ${\tilde{Z}}_{c0,c1,c2}$ should also exist if Z _c (4025) is a $D^{*}\bar{D}^{*}$ molecular state in the framework of the one-pion-exchange model. Z _c0 can be searched for in the channel e ⁺ e ^?→Y→Z _c0(4025)(ππ)_P-wave where Y can be Y(4260) or any other excited 1^?? charmonium or charmonium-like states such as Y(4360), Y(4660), etc. The isoscalar $D^{*}\bar{D}^{*}$ molecular states ${\tilde{Z}}_{c0,c2}$ with 0⁺(0⁺⁺) and 0⁺(2⁺⁺) can be searched for in the three pion decay channel $e^{+}e^{-}\to Y \to {\tilde{Z}}_{c0,c2} (3\pi)^{I=0}_{\text{P-wave}}$ . The isoscalar molecular state ${\tilde{Z}}_{c1}$ with 0^?(1^+?) can be searched for in the channel ${\tilde{Z}}_{c1}\eta$ . Experimental discovery of these partner states will firmly establish the molecular picture.     

Z 2 monopoles in the standardSU (2) lattice gauge theory model

The standardSU(2) lattice gauge theory model without fermions may be considered as aZ ₂ model with monopoles and fluctuating coupling constants. At low temperatures β^?1 (=small bare coupling constant) the monopoles are confined.     

N=2 (Z3-graded) paragrassmann supersymmetry with slq(2) symmetry

N=2 Z₃-graded SUSY is discussed by introducing two Z₃-graded variables which are q-commutative. The action for an N=2 Z₃-graded superfield is obtained so that it has Z₃-SUSY and sl_q(2) symmetry.     

A string calculation of the Kähler potentials for moduli of ZN orbifolds

We present a method for calculating the Kähler potentials of the moduli of Z_N orbifolds directly from string theory. The explicit Kähler potentials associated with b_(1,1) and b_(1,2) moduli are given for any (2,0) symmetric Z_N orbifold. These results are exact at the string tree level.     

Confining string formed by P vortices in the indirect Z(2) projection of SU(2) lattice gauge theory

We study the distribution of P vortices near the confining string in the indirect _Z(2) projection of SU(2) lattice gauge theory. We find that the density of vortices approaches the vacuum value at large distances and is strongly suppressed near the line connecting the test quark-antiquark pair. This implies that the condensate of P vortices is broken inside the confining string. The width of the _P-vortex density distribution increases with increasing distance between the quark and antiquark. Our best fit indicates the logarithmic dependence of this width on q q? separation.     

Statistical mechanics of Z(M) models on Cayley trees

The problem of “small-field” phase transitions for Z(M) models on Cayley trees is solved in detail. Phase diagrams for zero field are obtained for M = 2, 3, 4, 5 and 6. As special cases, Potts models are also considered and all phases (not only those in zero field) are identified. The M → ∈ limit, the planar rotator model, is also solved completely for the zero-field case. The relevance of the results (especially of the phase diagrams) for the problems associated with Z(M) models on real lattices is discussed.     

Limits on anomalous top couplings from Z pole physics

We obtain constraints on possible anomalous interactions of the top quark with the electroweak vector bosons arising from the precision measurements at the Z pole. In the framework of SU(2)_L ⊗ U(1)_Y chiral Lagrangians, we examine all effective CP-conserving operators of dimension five which induce fermionic currents involving the top quark. We constrain the magnitudes of these anomalous interactions by evaluating their one-loop contributions to the Z pole physics. Our analysis shows that the operators that contribute to the LEP observables get bounds close to the theoretical expectation for their anomalous couplings. We also show that those which break the SU(2)_C custodial symmetry are more strongly bounded.     

Projectile Z dependence of double K-shell ionization in light elements by hydrogen- and helium-ion bombardment

The K² X-rays from Be, B and O atoms by H- and He-ion bombardment were measured. The ratio of σ_2K(He) to σ_2K(H) exhibits the projectile Z⁴₁ dependence. This is the first observation of the Z₁-dependence of σ_2K predicted by the Coulomb excitation.     

A Mössbauer study of the bipyramidal lattice site (2b) in BaFe12O19

The hyperfine fieldsH _f(T), center shifts δ(T) and relative recoilless fractionsf _a(T) at different lattice sites of barium ferrite were determined by Mössbauer spectroscopy of⁵⁷Fe over a temperature range from 12 to 723 K. For ferric iron in the crystalline site (2b), the recoilless fractionf _a(T) decreases most with increasing temperature in comparison with that of other sites, corresponding to a characteristic temperature {ie219-1}. These results indicate that the ferric iron in the site (2b) oscillates between two equivalent positions (4e) on either side of the symmetry plane normal to thec-axis.     

Analysis of t-b-W and t-t-Z couplings from CLEO and LEP/SLC data

We update the constraints on anomalous dimension four t-b-W and t-t-Z couplings by using CLEO b→sγ and LEP/SLC precision Z-pole data. It is found that the data imposes very stringent bounds on them. Moreover, the 2σ pull from SM predictions of A_LR(hadrons), A_b and A_FB(b) have little chance of being explained by the strongly constrained anomalous couplings.     

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.