Quark Confinement and the Hadron Spectrum V

Preface.

CONTENTS.

We review lattice evidence for the vortex mechanism of quark confinement and study the influence of charged matter fields on the vortex distribution.

Quantum Yang–Mills theory and the Wilson loop can be rewritten identically in terms of local gauge-invariant variables being directly related to the metric of the dual space. In this formulation, one reveals a hidden high local symmetry of the Yang–Mills theory, which mixes up fields with spins up to J = N for the SU(N) gauge group. In the simplest case of the SU(2) group the dual space seems to tend to the de Sitter space in the infrared region. This observation suggests a new mechanism of gauge-invariant mass generation in the Yang–Mills theory.

QCD predicts that at a certain critical temperature of the order of Λ_QCD, strongly interacting matter undergoes a phase transition from the colour singlet hadronic state to a deconfined plasma of quarks and gluons. This review summarizes experimental observables that support the evidence that a new state of matter with properties as predicted for the QGP was observed at the CERN SPS as well as novel experimental probes accessible at the RHIC heavy-ion collider at BNL.

We discuss how hadronic particle production can help to identify the new form of matter created at RHIC and SPS. We use statistical hadronization approach and allow for chemical non-equilibrium. Strangeness production is shown to lead to near full saturation of the deconfined quark–gluon phase space as is seen in terms of highly over saturated final state hadron phase space.

I discuss my friendship with Nathan Isgur (25 May 1947 - 24 July 2001) and the work we did together in the mid-eighties.

I summarize the current status of the comparison between experiment and the predictions of the NRQCD factorization approach to quarkonium decay and production. I also present the results of some recent calculations and theoretical developments in the NRQCD factorization approach.

I review some recent progress and open problems in the calculation of heavy-quarkonium inclusive decay widths into light particles in the framework of QCD non-relativistic effective field theories.

I discuss the physics of confinement and deconfinement in 2+1 dimensional non-abelian gauge theories at weak coupling. I show that the low-energy dynamics is determined universally by the spontaneous breaking of the magnetic symmetry introduced by 't Hooft more than 20 years ago. The degrees of freedom in the effective theory are magnetic vortices. I give an explicit derivation of the effective low energy theory for the vortex field. Confinement in this effective theory is a very simple classical statement about the long range interaction between topological solitons, which follows (by virtue of a simple direct classical calculation) from the structure of the effective Lagrangian. I demonstrate that above the critical temperature the magnetic symmetry is restored and that this transition is identical with the deconfining phase transition.

Over the last decade charm Dalitz-plot analysis has emerged as an excellent tool for studying the dynamics of three-body decays. In more recent years it has also proved to be a source of novel information in the quest to decipher the light-meson spectrum. A review of the most interesting results will be presented together with a discussion of possible improvements in the formalism that could enhance our comprehension of charm decays.

A brief phenomenological review on the status of glueballs and hybrids is presented. Recent results for scalar mesons in hadronic reactions and in γγ-collisions suggest that f₀(1500) has a large glue content and forms the dominant component of the ground state scalar glueball, while f₀(1710) is mainly . The first excited glueball state, a tensor, has not been identified yet, although more tensor states have been reported than can be accommodated in the nonets. We have now evidence for two isovector mesons, π₁(1400) and π₁(1600), with quantum numbers incompatible with states, which could be hybrid mesons or four-quark states.

We discuss how one can extract information about the size of the condensate from data on ππ scattering close to threshold. These data come from K_e4 decays which have been recently remeasured by the E865 experiment at Brookhaven. The translation of the data on ππ scattering on information about the condensate requires the combined use of chiral perturbation theory and dispersion relations. The principles and some details of the combined use of these two theoretical methods are illustrated.

The goal of the DIRAC experiment is to measure the π⁺π⁻ atom lifetime of order 3 · 10⁻¹⁵ s with 10% precision. This measurement will provide in a model independent way the difference between the S-wave ππ scattering lengths for isospin 0 and 2, |a₀ – a₂|, with 5% accuracy. Low energy QCD — chiral perturbation theory — predicts nowadays scattering lengths with the accuracy of 2%. Therefore, such a measurement will be a sensitive check of the understanding of chiral symmetry breaking of QCD by giving an indication about the value of the quark condensate, an order parameter of QCD. A statistics of 5000 π⁺π⁻ atoms collected. This sample provides a statistical accuracy for the lifetime measurement at the 20% level.

In recent years it has been realized that effective interactions—those valid over a limited range of energy-momentum—are often preferable even when more complete theories are available. We shall present examples of such methods in a range of physical applications—from classical and quantum mechanics, to quantum gravity.

Chiral Perturbation Theory and lattice simulations of QCD can be used concurrently to produce precise estimates for the light quark masses, and to determine the coupling constants in the effective chiral Lagrangian. I review the status of lattice calculations of the strange quark mass, the quark condensate and various effective coupling constants, whose values are needed to decide whether the up-quark is massless.

The Kugo–Ojima confinement criterion and its relation to the infrared behaviour of the gluon and ghost propagators in Landau gauge QCD are reviewed. The realization of this confinement criterion (which in Landau gauge relates to Zwanziger's horizon condition) results from quite general properties of the ghost Dyson–Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson–Schwinger equations provide an explicit example for the anticipated infrared behaviour. These results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, α(0) = 8.9/N_c. Solutions for the coupled system of Dyson–Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry is found. In the quenched approximation the quark propagator functions agree well with those of corresponding lattice calculations. For a small number of light flavours the quark, gluon and ghost propagators deviate only slightly from the quenched ones. While the positivity violation of the gluon spectral function is apparent in the gluon propagator, there are no clear indications of positivity violations in the Landau gauge quark propagator.

Dynamical chiral symmetry breaking is a nonperturbative phenomenon that may be studied using QCD's gap equation. Model-independent results can be obtained with a nonperturbative and symmetry preserving truncation. The gap equation yields the massive dressed-quark propagator, which has a spectral representation when considered as a function of the current-quark mass. This enables an explication of the connection between the infrared limit of the QCD Dirac operator's spectrum and the quark condensate appearing in the operator product expansion.

Three subjects are reviewed. (1) The dual Meissner effect of three quark system (a baryon) is studied using Monte Carlo simulations of full QCD with nonperturbatively O(a) improved Wilson fermion action. The Y-type flux distribution is observed. (2) Gauge problem of monopole dynamics is studied in pure SU(2) QCD. It is found that maximally abelian gauge is not a unique good gauge. The renormalization flows of effective monopole actions in various gauges look to converge to a unique curve. (3) The screening and the confinement in the framework of infrared effective actions are clarified qualitatively.

Perturbative QCD uses the Faddeev-Popov gauge-fixing procedure, which leads to ghosts and the local BRST invariance of the gauge-fixed perturbative QCD action. In the asymptotic regime, where perturbative QCD is relevant, Gribov copies can be neglected. In the nonperturbative regime, one must adopt either a nonlocal Gribov-copy free gauge (e.g., Laplacian gauge) or attempt to maintain local BRST invariance at the expense of admitting Gribov copies. These issues are explored and discussed. In addition, the relationship between recent Dyson-Schwinger based calculations of the infrared behavior of QCD Green's functions and the lattice calculation of these quantities is examined.

The topological charge of center vortices is discussed in terms of the self-intersection number of the closed vortex surfaces in 4-dimensional Euclidian space-time and in terms of the temporal changes of the writhing number of the time-dependent vortex loops in 3-dimensional space.

No abstract received.

We show how an effective field theory of long distance QCD, describing a dual superconductor, can be expressed as an effective string theory of superconducting vortices. We use the semiclassical expansion of this effective string theory about a classical rotating string solution in any spacetime dimension D to obtain the semiclassical meson energy spectrum. We argue that the experimental data on Regge trajectories along with numerical simulations of the heavy quark potentials provide good evidence for an effective string description of long distance QCD.

I discuss some new results related to physics of color confinement.

A summary on Chiral effective theories, Schwinger-Dyson equations, spectra and decays, light scalars and experimental results, presented at Section B, is given.

Heavy-light mesons, heavy quarkonium and doubly heavy baryons are briefly discussed. Effective field theories (EFTs) of QCD based on the heavy quark mass expansion 1/m_Q provide a unified framework to describe all three systems. They produce a number of model-independent results and simplify non-perturbative (lattice) calculations. Nevertheless, models are still very useful to obtain inexpensive estimates of many observables. It is emphasized that certain models can be accommodated in the EFT framework, like non-relativistic potential models for heavy quarkonium. It is also outlined how to build a suitable EFT for doubly heavy baryons which might also accommodate existing models for these systems. Finally, a few lattice calculations which are badly needed as inputs for EFTs are pointed out.

No abstract received.

We report on a lattice study of the gauge boson propagator of 3D compact QED in Landau gauge at zero and finite temperature. Non-perturbative effects are reflected by the generation of a mass m and by an anomalous dimension α. These effects can be attributed to monopoles and are absent in the propagator of the regular part of the gauge field.

We show that the dual Abrikosov vortex between quark and antiquark in Abelian Projected SU(2) gauge theory is insensitive to truncation of all loops except the large monopole cluster noted by Hart and Teper. As the transverse distance increases the discrepancy decreases, suggesting that the London penetration depth determined by tail is invariant under the truncation of short loops.

We consider an approach for extracting area law, or exponential decay of correlations, from the well-known loop equations of LGT, and their analogues in spin systems. In several cases, in particular in the case of the 2-dimensional O(N) spin model where large N analytical results are available, the method easily reproduces results that otherwise require considerable effort to obtain. We suggest the possible application of this technique to the 4-dimensional problem of area law for the Wilson loop in LGT at large β.

The string breaking is discussed in U(1)^N−1 Abelian effective theories of QCD. When a screening is expected, the static potential shows a flattening in the long-range region and a linear behavior in the intermediate region. We show why the screening is better observed in the Polyakov-loop correlators than in the Wilson loops. The breaking of the adjoint string is explained without the Z(N) picture.

We present evidence that in full QCD with two dynamical quarks confinement is produced by dual superconductivity of the vacuum, as in the quenched theory. Preliminary results about the nature of the deconfining transition are discussed.

We report the observation of calorons with nontrivial holonomy and fractional topological charge objects in cooled lattice samples derived from SU(2) equilibrium ensembles at T < T_c.

An algorithm is proposed, which in principle can give a canonical formulation of semi-classical Yang-Mills theory in terms of canonical variables without constraints. For the Abelian case of electrodynamics, it is shown that the algorithm leads to the result that the configuration space is the space of transverse potentials. The non-Abelian case is technically more complicated, and not yet completely worked out.

We show results for the quark–gluon vertex in the Landau gauge, using a mean-field improved Sheikholeslami–Wohlert fermion action. We compute all the three non-zero form factors of the vertex at zero gluon momentum, and compare them to the abelian vertex. The quark mass dependence of the vertex is also investigated and found to be negligible for the range of masses considered.

We consider spacetime to be a 4-manifold equipped with a Lorentzian metric and an affine connection. The components of the metric tensor and the connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature and study the resulting system of Euler–Lagrange equations. We first look for Riemannian solutions, i.e. solutions whose connection is Levi-Civita. We find two classes of Riemannian solutions: 1) Einstein spaces, and 2) spacetimes with metric of a pp-wave and covariantly constant Ricci curvature. We prove that for a generic quadratic action these are the only Riemannian solutions. We then look for non-Riemannian solutions. We introduce the notion of a 'Weyl pseudoinstanton' (metric compatible spacetime whose Riemann curvature is purely Weyl) and prove that a Weyl pseudoinstanton is a solution of our field equations. Using this approach we construct explicitly a non-Riemannian solution which is a wave of torsion in Minkowski space. We discuss the possibility of using this solution as a mathematical model for the graviton or the neutrino.

The structure of the Abelian-projected (AP) flux tube in SU(2) gauge theory in the maximally Abelian gauge is studied by applying the Hodge decomposition to the Abelian Wilson loop. It is shown that the profile of the AP flux tube has the same structure as the classical flux tube solution in the dual Abelian Higgs model, which is composed of a Coulombic and a solenoidal electric field linked by monopole supercurrent.

The effective string action of the color-electric flux tube in the dual Ginzburg-Landau (DGL) theory is studied by performing a path-integral analysis by taking into account the finite thickness of the flux tube. A modified Yukawa interaction appears as a boundary contribution and is reduced into the ordinary Yukawa interaction in the London Limit.

The color–flavor transformation is applied to a U(N_c) pure lattice gauge model, in which the gauge theory is induced by a heavy chiral scalar field.

We consider the correspondence between solutions of non-gravitational field theories formulated in Euclidean space-time and Minkowski space-time. Infinitely many "Euclidean" spaces can be obtained from M⁴ via a group of transformations in which the Wick rotation is a special case. We then discuss how the solutions of gauge field theories formulated in these "Euclidean" spaces have a one-to-one correspondence with the solutions of field theories formulated in Minkowski space-time, provided we avoid the one-point compactification into S⁴ = E⁴ ∪ ∞.

No abstract received.

The hadronic string is built over the chirally non-invariant QCD vacuum by means of the boundary interaction with background chiral fields associated with pions. To make this interaction compatible with the conformal symmetry the equations of motion for the chiral fields are imposed and the Lagrangian of non-linear sigma model of pion interactions is reconstructed. The obtained chiral structural constants fit well the phenomenological values.

Results of the study of lattice QCD with two flavors of nonperturbatively improved Wilson fermions at finite temperature are presented. The transition temperature for and lattice spacing α ~ 0.12 fm is determined. A two-exponent ansatz is successfully applied to describe the heavy quark potential in the confinement phase.

No abstract received.

We study how far the Index Theorem can be extrapolated from the continuum to finite lattices with finite topological charge densities. To examine how the Wilson action approximates the Index theorem, we specialize in the lattice version of the Schwinger model. We propose a new criterion for solutions of the Ginsparg-Wilson Relation constructed with the Wilson action. We conclude that the Neuberger action is the simplest one that maximally complies with the Index Theorem, and that its best parameter in d = 2 is m₀ = 1.1 ± 0.1.

The free energies of static charges and center monopoles are given by their fluxes. While electric fluxes show the universal behaviour of the deconfinement transition, the monopole free energies vanish in the thermodynamic limit at all temperatures and are thus irrelevant for the transition. Magnetic fluxes may, however, be used to measure the topological susceptibility without cooling.

QCD vacuum gluon fields are modelled by hyperspherical domains of constant field strength. The pure glue theory confines static quarks. Solutions of the Dirac operator have chirality properties in agreement with lattice results.

I give a brief description of Gribov's light quark confinement scenario and of the Gribov–Dyson–Schwinger equation for light quarks. It is shown that the Green function obtained with this equation exhibits chiral symmetry breaking.

Recently, we have pointed out that sign-coherent 4-dimensional structures can not dominate topological charge fluctuations in QCD vacuum at all scales. Here we show that an enhanced lower-dimensional coherence is possible. In pure SU(3) lattice gauge theory we find that in a typical equilibrium configuration about 80% of space-time points are covered by two oppositely-charged connected structures built of elementary 3-dimensional coherent hypercubes. The hypercubes within the structure are connected through 2-dimensional common faces. We suggest that this coherence is a manifestation of a low-dimensional order present in the QCD vacuum. The use of a topological charge density associated with Ginsparg-Wilson fermions ("chiral smoothing") is crucial for observing this structure.

The influence of nonperturbative fields on instantons in quantum chromodynamics is studied. Nonperturbative vacuum is described in terms of nonlocal gauge invariant vacuum averages of gluon field strength. Effective action for instanton is derived in bilocal approximation and it is demonstrated that stochastic background gluon fields are responsible for infra-red (IR) stabilization of instantons. Comparison of obtained instanton size distribution with lattice data is made.

The SU(3) Gauss law is solved using a non-Abelian generalisation of the Hodge decomposition. The behaviour of the solution is discussed near points where one component of the colour-magnetic field possesses coinciding eigenvalues. It turns out that the singularities in the solution formula can be removed, but three degrees of freedom are lost if the solution is assumed to be continuous everywhere.

A numerical calculation on a toy model shows that, besides avoiding the Landau pole, the y-expansion may also overcome the renormalon problem.

Crystal Barrel data on interactions in flight reveal an almost complete spectrum of non-strange states up to 2400 MeV. There are 6 'extra' states. Four of these follow the pattern extected for glueballs; their mass ratios show remarkable agreement with predictions from Lattice Gauge calculations. The other two, close to 1870 MeV, are candidates for J^PC = 2⁻⁺ hybrids with isospin 0 and 1.

Effects of isospin breaking at the level of the Goldberger-Treiman discrepancies involving the neutral isotriplet axial and pion-nucleon couplings are analyzed to leading non-trivial order in chiral perturbation theory.

The possibility that the magnetic dipole moment (MDM) of light charged vector mesons could be measured from radiative processes involving the production (τ → ρνγ) and decay (ρ → ππγ) of vector mesons is studied in a model independent way, via the soft-photon approximation. The angular and energy distribution of photons emitted at small angles respect to the final charged particle is found be sensitive to the effects of the MDM. We also show that model dependent contributions have a general structure, by gauge invariance requirements, that allows suppress them in the same kinematical region where the MDM effect is more important in the model independent approach.

We present a vector dominance model to describe radiative decays involving the light scalar mesons. Assuming that the light scalar mesons form a nonet this model gives relations among various decay amplitudes of the form S → γγ, V → Sγ and S → Vγ, where S and V denote scalar and vector mesons. By comparing with experimental radiative decay rates, including those recently measured for ϕ → PP′γ, we obtain various predictions. We discuss briefly ongoing extensions of the present work in an attempt to describe the radiative ϕ decay measurements in detail.

We report the results on the radiative decays ϕ → η′γ, ϕ → f₀γ and ϕ → α₀γ obtained with the KLOE detector at DAΦNE, using a sample of ~ 16 pb⁻¹.

I discuss how an extra light scalar meson multiplet (such as σ(600), a₀(980), f₀(980), κ) might possibily be understood as an effective Higgs nonet of a hidden local U(3) symmetry.

We observe 147 events of the axial vector pair K₁(1270)-K₁(1400) produced in the Coulomb field of a Pb target and measure the radiative widths Γ(K₁(1400) → K⁰ + γ) = 280.8 ± 23.2(stat) ± 40.4(syst) keV and Γ(K₁(1270) → K⁰ + γ) = 73.2 ± 6.1(stat) ± 28.3(syst) keV. These first measurements are lower than the quark-model predictions. We also place upper limits on the radiative widths for K*(1410) and and find that the latter is very small in accord with SU(3) invariance in the naive quark-model.

We show the results for the scattering poles associated to the ρ, f₀, a₀, K*, σ and κ resonances in meson-meson scattering. Our amplitudes are obtained from the complete one-loop meson-meson scattering amplitudes from Chiral Perturbation Theory. Once unitarized with the Inverse Amplitude Method, they describe remarkably well the data simultaneously in the low energy and resonance regions up to 1.2 GeV, using low energy parameters compatible with present determinations.

We briefly report on a relativistic quark model scheme to calculate the O(P⁴) pion-pion vertex in the planar approximation and in the chiral limit. The calculation is reduced to the solution of simple integral equations (Bethe-Salpeter like) by an effective use of chiral Ward Identities. Specific model computations are provided.

The valence-quark contribution to the electric polarizability of the charged pion in a semirelativistic description is shown to be smaller than in the nonrelativistic limit.

Using a simple relativistic QFT model of scalar fields we demonstrate that the analytic confinement (propagator is an entire function in the complex p²–plane) and the weak coupling constant lead to the Regge behaviour of the two-particle bound states. In QCD we assume that the gluon vacuum is realized by the self-dual homogeneous classical field which is the solution of the Yang-Mills equations. This assumption leads to analytical confinement of quarks and gluons. We extract the colorless 0⁺⁺ two-gluon state from the QCD generating functional in the one-gluon exchange approximation. The mass of this bound state is defined by the Bethe-Salpeter equation. The glueball mass is 1765 MeV for α_s = 0.33 if the gluon condensate is .

The relations between masses and decay constants of variety of meson resonances in the energy range 0–3 GeV are analyzed which follow from the string-like, linear mass spectrum for vector, axial-vector, scalar and pseudoscalar mesons with a universal slope. The way to match the universality with the Operator Product Expansion (OPE) is proposed.

Can non-perturbative field theories be solved using its Schwinger-Dyson equations in a regulator-independent way? We would like to answer this question by introducing the regulator-free method and discussing it in the context of QCD. We can then write down the 2-point Green's functions in terms of renormalized quantities rendering the equations completely finite.

We study the effect of the infrared behavior of the running coupling constant on the quark-antiquark spectrum.

In this paper we discuss a number of techniques developed and problems solved for a consistent implementation of the RPA for mesonic systems.

Using the electro-weak theory, we find the lowest order perturbative correction to a spin-1 particle in an external Coulomb field. We show this leads to a correction of order (Zα)⁴ and is independent of the mass of the external field. Previous work with Duffin-Kemmer-Petiau ¹ and the Proca equation has failed to produce this correction.

Quantum field theory is used to describe the contribution of possible new QCD vacuum replica to hadronic processes. This sigma-like new state has been recently shown to be likely to appear for any realistic four-quark interaction kernel as a consequence of chiral symmetry. The local operator creating the replica vacuum state is constructed explicitly. Applications to physical processes are outlined.

We study the quark-gluon mixed condensate , which is another chiral order parameter, using the SU(3)_c lattice QCD with the Kogut-Susskind(KS) fermion at the quenched level. We generate 100 gauge configurations on the 16⁴ lattice with β = 6.0, and measure at 16 points in each gauge configuration for each current-quark mass of m_q = 21, 36, 52 MeV. From the 1600 data for each m_q, we find at the lattice scale of α⁻¹ ≃2GeV in the chiral limit. The large value of suggests its importance in the operator product expansion(OPE) in QCD.

We calculate polarized quark distribution functions and g₁ structure functions for the nucleon. The calculation is performed in the light-cone frame. The dressed nucleon is assumed to be a superposition of the bare nucleon plus virtual light-cone Fock states of baryon-meson pairs. For bare nucleon we consider both the case of diquark-quark clusteration and the case which there is no quark clusteration inside the nucleon. The initial distributions are evolved. The evolved distributions are used to calculate polarized structure function for proton and neutron and the Bjorken sum-rule and EIlis-Jaffe sum-rule.

The thermal glueball is studied at finite temperature by using SU(3) anisotropic lattice QCD with β_lat = 6.25, the renormalized anisotropy ξ ≡ a_s/a_t = 4 over the lattice of the size 20³ × N_t with various N_t at the quenched level. While the narrow peak ansatz leads to the significant pole-mass reduction of about 300 MeV near the critical temperature T_c, Breit-Wigner ansatz which can take into account the possible appearance of the thermal width leads to the significant thermal width broadening of about 300 MeV with a modest reduction of the peak center of about 100 MeV.

The pion structure function is investigated in a simple pseudo-scalar coupling model of pion and constituent quark fields. The imaginary part of the forward Compton scattering amplitude is evaluated. We show that the introduction of non-perturbative effects, linked through a cut-off to the size of the pion, allows the reproduction of important features of the pion quark distribution function.

b- and c-quarks are produced in abundance at the KEKB asymmetric e⁺e⁻ collider, and the events are detected with high efficiency by the Belle detector. Some of the recent results from Belle that pertain to heavy quark spectroscopy and decay phenomena are presented, including the observation of , a comparison among exclusive B meson decays to final states that include the various charmonia, charmonium and double charm production on the e⁺e⁻ continuum, and decays of B mesons to η′.

In this work the charm and bottom quark masses are determined from QCD moment sum rules for the charmonium and upsilon systems. In our analysis we include both the results from non-relativistic QCD and perturbation theory at next-next-to-leading order. For the pole masses we obtain M_c = 1.75 ± 0.15 GeV and M_b = 4.98 ± 0.125 GeV. Using the potential-subtracted mass in intermediate steps of the calculation the -masses are determined to m_c(m_c) = 1.19 ± 0.11 GeV and m_b(m_b) = 4.24 ± 0.10 GeV.

Preliminary results on the partial wave analyses of J/ψ → γπ⁺π⁻, , the observation of an enhancement near threshold in , and the mass and width of η_c are presented based on 58M J/ψ data sample. The ψ(2S) total width; partial widths to hadrons, π⁺π⁻ J/ψ and l⁺l⁻ final states; and corresponding branching fractions are reported. The ψ(2S) branching fractions of nine exclusive hadronic decays are given.

The η_b(1S) is the ground state, and has not yet been experimentally observed. Theorists have recently suggested that it could be observed at the Fermilab Tevatron through its decay to J/ψJ/ψ, if not in the 1992-96 ("Run 1") dataset, then in Run 2. This article describes a search for this particle at CDF in Run 1 using this decay channel. A small cluster is seen, with 7 events where 1.8 events are expected from background. The statistical significance is estimated to be 2.2σ, and an upper limit is set on the product of cross section and branching fractions.

The recent Belle and Babar measurements of the branching ratios B⁻ → π⁺π⁻K⁻ and B⁻ → K⁺K⁻K⁻ and B^± → χ_c0K^± have renewed interests in these decays as another mean to look for direct CP violation in B decays. In this talk, I would like to discuss a recent analysis of the CP violating asymmetry in the partial widths for the decays B⁻ → π⁺π⁻K⁻ and B⁻ → K⁺K⁻K⁻, which results from the interference of the non resonant amplitude with the resonant amplitude B^± → χ_c0K^± → π⁺π⁻K^± and B^± → χ_c0K^± → K⁺K⁻K^±. For γ ≃ 58° we predict that the partial width asymmetry could reach 10% for the B⁻ → π⁺π⁻K⁻ decay and 16% for the B⁻ → K⁺K⁻K⁻ decay.

In our earlier work, the charge and matter radial distributions of heavy-light mesons were measured on a 16³ × 24 lattice with a lattice spacing of α ≈ 0.17 fm and a light quark mass about that of the strange quark.

Several major improvements have now been made:

1) Dynamical fermions are used with α ≈ 0.14 fm;

2) More gauge configurations are included (78 vs 20);

3) Off-axis, in addition to on-axis, insertions are made;

4) The data analysis is much more complete. In particular, distributions involving excited states are extracted.

We present a preliminary result on a search for narrow width resonances that decay into pairs using 130 pb⁻¹ of lepton plus jets data in collisions at . No significant deviation from Standard Model prediction is observed. 95% C.L. upper limits on the production cross section of the narrow width resonance times its branching fraction to are presented for different resonance masses M_X. We also exclude the existence of a leptophobic topcolor particle, X, with M_X < 560 GeV/c² for a width Γ_X = 0.012M_X.

Mass spectra of orbitally and radially excited heavy-light (B and D) mesons and doubly heavy baryons are presented. The light-quark – heavy-diquark structure of the baryon is assumed. The expansion in only inverse powers of the heavy (di)quark mass is carried out, while the light quark is treated completely relativistically. The relativistic treatment of the light quark plays an essential role. It is argued that P levels are inverted in the infinitely heavy quark limit. The close similarity of the mass spectra of heavy-light mesons and doubly heavy baryons is revealed.

The heavy quarkonium and resonances have a rich spectroscopy with numerous narrow S, P, and D-wave levels below the production threshold of open charm and beauty mesons. The mass predictions for these states are an important test of QCD calculations. We review some recent work describing the production of missing η_b(nS), and and states.

The results of a first exploration of two–fermion bound states in QED through a generalization of the Gell-Mann–Low Theorem are presented. In particular, gauge invariance is discussed at the lowest non–trivial order, and the relation to the Dirac and Salpeter equations is established and used to demonstrate the correct reproduction of the fine and hyperfine structure.

Strangeness production has been a useful diagnostic tool in understanding nucleus-nucleus collisions. The role of strangeness production studies is discussed, and current trends for different aspects of strangeness production briefly reviewed.

The CERN WA97 and NA57 experiments have been designed to study strange and multistrange particle production in Pb–Pb interactions at SPS energies. The strange baryon and antibaryon enhancements in Pb–Pb with respect to proton induced reactions, first observed by WA97 at 160 A GeV/c beam momentum, nicely fit with the expectations for the formation of a deconfined state of matter in relativistic heavy ion collisions. The results on the experimental program performed by its successor, NA57, to investigate the onset of deconfinement are presented.

Hadron production in A+A interactions is studied by the CERN experiment NA49 in dependence on energy and system size: p+p, central C+C, Si+Si and Pb+Pb collisions were measured at 158 AGeV, Pb+Pb also at 40 and 80 AGeV. Spectra and particle yields are interpreted on the basis of thermal models assuming an equilibrated hadron gas. Special emphasis is put on a systematic investigation of strangeness production. It is found to increase with system size. The energy dependence indicates a maximum for central Pb+Pb collisions at about 40 AGeV.

We analyse particle production from particle and nuclear collisions using a thermal model and extrapolating to zero baryochemical potential (µ_B). After eliminating µ_B universal features of strangeness production in particle and nuclear collisions appear. Within the assumptions made, this method allows to extract from the data the critical energy density of the QCD phase transition independent of predictions. We estimate ε_crit ~ 0.6 ± 0.2 (stat) ± 50% (syst) GeV/fm³. This is within the reach of CERN SPS or the future GSI facility. The observation of critical behaviour nearby (e.g. fluctuations) could lead to a definitive prove of the QCD phase transition. We discuss new analysis methods which will become possible with RHIC and LHC.

A Fermi sea of nucleon clusters of three constituent quarks is introduced to study the density dependence of the quark condensate. We find that quark clustering in the context of the Nambu–Jona-Lasinio model does not change the usual findings of in-medium chiral symmetry restoration. We conclude that recent claims in the literature that quark clustering might enhance chiral symmetry breaking in medium are very dependent on the microscopic model dynamics.

Our quasi-particle model for deconfined matter near T_c is reviewed. The extrapolation of lattice QCD data to finite baryo-chemical is discussed. Determined by the chiral transition temperature T_c, the resulting equation of state of neutral and β stable deconfined matter is soft and limits size and mass of pure quark stars.

The study of dilepton production plays a fundamental role in our understanding of ultrarelativistic heavy-ion physics. In this short review, I will address the main topics presently under study at SPS and RHIC energies, with an emphasis on heavy quarkonia and open charm production.

New measurements have been performed by the NA50 Collaboration to study the J/Ψ production in Pb–Pb collisions at 158 GeV per nucleon in improved experimental conditions. The preliminary results confirm the threshold effect already observed in the past, i.e. a departure from the normal nuclear absorption (determined with greater precision using the most recent NA50 p–A data, together with NA38 and NA51 results) and a steady decrease for the most central collisions.

The ALICE experiment at the CERN LHC is optimized to study heavy-ion physics at a novel energy regime where hard probes become readily available and relevant theoretical concepts can be tested. A brief overview of the ALICE apparatus, performance and physics potential is presented.

The ALICE experiment at the CERN LHC collider is devoted to the study of heavy-ion collisions at a centre of mass energy of 5.5 TeV per nucleon.

We present the results of a feasibility study for the detection of D⁰ → K⁻π⁺ decays in Pb–Pb collisions with ALICE.

We describe a strategy for the detection of open beauty in the semi-electronic channel with ALICE evaluating the expected S/(S+B) ratio.

We study the finite size effects on the deconfinement phase transition (DPT) of hot and/or dense hadronic matter, using a simple thermodynamic model based on the assumption of coexistence of confined and deconfined phases in a finite volume, including the color singleteness condition (CSC). It turns out that in a finite size system, all singularities occuring in some physical quantities in the thermodynamic limit (TL) (V→∞) are smoothed out. For the temperature driven DPT, an analysis of the finite size scaling (FSS) behavior at criticality of some characteristic quantities allows us to determine the scaling critical exponents characterizing the DPT. The obtained results are in good agreement with those predicted by other studies for a first-order phase transition.

From Dalitz-plot analyses of D⁺ → π⁻π⁺π⁺ and D⁺ → K⁻π⁺π⁺ decays, we find evidence for light and broad scalar resonances σ(500) and κ(800). From a Dalitz-plot analysis of decays, we measure the masses and decay widths of the scalar resonances f₀(980) and f₀(1370).

We present studies of the angular and momentum distributions of charged particles in hadronic final states of e⁺e⁻ annihilation. Some results are derived from reanalysis of data of the JADE experiment operating at the PETRA e⁺e⁻ collider at DESY from 1979 to 1986 [1] while other data are from OPAL [2].

Double parton scattering, i.e. two parton hard scattering in the same hadron-hadron collision, may constitute an important way for multiple weak gauge boson production and other new particles search. We prsent calculations of the relevant cross-section for pair, triple and four weak gauge bosons at the LHC.

Fermilab experiment E835 has used annihilations to search for charmonium in the π⁰π⁰ final state. An enhancement in the cross section was observed and attributed to interference between the χ_c0 and the non-resonant continuum. The general helicity structure of the π⁰π⁰ differential cross section was studied and a preliminary measurement of the product of was made.

The high energy two body deuteron photodisintegration is a very well suited process to identify quark effects in nuclei. In particular, its study in the few GeV region can clarify the transition from the nucleonic to the QCD picture of hadrons. The Cebaf Large Angle Spectrometer (CLAS) at JLab allowed for the first time the complete measurement of the angular distributions of the process differential cross section at photon energies from 0.8 to 2.95 GeV. Preliminary results from the analysis of 30% of the total collected data show persistent forward-backward asymmetry and are well described by a calculation derived in the non perturbative framework of the Quark Gluon String Model (QGSM).

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The Weinberg theorem for the pion-pion scattering is proved analytically in full detail for quark models in the ladder truncation. The proof is displayed with Feynman diagrams. The axial and vector Ward identities, for the quark propagator and for the ladder, exactly cancel any model dependence. Off mass shell and finite size effects are included in the quark-antiquark pion Bethe Salpeter vertices. This is applied to compute the isospin 0, 1 and 2 scattering matrices off the mass shell.

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The electromagnetic form factors of the proton contain all the information about the charge structure, and thus provide a strong constraint on the fundamental theory of the strong interaction. We adoted the quark-parton model for calculating and understanding the charge structure of the proton in terms of the charge form factors. A remarkable agreement with the available experimental values is found.

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