Narrow Results

Data of the Crystal Barrel and L3 collaborations clarified essentially the situation in the 2⁺⁺ sector in the mass region up to 2400 MeV, demonstrating the linearity of (n, M²) trajectories, where n is the radial quantum number of a quark–antiquark state with mass M. We discuss these data and show that there exists a superfluous state for the (n, M²) trajectories: a broad resonance f₂(2000). We pay special attention to the reactions in the mass region 1990–2400 MeV where, together with f₂(2000), four relatively narrow resonances are seen: f₂(1920), f₂(2020), f₂(2240), f₂(2300). We analyze the branching ratios of all these resonances and show that only the decay couplings of the broad state f₂(2000) → π⁰π⁰, ηη, ηη′ satisfy relations inherent in the glueball decay.

We present a short review of the current understanding of the scalar meson sector, with special attention to the problem of the low-mass σ. The dispersion relation N/D-method used for the restoration of the low-energy ππ (IJ^PC = 00⁺⁺)-wave amplitude is discussed. The low-energy ππ amplitude was determined from the data in the energy region 280–500 MeV and it was sewn with the previously found K-matrix solution for the region 450–1950 MeV. The N/D-amplitude has a pole on the second sheet of the complex-s plane, near the ππ threshold at , that corresponds to the low-mass σ-meson. We discuss the hypothesis that this pole may be related to the confinement forces, thus being the eyewitness of confinement.

We discuss the scalar meson mixing scenario and present an OZI rule violation mechanism for understanding the scalar productions in charmoium hadronic decays. We stress that the OZI violation could play a key role in disentangling the structure of the scalars: f₀(1370), f₀(1500) and f₀(1710).

We investigate 3D Yang-Mills theory coupled to an adjoint scalar, which can be regarded as a zeroth order approximation in (de)constructing 4D Yang-Mills theory. We develop a new algorithm to obtain the renormalized Hamiltonian with the Karabali-Nair variable, by carefully identifying finite local counterterms. We also discuss how this formalism can be applied to obtain glueball spectrum.

We report here on recent advances that shed light on the topic of scalar meson sector, which is controversial up to date. We study the scattering and spectroscopy of the strongly interacting mesons in coupled channels with quantum numbers J^PC = 0⁺⁺ and I = 0 and I = 1/2, up to a center of mass energy . Our framework is based on Unitary Chiral Perturbation Theory, but extended now to include many more channels. The resonant content of our fits is discussed, with the appearence of σ, f₀(980), f₀(1310), f₀(1500), f₀(1710) and f₀(1790) for I = 0 and the κ and the for I = 1/2.

I give a brief introduction to central exclusive production in hadron–hadron collisions, the subject of this special issue of the International Journal of Modern Physics A.

The CERN Intersecting Storage Rings, with from 22 GeV to 63 GeV and , allowed the first observations of p + p → p + X + p with two leading protons (x_F > 0.95) or two rapidity gaps Δy > 3. Studies of the central hadronic system (X) were made to search for glueballs, finding f₀ and f₂ resonances, and to advance our understanding of hadronic diffraction. I review the experiments, not including those at the Split Field Magnet (SFM) facility covered elsewhere in this volume. Some double pomeron exchange studies at the CERN Collider are also covered.

At CERNs Large Hadron Collider, a unique possibility to study central exclusive processes such as the production of low mass resonances, charmonium states and jets, as well as to search for missing mass or momentum signatures opens up by the detection of both leading protons with the special β* = 90 m optics. At with that optics the leading proton acceptance of the TOTEM Roman Pots covers all diffractive masses, provided that the proton four-momentum transfer |t| ≳ 0.04 GeV². This paper describes the physics potential with an integrated luminosity of 10 pb^-1 and 100 pb^-1 for common CMS and TOTEM data taking at β* = 90 m optics.

We derive the bound state equation for two gluons in relativistic quantum field theory, i.e. the Bethe–Salpeter (BS) equation for two gluons. To solve it, we choose the kernel as the sum of a one-gluon exchange potential, a contact interaction and a linear confining potential. Under instantaneous approximation, this BS equation is solved numerically. The spectrum and the BS wave function of the glueballs are obtained in this framework. The numerical results are in agreement with that of recent lattice calculation.