General results on glueball masses in QCD

A number of authors have investigated mass inequalities for mesons and baryons in QCD. These provide rigorous non-perturbative constraints on the mass spectrum. Similar inequalities for glueballs are investigated. For nonzero spin J, in the large-N_c approximation, m_J⁻⩾m_J⁺ is found. (For J = 0, the existence of a gluon condensate can modify this statement.) There are also constraints on how fast m_J can grow with J. For example, for m_J = a + bJ^α, 0 ⩽ α ⩽ 1 is found, a result consistent with Regge behaviour.     

A possible description of baryon dynamics in dual and gauge theories

We present an attempt to generalize to baryons a framework recently proposed in order to unify gauge, dual and Regge-Gribov theories of mesons. We find it necessary to depart from the $\text{1}\text{N}{}_{\mathrm{<mtext>colour</mtext>}}$ expansion of quantum chromodynamics (QCD) and to replace it by a more general definition of a “dual” approximation of QCD, based on the zero-width limit. Theoretical and phenomenological consequences of the scheme are derived. For N_colour = 3, the baryon resembles a Y shaped string; three families of new “baryonium” bound states are predicted and rough estimates of intercepts and slopes of the associated Regge trajectories are given. A new type of Zweig-like selection rule is found to hold in leading order and its violations through higher-order topologies are discussed. Duality diagrams for baryons are ambiguous unless implemented with extra lines indicating the flow of certain colour indices. Duality between scattering and annihilation channels is found in B$\text{B}$ scattering and its consequences are discussed. Some justification is given for the quark counting rule for total cross sections. Finally, implications of our scheme for the Regge-Gribov calculus in processes involving baryons are discussed.     

Factorization of Regge slopes for ordinary and new hadrons

We propose a factorization property of Regge slopes between ordinary and new hadrons. We derive three (six) relations for bosons (baryons). This is supported experimentally in a known case and several predictions are made. The D⁷ mass is predicted to be 2.36 GeV.     

Regge trajectories in the quark model

We prove that the large angular momentum behaviour of the leading Regge trajectory of a meson (q \(\bar q\) ) or a baryon (qqq) can be obtained by minimizing the classical energy of the system for given angular momentum. A two-body quark-antiquark linear potential plus relativistic kinematics produces asymptotically linear Regge trajectories for mesons. For baryons we take either a sum of two-body potentials with half strength or a string of minimum length connecting the quarks, and find in both cases that the favoured configuration is a quark-diquark system and that the baryon and meson trajectories have the same slope. Short-distance singularities of the potential are shown to be unimportant.     

Instantons and the hyperfine splitting ofB andB Smesons

In this short note we wish to point out that the instanton model, which was theoretically fascinating, has recently found application in explaining the hyperfine splitting of mesons and baryons. In particular, the flavour independence ofM _v ² -M _P ² (i.e. the squared mass difference of the vector and the pseudoscalar mesons), known to be constant for the strange and non-strange mesons in theu,d and the charm quark sectors, have recently been shown to be the same for the beauty sector through experiments. This flavour independence and the magnitude of the splitting agrees remarkably well with the instanton model.     

Implications of duality,unitarity and SU6 symmetry for baryons and baryonium

It is shown that there exists a limit, involving both an exactly SU₆ symmetric spectrum and exactly exchange degenerate Regge trajectories, in which the OZI like selection rule for baryonium is exact. Deviations from the rule occur when SU₆ is broken and when unitarity forces the breaking of exchange degeneracy. By combining both of these latter effects we can qualitatively account for the observed pattern of broken exchange degeneracy among baryons. The strength of the baryonium coupling to mesons is related to the breaking of exchange degeneracy.     

Hyperon structure and projectile fragmentation

We investigate the hadron productions in hyperon proton collisions in terms of the quark-diquark cascade model with diffractive component. We compare our predicted spectra Ξ^?→Ξ^? X and Ξ^?→Ω^? X with the experimental data. The distribution functions of constituents in incident hadrons and the momentum sharing functions of cascade processes are characterized by the intercepts of Regge trajectories, revealing the difference betweens quark and non-strange quark.     

A relativistic Hartree-Fock model for quark systems

The “relativistic H—F” scheme is applied to baryons and finite multiquark sustems. A two-body confinement potential (r, r² or r³) and the one-gluon-exchange interaction are incorporated. The electric OGE term is treated consistently in all considered systems. With the electric OGE term included, the solutions indicate the little bag. (Os)-closed multiquark states, strange or non-strange, cannot be lower in energy than an aggregate of Δ or Λ.     

Quarks and reggeons

We propose a new algebra which will hopefully contribute to the joint understanding of electromagnetic and weak structure functions and of Regge couplings. It involves an infinite number of form factors of arbitrary complex spin J (with Re(J?1) > 0) and definite signature. The algebra holds exactly in a quark-gluon model when quantized canonically on equal light fronts. If all form factors have k = 0 and J = 1, the algebra closes and becomes U(6) × U(6), with the connecting subgroups being associated with pure quarks and pure antiquark currents, respectively. This doubling of the group leads to exact exchange degeneracy if baryons and mesons consist of qqq and q$\text{q}$ wave functions only.To some lowest approximation, Regge couplings can be calculated by representing U(6) × U(6) on properly mixed quark wave functions. With the mixing parameters fixed by the chiral subgroup, these couplings are determined up to an overall normalization.As an illustration, the coupling of the trajectories ?, ω; A₂, f; A₁, D; Z, Z_sg; π, η; B, H trajectories are estimated for the meson resonances ?, ω; π, η; A₂, f; A₁, D; B, H; A₀, σ. The trajectories π, η; B, H are not in the algebra initially but can be inferred from an extension of PCAC to the bilocal currents (“PCBC”).     

A QCD Sum Rule Approach with an Explicit Di-quark Field

We introduce a phenomenological QCD sum rule with an explicit diquark field. We investigate certain configurations of hadrons are expected to have a good diquark structure. The parameters of the model are a diquark mass ${(m_\phi)}$ and condensate ${(\langle \phi^2\rangle)}$ . Assuming that Λ baryons can be represented by a diquark and a spectator quark configuration, we find the sum rule works well for Λ, Λ _c , and Λ _b . We also find a duality relation between the mass and the condensate for which the parameter sets give good Borel curves. To maintain good Borel curve, a smaller diquark condensate is needed for an increased diquark mass. Using these parameter sets, we test the diquark structure in some hadrons which contain both good and bad diquark configurations.     

Parity doubling among the baryons

We study the evidence for and possible origins of parity doubling among the baryons. First we explore the experimental evidence, finding a significant signal for parity doubling in the non-strange baryons, but little evidence among strange baryons. Next we discuss potential explanations for this phenomenon. Possibilities include suppression of the violation of the flavor singlet axial symmetry (U(1_)A$U(1{)}_A$) of QCD, which is broken by the triangle anomaly and by quark masses. A conventional Wigner–Weyl realization of the SU(2_)L×SU(2_)R$\mathit{SU}(2{)}_L\times \mathit{SU}(2{)}_R$ chiral symmetry would also result in parity doubling. However this requires the suppression of families of chirally invariant   operators by some other dynamical mechanism. In this scenario the parity doubled states should decouple from pions. We discuss other explanations including connections to chiral invariant short distance physics motivated by large _Nc$N_c$ arguments as suggested by Shifman and others, and intrinsic deformation of relatively rigid highly excited hadrons, leading to parity doubling on the leading Regge trajectory. Finally we review the spectroscopic consequences of chiral symmetry using a formalism introduced by Weinberg, and use it to describe two baryons of opposite parity.     

Baryon mass splitting by the strong hyperfine interaction and SU(3) breaking

We calculate mass splittings of strange and non-strange baryons in the [56, 0⁺] and the [70, 1^?]. As the most important spin-dependent force we only analyse the hyperfine interaction. The exact treatment of the quark mass breaking shows contributions which have not been considered in similar investigations up to now. Taking $\text{mλ}\text{m}{}_{\mathrm{<mtext>p</mtext>}}\text{? 2}$ and popular values for the slope of the linear potential a, the strong coupling constant α_s and the p-quark mass, we get excellent results for the four mass splittings 〈Σ-Λ〉, $\text{〈Σ}{}^1\text{? Σ〉}$, 〈Δ-N〉 and $\text{〈Ξ}{}^1\text{? Ξ〉}$ in the [56, 0⁺]. The structure of mass spectrum in the [70, 1^?] is well described, too; the strong SU(3) mixing of Σ and Λ states is seen to be due to the quark mass breaking. Predictions for missing Σ states in the [70, 1^?] as as for splittings between charmed baryons can be made.     

Kaon-nucleon finite energy sum rules revisited

Kaon-nucleon finite energy and continuous moment sum rule integrals are evaluated using recent phase-shift solutions to extract the t-channel exchange amplitudes and the results are compared with Regge pole models. The exchange degeneracy breaking previously observed in the ? and A₂ amplitudes is confirmed, and it is suggested that this may be due to an exotic P₀₁ KN resonance. Regge trajectories are extracted from the integrals and are in good agreement with those found from direct fits to high-energy data.     

Strange charmed baryons in QCD

QCD sum rules are used to predict the mass differences between strange and nonstrange single charmed baryons inSU (3) sextets 1/2⁺, 1/2^?, 3/2⁺ and antitriplet 1/2⁺ as well as the mass of the lowest nonstrange stateΣ _c ^++′ in the 3/2⁺ sextet. The mass difference obtained for the antitriplet 1/2⁺ is in a good agreement with the available experimental data.     

Mesonic and baryonic Regge trajectories with quantized masses

We have constructed some Regge trajectories for mesons and baryons by taking the 70 MeV spinless mass quanta as the ultimate building block for the light hadrons. In order to make masses integral multiples of seventy, small changes in masses has been made with due explanation. We have shown how a linear relationship between J and M ² is maintained by considering quantized hadron masses, which is a direct consequence of the string model and gives a strong clue for quark confinement. It has also been established that mesons and baryons have different slopes and the slopes of baryons is less than the slope of the mesons. This clearly defies the concept of universality of slopes (α ≈ 1.1 GeV²) of hadrons, which can only be achieved if the strings joining the quarks have constant string tension α = 1/(2πσ) (where σ is the string tension).