High-energy scattering in a two-dimensional gauge theory

We study high-energy scattering in two-dimensional quantum chromodynamics in the 1/N_colour expansion. To first order, high-energy forward scattering amplitudes are power-behaved with the factorization, signature and exchange degeneracy properties found in dual Regge models. Backward scattering has deviations from naive quark power-counting rules which are related to the form factor and “Regge” behaviours. In the second order of 1/N_colour vacuum exchange diagrams do not give a new Pomeron singularity, but do break exchange degeneracy.     

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.     

On the bare pomeron graph in two-dimensional QCD

We present a detailed study of the bare pomeron graph in two-dimensional QCD in the 1/N_c approximation. The absence of a new singularity unrelated to quark parameters is derived. The “cylinder” graph is shown to induce renormalization of the vertex and intercept associated with quark andti-quark exchange in the vacuum channel.     

Instantons and meson correlation functions in QCD

Various QCD correlators are calculated in the instanton liquid model in zeromode approximation and 1/N _c expansion. Previous works are extended by including dynamical quark loops. In contrast to the original “perturbative” 1/N _c approximation, not all quark loops are suppressed. Renormalization of the instanton density allows the identification of the density with the gluon condensate even in presence of dynamical quark loops. In the flavor singlet meson correlators a chain of quark bubbles survives the N _c → ∞ limit causing a massive η′ in the pseudoscalar correlator while keeping massless pions in the triplet correlator. The correlators are plotted and meson masses and couplings are obtained from a spectral fit. They are compared to the values obtained from numerical studies of the instanton liquid and to experimental results.     

Spin distributions in the quark parton model

Spin-dependent parton distributions are described in a broken SU(6) quark parton model. The model predicts definite forms for the spin-dependent structure functions in deep inelastic lepton-nucleon scattering and leads to several relations between Regge intercepts and couplings. Resonance electroproduction at large momentum transfer is explored via Bloom-Gilman duality.     

A topological approach to high-energy large transverse momentum interactions

We discuss the high p_T strong interaction from a topological (1/N_f) expansion viewpoint. Topology of quark line graphs is used to classify the underlying process rather than constituent scattering, all constituents being implicitly confined. The distinction between “jets” and “background” is clarified in a very simple dynamical model. Although the model does not require quarks as dynamical entities, many of its features are in agreement with parton model predictions.     

OddC gluonic regge singularities of perturbative QCD and their decoupling from deep inelastic neutrino scattering

The QCD motivated integral equation for three reggeised gluons in the oddC colour singlet channel is solved for large external masses of gluons. It generates a Regge singularity forj?1. Possible contribution of this singularity to the “non-singlet” structure functionxF ₃ is examined atx?0, where in principle it should give a constant term and dominate over the valence quark contribution. The coupling of the three gluon system to currents is, however, shown to vanish in the lowest order and in higher orders in the multi-Regge approximation.     

Mesons in the large-N collective field method

The large-N limit of SU(N) matrix quantum mechanics has been studied recently as a model for large-N Yang-Mills theory. Here we solve this model with fundamental representation fermions (“quarks”) added. The “meson” spectrum is given by an integral equation and exhibits asymptotically linear “Regge trajectories” with the same spacing as that of the “glueballs”.     

Quasiparticle picture of quarks near chiral phase transition

We study how the quasiparticle picture of the quark can be modified near but above the critical temperature (T _c) of the chiral phase transition; we incorporate into the quark self-energy the effects of the precursory soft modes of the phase transition, i.e. ‘para-σ(π) meson’. It is found that the quark spectrum has a three-peak structure near T _c: We show that the additional new spectra originate from the mixing between a quark (antiquark) and an antiquark-hole (quark-hole) caused by a “resonant scattering” of the quasi-fermions with the thermally-excited soft modes.     

Reggeon phases and the dual bootstrap program

Analyticity requirements lead to complex Regge vertices in multiparticle production amplitudes. Their effect is discussed within a dual, unitary and exchange-degenerate multi-Regge model. A resulting complex Regge vertex is incorporated in fixed-t model calculations of the reggeon bootstrap and the topological pomeron. The bootstrap condition for particle-particle scattering is unaffected but new j-plane singularities appear in Regge-Regge scattering amplitudes. The pomeron and reggeon intercepts determine the two parameters of our Regge vertex and admit two possible solutions: one is close to the naive phase rule (real vertex) and the other is complex and leads to a high lying non-leading pole in the pomeron channel.     

Color,flavor, duality,and the pomeron

AtN _c /N _f =∞ such that quark loops are absent the Harari-Freund (HF)P+f model of diffraction can be motivated through the identification Pomeron ≈ glueball,f≈leading planar trajectory. AtN _c =3, the presence of confinement-related mass scales introduced by quark loops is a basic complication that can easily change this situation to, e.g., a dominantP?f identity structure. Aurenche and Gonzales Mestres (AGM) have argued that diffraction is essentially identical atN _c /N _f =∞ and atN _c =3. They further claim to have generated the HF scheme directly atN _c =3 through the novel mechanism of a multiperipheral iteration of daughters that becomes theP. We respond to these arguments. We give a general qualitative discussion of changes expected in theN _c /N _f =∞ toN _c =3 transition. Important hadron scattering quantities like particle multiplicities are very different in dynamics dominated by glue and atN _c =3, unlike other quantities like resonance width to mass ratios. We argue that the weak coupling dual model is not a reliable guide toN _c =3 dynamics. We criticize AGM's “daughter generated Pomeron”, and we close with a brief summary of other attempts to generate theP+f model.     

Nuclear physics in colourful worlds: Quantumchromodynamics and nuclear binding

When quantumchromodynamics (QCD) is generalized from SU(3) to an SU(N_c) gauge theory, where N_c is the number of colours, it depends on only two parameters: N_c and the bare quark mass m_q. A more general understanding of nuclear physics can be achieved by considering what it would be like in worlds with the number of colours different from 3, and bare quark masses different from the “empirical” ones. Such an investigation can be carried out within a framework of meson-exchange interactions. The empirical binding energy of nuclear matter results from a very near cancellation between attractive and repulsive terms which are two orders of magnitude larger and may be expected to depend sensitively on the parameters of QCD. It is indeed found that our world is wedged into a small corner of the two-dimensional manifold of m_q versus N_c. If the number of colours were decreased by one, or the bare quark masses raised by more than 20%, nuclear matter would become unbound. By tracing the origin of this state of affairs, one obtains a clearer picture of the relative importance of various effects on the behaviour of the bulk nuclear matter. In particular, correlations like those embodied in the Coester band of saturation points appear to have a broader degree of validity than is implied by fits to the actual physical world only.     

N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution

We further investigate, in the planar limit of N=4 supersymmetric Yang–Mills theories, the high energy Regge behavior of six-point MHV scattering amplitudes. In particular, for the new Regge cut contribution found in our previous paper, we compute in the leading logarithmic approximation (LLA) the energy spectrum of the BFKL equation in the color octet channel, and we calculate explicitly the two-loop corrections to the discontinuities of the amplitudes for the transitions 2→4 and 3→3. We find an explicit solution of the BFKL equation for the octet channel for arbitrary momentum transfers and investigate the intercepts of the Regge singularities in this channel. As an important result we find that the universal collinear and infrared singularities of the BDS formula are not affected by this Regge-cut contribution. Any improvement of the BDS formula should reproduce this cut to all orders in the coupling.     

Impact parameter analysis of KN and πN scattering in the intermediate energy region

We have evaluated the s-channel-helicity partial-wave amplitudes for $\text{K}\text{N and πN}$ scattering as functions of the impact parameter using partial-wave data in the energy range P_L≈1.0–2.0 GeV/c. We find that the $\text{K}\text{N}$ background and resonance amplitudes exhibit features consistent with the dual absorptive picture for pomeron and f + ω and A₂ + ? exchanges. Comparison of the πN low-energy amplitude with the partial-wave decomposition of a quantitative Regge model gives evidence for local duality between the s-channel resonance and t- and u-channel Regge exchanges.     

Nonlocal PNJL model beyond mean field

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/N _c expansion scheme. It is found that the 1/N _c corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/N _c expansion breaks down and a nonperturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition region.     

Two body reactions and the quark model

A simple quark model for two-body hadronic amplitudes is presented and applied to pp ($\text{p}\text{p}$) and K^±p elastic scattering. Hadronic processes are described in terms of quark-quark scattering, using Glauber theory to take into account the effects of multiple scattering. Exchange degenerate Regge poles are introduced at the quark level. A predictive model for Regge cuts is obtained. It has some features in common with the dual absorption model in its correlation of dip structure and shrinkage in elastic processes with the exoticity of the s-channel but also significant differences, for example in the interpretation of the $\text{p}\text{p}$ dip. The qualitatively different structure in the pp differential cross section is also reproduced. It breaks exchange degeneracy in a well-defined way and in doing so offers an explanation of the differences between pp and K⁺p total cross sections. The difference in their differential cross sections is a natural consequence of the model and structure similar to the pp structure is predicted to appear in the K⁺p differential cross section in the region t ≈ ?2(GeV/c)².     

Chiral symmetry breakdown,anomaly, and the PCAC relation on a lattice

Lattice fermion formulation is investigated using a solvable model which resembles quantum chromodynamics. CP₂^N?1 models with quarks are formulated on a lattice. For dynamical quarks, a generalized formulation of the Wilson and the Osterwalder-Seiler lattice fermion is used. In the $\text{1}\text{N}$ expansion, the spontaneous breakdown of chiral symmetry (which is softly broken by the quark mass) apparently occurs in this model, and the “pion” mass is calculated. From the above results, it is shown that the above lattice fermion formulations have the desired continuum limit. The axial-vector current is investigated and it is proved that the usual anomaly appears in the continuum limit and the PCAC relation is satisfied.     

Charmed Deuteron

Possible existence of bound states of a charmed baryon, Λ _c , Σ _c , Σ* _c with a nucleon, N, as well as two charmed baryons, Λ _c Λ _c , etc., are examined in the meson exchange potential approach. The heavy quark spin symmetry induces a strong tensor coupling between Λ _c N, Σ _c N and Σ* _c N states, which causes a bound state of Λ _c N (J = 0⁺ and 1⁺) states. Such a bound state is also seen in the spin-singlet Λ _c Λ _c channel, which resembles the H dibaryon in the strange sector.