s-channel discontinuities of the torus insertion in the dual unitarisation scheme

The refined analysis of the s-channel discontinuities of the torus insertion in the topological expansion is performed. Assuming the dependence on reggeon masses of the fixed-pole residue similar to that given by the Veneziano model we obtain almost exact cancellations of the discontinuities which in the one-dimensional approximation were argued to be responsible for the exchange degeneracy breaking between ? and A₂ trajectories. Implications on different f-IP schemes are discussed.     

Axial vector meson production

Recently available differential cross section and density matrix information on π^?p → B^?p at 4 GeV/c are successfully described in terms of t channel exchanges and s channel absorptive effects. The s channel helicity amplitude which is dominant at small |t| (zero net helicity flip ω exchange) is found to have a zero at ?t = 0.2 GeV². SU(3) and higher symmetries are used to predict cross sections for further axial vector meson production processes, in particular non-diffractive A₁ production. The importance of these processes with regard to Regge phenomenology and meson spectroscopy is emphasized.     

Analysis of K−K+ and π−π+ final states in 13 GeV K−p interactions

The differential cross sections and density matrix elements for the φ and ?⁰ mesons have been measured in the reactions K^?p → K^?K⁺ (Λ, Σ⁰) and K^?p → π^?π⁺ (Λ, Σ⁰) at 13 GeV using a wire chamber spectrometer. The analysis shows that while the vector meson production is dominated by the natural parity exchange amplitude, some unnatural parity exchange is also required. Furthermore the φ and ? natural exchange cross sections are identical in shape and have the 2:1 relative strength expected in the quark model with K¹ and K⁷ exchange degeneracy. The analysis of the clear peak-dip ?^0?ω interference pattern observed in the π^?π⁺ data indicates that the ω production is in phase with the ? and of similar magnitude. Both the S¹ and f′ meson are clearly observed in this experiment. The S¹ data are found to be consistent with S¹ parameters deduced from ππ scattering analyses. The f′ density matrix elements and a new limit of the f′ → π^?π⁺ branching ratio are presented.     

Instanton induced flavour mixing in the presence of vector mesons

An extended version of the Nambu-Jona-Lasinio model is supplemented with the 't Hooft determinant and bosonized for an arbitrary number of flavours. The resulting effective meson lagrangian is in good agreement with the experimental low-energy mesonic data. The presence of the 't Hooft determinant leads to a flavour mixing of the scalar and pseudoscalar mesons with diagonal flavour content. This instanton induced flavour mixing in the scalar and pseudoscalar channel is noticeably effected by the coupling to the vector and axial-vector meson sector. If the latter is taken into account the η?η′ mixing angle is shifted from ?31° to ?22° in good agreement with the experimental value.     

Gluons in the hadronicS matrix

We derive a theoretical explanation of the similarities which have been experimentally observed between final state distributions in soft processes (K ^? p interactions andpp collisions at ISR) and hard processes (e ⁺ e ^? annihilations and deep inelastic scattering). The theoretical framework is the correspondence between QCD and dual topological unitarization (DTU), which expresses confinement as the equivalence of the hadron and parton bases to account for unitarity. Starting from the interpretation of the zero handle topology in DTU in terms of the naive quark parton model, we show how to characterize gluons in the hadron basis: primordial gluons are associated with the one handle topology, and the cascading of hard gluons is related to the sum of all higher topologies in DTU. We get this way a QCD interpretation of the reggeon calculus which is the theoretical framework of soft hadronic processes at asymptotic energies.     

Multiple parton scattering in nuclei: twist-four nuclear matrix elements and off-forward parton distributions

Multiple parton scatterings inside a large nucleus generally involve higher-twist nuclear parton matrix elements. The gluon bremsstrahlung induced by multiple scattering depends not only on direct parton matrix elements but also on momentum-crossed ones, due to the Landau–Pomeranchuk–Migdal interference effect. We show that both types of twist-four nuclear parton matrix elements can be factorized approximately into the product of twist-two nucleon matrix elements in the limit of extremely large nuclei, A→∞, as assumed in previous studies. Due to the correlative nature of the twist-four matrix elements under consideration, it is actually the off-forward parton distributions that appear naturally in this decomposition, rather than the ordinary diagonal distributions probed in deeply-inelastic scattering. However, we argue that the difference between these two distribution classes is small in certain kinematic regimes. In these regions, the twist-four nuclear parton matrix elements are evaluated numerically and compared to the factorized form for different nuclear sizes within a schematic model of the two-nucleon correlation function. The nuclear size dependence is found to be A^4/3 in the limit of large A, as expected. We find that the factorization is reasonably good when the momentum fraction carried by the gluon field is moderate. The deviation can be more than a factor of 2, however, for small gluon momentum fractions, where the gluon distribution is very large.     

Solution of twist-3 evolution equation in double logarithmic approximation in QCD

The solution of the DGLAP evolution equation for the twist-3 gluon operators is obtained in the double logarithmic approximation of QCD perturbation theory. The method used for the solution is similar to the reggeon field theory. The asymptotics of the twist-3 parton correlation function for small Bjorken variables x_B is found.Received: 5 February 2004, Published online: 23 April 2004     

Spontaneous dynamical breaking of gauge symmetry in dual models

The consequences of gauge invariance are re-examined in dual models with unit intercept when the dimension of space-time has the maximum value compatible with the absence of ghosts. In that case, reggeon-reggeon bound states of zero mass are formed already at second order of perturbation theory. Gauge invariance no longer guarantees that the initially massless SU(3) singlet vector meson remains massless, and the mixing between the reggeon and pomeron sectors of the model yields a massive unitary singlet vector meson already at order g². A Lagrangian model which exhibits similar features to the dual situation is discussed.     

Exploiting the equivalence of reggeon field theory in zero transverse dimensions and reaction–diffusion processes

The reggeon field theory in zero transverse dimensions is investigated. Two versions of the theory are considered: one that allows for at most triple pomeron interactions and the other that embodies an additional 2→2 quartic reggeon coupling. The behavior of the scattering amplitude at asymptotic rapidities is obtained in both cases. In an s-channel picture of the high energy scattering both models can be viewed as reaction–diffusion processes. We derive known results in reggeon field theory rather easily using the reaction–diffusion formalism. We find that some results which are surprising from the reggeon field theory point of view turn out to have a simple interpretation from the reaction–diffusion point of view.     

ω Production in the reaction π−p → π+π−π0n at 8 and 12 GeV/c

The reaction π^?p → ωn has been studied at 8 and 12 GeV/c incident momenta with the CERN Omega spectrometer using a neutron time of flight trigger. The differential cross sections and the ω-decay density matrix elements are presented as functions of the momentum transfer squared ?t in the range of 0.02 to 0.80 GeV². The data are used to evaluate the intercept and slope of both the natural and unnatural parity exchange trajectories. Regge exchange amplitude factorisation tests involving the reaction πN → ωN are investigated.     

Dynamics of collective decoherence and thermalization

We analyze the dynamics of N interacting spins (quantum register) collectively coupled to a thermal environment. Each spin experiences the same environment interaction, consisting of an energy conserving and an energy exchange part.We find the decay rates of the reduced density matrix elements in the energy basis. We show that if the spins do not interact among each other, then the fastest decay rates of off-diagonal matrix elements induced by the energy conserving interaction is of order N², while that one induced by the energy exchange interaction is of the order N only. Moreover, the diagonal matrix elements approach their limiting values at a rate independent of N. For a general spin system the decay rates depend in a rather complicated (but explicit) way on the size N and the interaction between the spins.Our method is based on a dynamical quantum resonance theory valid for small, fixed values of the couplings. We do not make Markov-, Born- or weak coupling (van Hove) approximations.     

Partons,the gambler's ruin,and pomerons

The parton picture of Regge theory is extended to the supercritical case α_p > 1. The essential results of Amati et al. and others are rederived by heuristic but mathematically very simple arguments. In addition, also some new results are obtained, in particular concerning the rôle of Pumplin's bound in reggeon theory. The transition between sub- and supercritical pomerons appears as a transition from total to partial ruin in a collective risk problem. In the subcritical case, some problems are encountered whose origin is not yet clear.     

Non-strange vector meson production in K−p interactions at 4.2 GeV/c

The vector meson production, hypercharge exchange reactions K^?p → (φ, ω, ?) Λ and (φ, ?) Σ⁰ are studied at 4.2 GeV/c incident momentum. The data come from a high statistics bubble chamber experiment with a sensitivity of ～ 120 events/μb. Total and differential cross sections are presented. The vector meson density matrix elements and hyperon polarization are investigated as functions of momentum transfer. Amplitude analyses are performed for all five reactions. The results are compared with duality and quark model predictions, as well as used to test current ideas in two-body phenomenology.     

Operators on the fock space,diagonal in the wave-packet formalism and in the mode representation

We establish the conditions that an operator on the Fock space, diagonal in the mode representation, must verify to have a diagonal form in the wave-packet (W. P.) formalism. And we show that, if these conditions are verified, there is only one set of W.P. on which such a given operator is diagonal. The interest of these results lies in the probabilistic interpretation of a diagonal density matrix in the W.P. formalism; indeed a field described by such a density matrix may be considered as a mixture of one particle W.P. In particular our results apply to chaotic density matrices and prove that there is one way only of describing a given chaotic field as a mixture of one particle W.P.     

The Cabibbo angle and the mass of thet-quark in anSU (2) L ⊗U (1) model with horizontal symmetry

Enlarging theSU (2) _L ?U (1) gauge theory with six quark flavours by anSU (3) _H horizontal symmetry, we calculate the Cabibbo angle and we obtain a mass relation for thet-quark by including one-loop corrections to the flavour diagonal zeroth order mass matrix.     

Reggeon field with non-vanishing vacuum expectation value

It is argued that if the vacuum expectation value of the reggeon field does not vanish, the solution of the reggeon calculus corresponds to the leading singularity of intercept one. The physical interpretation of the reggeon field theory with unstable vacuum is discussed.     

Dual model foru,d, s andc quark fragmentation functions

In the dual topological unitarization scheme, we derive a model for theu, d, ands quark fragmentation into mesons by considering the parton interpretation of planar one particle inclusive cross sections. A good agreement with experiment is obtained. Relying on these results, we generalize the model in order to include the charm fragmentation functions into any meson and again get a nice agreement with data.     

The riemann surface of a static dispersion model and regge trajectories

The S matrix in the static limit of a dispersion relation is a matrix of a finite order N of meromorphic functions of energy ω in the plane with cuts (?∞, ?1] and [+1, +∞). In the elastic case, it reduces to N functions S _i(ω) connected by the crossing-symmetry matrix A. The scattering of a neutral pseudoscalar meson with an arbitrary angular momentum l at a source with spin 1/2 is considered (N=2). The Regge trajectories of this model are explicitly found.     

Corrections to the single-particle M1 and Gamow-Teller matrix elements

Consideration of second-order core-polarisation, isobar-current and meson-exchange-current processes gives a satisfactory understanding of the ground-state magnetic moments and mirror β-decay transition probabilities in closed-shell-plus- (or minus) one nuclei, A = 3, 15, 17, 39 and 41. Perturbation contributions from high-lying excited states (tensor correlations) from one-body and two-body meson-exchange operators cancel strongly in diagonal matrix elements, but in off-diagonal matrix elements between spin-orbit partners the cancellation is less. Similarly, with isobar currents, there is a strong cancellation between direct and exchange contributions in diagonal matrix elements, while the exchange term is suppressed in off-diagonal cases. Of the two contributions, tensor correlations are found to be as important as, if not more important than, isobar currents. The calculated lowest-order meson-exchange-current contributions to magnetic moments are close to the soft-pion limit predictions.