Theory of interacting Pomerons

The quantitative theory of Pomeron interaction is developed on the basis of strong coupling methods and ?-expansion. The theory is consistent with all unitarity conditions. At asymptotic energy total cross section increases as (ln s)^η, the multiplicity as (lns)^η+1, and diffraction cone shrinks as (lns)^?ν, where $\text{η ≈}\text{1}\text{6}\text{, ν ≈}\text{13}\text{21}$. At modern energy the theory gives small corrections to the Regge model.     

Two-photon exchange in p⊆)p→ℓ+ℓ−X and a comparison with QCD

A thorough study of lepton-pair production from two-photon annihilation in p?)p collisions is presented. The differential cross section is calculated over a large range of energies (27?√s?800 GeV as a function of the dilepton mass M as well as the dilepton transverse momentum Q_T and the Feynman variable x_F. No kinematical approximations (such as the equivalent photon approximation) are made. For Q_T ≈ 0 the two-photon mechanism represents an important fraction of the pp→e⁺e^?X cross section already at ISR energies, whereas at ISABELLE energies it dramatically dominates in the interval 0?Q_T?1 GeV. At ISR energies these conclusions follow from a direct comparison of the two-photon contribution with pp→e⁺e^?X data. For the ISABELLE energy range the expected O(α_s) QCD contribution to pp→?⁺?^?X, corrected for soft gluon radiation to all orders (in leading bilogarithmic approximation), was taken as a reference. At larger Q_T and ISR energies the γγ contribution is negligible, whereas at √s = 800 GeV γγ/QCD? 10–20% almost everywhere. Furthermore, two-photon candidate events from the ISR are shown to be in reasonable agreement with theory. A decomposition of the γγ cross section into contributions from both proton vertices being elastic, inelastic and of mixed configuration is given. The results provide important clues for a future isolation of the two-photon mechanism.     

Behaviour of the proton-proton total cross section at ISR energies in the reggeon calculus

We study the behaviour of σ^pp_T at ISR energies in the Reggeon calculus with a bare triple Pomeron coupling non vanishing at q² = 0. The parameters are determined from elastic and inclusive data. A sizable increase of σ_T with s can only be obtained when the bare Pomeron intercept is such that the renormalized Pomeron singularity is above one, in the forward direction.     

The BFKL Pomeron in deep inelastic diffractive dissociation neart=0

The small-t behaviour of the deep inelastic diffractive dissociation cross section in the triple Regge region is investigated, using the BFKL approximation in perturbative QCD. We show that the cross section is finite att=0, but the diffusion in lnk _t ² leads to a large contribution of small momenta at the triple Pomeron vertex. We study the dependence upon the total energy and the invariant mass. Att=0, there is a decoupling of the three BFKL singularities which is a consequence of the conservation of the conformal dimension. For large invariant masses, the four gluon state in the uppert-channel plays an important role and cannot be neglected.     

Analysis of the3 He(K−,K +)n reaction by the potential quark model

We analyze the production of H dihyperson (J ^π=0⁺,S=?2) via the (K ^?, K⁺) reaction by means of the non-relativistic quark model. First, the H mass and mass spectrum of single baryons are calculated. When the single baryon spectrum is well reproduced, the H dihyperson has the binding energies about 20 MeV or 60 MeV corresponding to the choice of the strength of the confinement potential. Using this model and parameters, cross sections for H production are estimated. A new effect, contributions from color-octetQ ³?Q ³ components of H dihyperson, is taken into account. The cross sections for H production are enhanced about ten times by these contributions. TheK ⁺-neutron coincidence cross section for H production is found to be 99–115 nb/sr² at theK ⁺ forward direction forM _H=2212 MeV and theK ^? beam momentum 1.8 GeV/c.     

A possibility of asymptotic freedom without non-Abelian gauge theories

We discuss solutions of the renormalization group equations for a Yukawa field theory. For an increasing effective boson mass we find that the leading terms in the vertex functions in the high-energy region are given by diagrams which contain no internal boson lines. In e⁺e^? annihilation into hadrons we get the parton model formula R(s) = Σ_iQ_i², whereas in the deep inelastic e^?p scattering the simple parton model behaviour is modified by the (in general) non-canonical dimension of the quark field.     

High-twist correction for inclusive hadron production in photon-photon collisions

The contribution of the QCD high-twist subprocess γq→πq′ to the inclusive cross section for e⁺ e^? → e⁺ e^? + π^± + X is calculated both in the PETRA/PEP and the LEP energy range, in the equivalent-photon approximation. Superposed on the Born cross section and its O(α_s) correction, it gives agreement with the data at relatively low transverse momenta. It is suggested that this high-twist contribution may be further isolated experimentally by triggering simultaneously on both a fast hadron and the opposite-side jet.     

Renormalization scheme dependence of electroweak radiative corrections

We compare two renormalization schemes of the electroweak standard model: the on-shell scheme withe, M _W ,M _Z ,M _H , and the fermion masses {m _f } as free parameters, and an intermediate scheme where theW boson self energy is renormalized atq ²=0 instead ofq ²=M _W ². TheM _W ?M _Z interdependence, and the differentiale ⁺ e ^?→μ ⁺ μ ^? cross section including polarized beams are calculated in both schemes to one-loop order. We find striking differences between the forward-backward asymmetries and the polarization asymmetries near theZ resonance after inclusion of weak and QED corrections.     

Calculable observables in quantum chromodynamics: (II). Heavy quark production

It is argued that the color-averaged inclusive cross section dσ/d³p for the production of a heavy quark of given momentum p and given flavor is infrared-singularity free and therefore calculable in perturbative QCD if it is evaluated away from heavy quark thresholds and if the typical reaction energy Q is such that α_s(Q)ln[Q/m(Q)] is small, α_s and m being the strong coupling constant and the heavy quark mass respectively. An interpretation of this cross section is proposed in terms of heavy flavor hadronic production.     

The content of unitarity constraints on a pomeron pole of intercept one

We present a consistent picture of a pomeron pole with intercept one, together with its cuts, which evades the decoupling arguments. We use the reggeon cut discontinuity formulae to introduce Gribov's reggeon calculus as an exact solution of multiparticle t-channel unitarity. We show how, within the calculus, two-pomeron iterations of a singular kernel can be responsible for the zero in the triple-pomeron vertex. Using the concept of a bare pomeron pole as a multiperipheral production process which is subsequently renormalised by other effects, we apply the reggeon calculus analysis to inclusive cross sections. We find that the inclusive sum rule decoupling arguments are avoided because of the addition of enhanced absorptive corrections to the conventional Regge pole contributions. However, we show that in this picture the combined pole and two-pomeron cut contribution to the total cross section factories to order (ln s)^?2.We also show that, when the correct helicity structure of the pomeron is taken into account, the s-channel unitarity condition for pomeron scattering amplitudes does not lead to any serious decouplings.     

Constraints on the behaviour of the e+e− hadron annihilation cross section in asymptotically free theories and in theories with anomalous dimensions

A new approach is proposed to the problem of the relationship between the e⁺e^? hadron annihilation cross section and the behaviour of the hadronic vacuum polarization tensor Π_μν(q) in the space-like region. By using this approach based on the principles of functional analysis, one can uniquely transform the information about the behaviour of Π_μν(q) at q² → ?∞, which is available in asymptotically free theories and in theories with anomalous dimensions, into constraints on the e⁺e^? total cross section.     

Breakdown of normal threshold dispersion relation for the vacuum polarization

Stating a concrete example, it is shown that the vacuum polarization develops anomalous singularities. The analytic structure of the vacuum polarization in these circumstances is discussed in some detail. It appears that its large q² behaviour is not linked anymore to the asymptotic form of the e⁺e^? total cross section. Since it is the large q² behaviour of the vacuum polarization which solely can be calculated in asymptotically free gauge theories (giving in leading order the naive quark model result), this is a warning to using the naive quark model result for the e⁺e^? total cross section as well in fitting the data.     

Factorization and the couplings of the vacuum trajectory

The decoupling theorems associated with an isolated factorizable pomeron pole of unit intercept are re-examined. It is found that the coupling of three such poles, Γ(t, t, 0), need not vanish, precisely at the point t = 0. This is demonstrated by summing only over states in the appropriate unitarity sum, and sum rule, which are consistent with the M², s/M² → ∞ limit. The triple-Regge region then makes a constant contribution to σ_total, insteadsb of the ln lns result obtained if the isolated pole is assumed to couple also to states such that s/M² = constant. The physical implications regarding factorization and the pole-cut relationship are discussed. The relationship between higher order optical theorems (Mueller discontinuities) and particular terms in the unitarity sum for the two → two absorptive part A₂₂ is exploited. Consistent contributions to the triple-Regge region contribute constant vertex corrections to pure pole behaviour in A₂₂. There is no cut contribution and the magnitude of the vertex corrections reflects the relative amount of diffractive production. The analysis is extended to multiple fireball production where pure multipole structures emerge. The series naturally terminates if the diffractive component is sufficiently small. The implications for the behaviour of the total cross section at machine energies are discussed.     

Sum rules fore + e − annihilation in general electroweak mixing models and extended gauge theories

We derive a lower bound for the integrated cross section for production of weak neutral bosons ine ⁺ e ^? annihilation within general electroweak theories containing an arbitrary number of weak bosons. The low energy parameterC of such theories is expressed in terms of integrals over the weighted cross section fore ⁺ e ^? annihilation at high energies.     

Minimal total cross section fore + e −→W + W −

The total cross section with the most general form for the gauge boson vertices is given at tree level for the processe ⁺ e ^?→W ⁺ W ^?. Each vertex is parametrized with 7 couplings and the minimum of the total cross section is studied in a wide energy range. Although there are large cancellations between the neutrino exchange diagram and the photon andZ annihilation diagrams, it is surprisingly not possible to get significantly below the standard model cross section for any value of the parameters.     

Theoretical studies of energy-energy correlation ine + e− annihilation

We calculate theO(α _s ² ) correction to the energy-energy corelation cross section ine ⁺ e^? annihilation using different resolution criteria in the limit of vanishing resolution cuts. We compare this in the back-to-back angular region with results of the logarithm approximation (LA) and deduce higher order corrections (beyondO(α _s ² )) from the LA formula. The final results are compared with recent TASSO data.     

Measurements of inclusive pion electroproduction

Measurements of the inclusive pion electroproduction reaction e^?+p → e^?+π^±+X made at the Wilson Synchrotron Laboratory are reported. Data were taken at points with nominal (Q², W) values of (0.6, 2.67), (1.2, 2.67), (2.0, 2.67) and (1.2, 2.15) in (GeV², GeV). A more complete angular distribution was taken at (1.2, 2.67). The virtual photoproduction cross section for π⁺ + missing mass is studied as a function of missing mass, Feynman scaling variables, Q² and W. The invariant cross section show a simple behavior as a function of Q² and W. Its dependenc on P_⊥², x′ and φ is determined.     

The process γγ → X by parton model and prediction of equivalent-photon method for ee → ee + X

A parton model for the virtual photon process γ → X is examined. It is assumed that a scaling property applies and the total cross section is σ_γγ→X = s^?1φ(ξ), where the function ? is dependent on the scaling variable ξ defined by ξ = s/(q²₁q²₂). The cross section for the process ee → + X is calculated using the equivalent-photon technique.     

Influence of anomalous thresholds in electron-positron annihilation into hadrons: The e+e− → ϱππ cross section

We calculate the cross section for e⁺e^? → ?ππ on the basis of partial-wave dispersion relations in the ππ channel taking proper account of anomalous singularity contributions. The appearance of anomalous thresholds is due to the fact that the vertex γ_V?(ππ) becomes internally unstable as the virtual photon mass is increased. Reasonable agreement with existing data is found. The anomalous singularity contributions provide by far the dominant part of the cross section which is a warning to using naive vector dominance extrapolations in estimating the electron-positron cross section.     

Double pomeron exchange in the reaction pp → ppπ+π−

We compute the cross section for pp → ppπ⁺π^? in the kinematical region for which two-pomeron exchange is important, assuming dominance of the pion-exchange pole. We include effects due to absorption, final-state interaction, and interference between the two contributing Feynman diagrams. These effects have been ignored in previous calculations. Consequently, our predicted cross section is smaller than previous predictions by a factor of ～ 3, and is consistent with experimental indications. We calculate the background cross section in the double pomeron exchange region, and find that it is sizable even at s ～ 3000 GeV². We discuss the two-particle inclusive process pp → ppX.