Spin dependence of deep inelastic diffraction

Using a perturbative model for diffractive interactions, we derive an expression for the polarized diffractive structure function in the high energy limit. This structure function is given by the interference of diffractive amplitudes with polarized and unpolarized exchanges. For the polarized exchange we consider both two-gluon and quark-antiquark amplitudes. The polarized diffractive amplitude receives sizable contributions from non-strongly ordered regions in phase space, resulting in a double logarithmic enhancement at small x. The resummation of these double logarithmic terms is outlined. We also discuss the transition from our perturbative expression to the nonperturbative region. A first numerical estimate indicates that the perturbative contribution to the spin asymmetry is substantially larger than the nonperturbative one. Received: 7 July 1999 / Published online: 14 October 1999     

Calculation of graviton scattering amplitudes using string-based methods

Techniques based upon the string organisation of amplitudes may be used to simplify field theory calculations. We apply these techniques to perturbative gravity and calculate all one-loop amplitudes for four-graviton scattering with arbitrary internal particle content. Decomposing the amplitudes into contributions arising from supersymmetric multiplets greatly simplifies these calculations. We also discuss how unitarity may be used to constrain the amplitudes.     

Next-to-next-to-leading-order logarithmic corrections at small transverse momentum in hadronic collisions

We study the region of small transverse momenta in q&qmacr;- and gg-initiated processes with no colored particle detected in the final state. We present the universal expression of the O(alpha(2)(s)) logarithmically enhanced contributions up to next-to-next-to-leading-order logarithmic accuracy. From there we extract the coefficients that allow the resummation of the large logarithmic contributions. We find that the coefficient known in the literature as B((2)) is process dependent, since it receives a hard contamination from the one-loop correction to the leading-order subprocess. We present the general result of B((2)) for both quark and gluon channels.     

A fresh look at generalized Veneziano amplitudes

The dual resonance model, which was a precursor of string theory was based upon the idea that two-particle scattering amplitudes should be expressible equivalently as a sum of contributions of an infinite number of s channel poles each corresponding to a finite number of particles with definite spin, or as a similar sum of t channel poles. The famous example of Veneziano [Nuovo Cimento A 57 (1968) 190] satisfies all these requirements, and is additionally ghost free. We recall other trajectories which provide solutions to the duality constraints, e.g. the general Mobiüs trajectories and the logarithmic trajectories, which were thought to be lacking this last feature. We however demonstrate, partly empirically, the existence of a regime within a particular deformation of the Veneziano amplitude for logarithmic trajectories for which the 4-point amplitude remains ghost free.     

Improved πN partial waves,consistent with analyticity and unitarity

Partial wave dispersion relations in a new formulation and fixed-s dispersion relations are used to calculate the long range contributions to the real parts of πN amplitudes. Recent results from a double spectral function calculation are applied for constraining the imaginary parts. We propose to use the new partial waves as starting values in future phase shift analyses and to treat our prediction for the tail of high partial waves as part of the input. — The differences between our new partial waves and the Karlsruhe-Helsinki 80 and CMU-LBL 80 solutions are discussed. Concerning measurable quantities, the new parital waves lead to significant changes in the forward logarithmic slopes of differential cross sections. — Thel-dependence of our partial waves is discussed up to large values ofl. We find a systematic even-l, odd-l splitting at all energies.     

Helicity conservation in gauge boson scattering at high energy

We remark that the high energy gauge boson scattering processes involving two-body initial and final states satisfy certain selection rules described as helicity conservation of the gauge boson amplitudes (GBHC). These rules are valid at the Born level, as well as at the level of the leading and subleading 1-loop logarithmic corrections, in both the standard model and the minimal supersymmetric standard model (MSSM). A "fermionic equivalence" theorem is also proved, which suggests that GBHC is valid at all orders in the MSSM at sufficiently high energies, where the mass suppressed contributions are neglected.     

Invariant Amplitudes for Coherent Electromagnetic Pseudoscalar Production from a Spin-One Target

A set of 13 linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle is derived which respect Lorentz and gauge invariance. The -matrix can be represented by a linear superposition of these amplitudes with invariant functions as coefficients, which depend on the Mandelstam variables only. Their explicit form is determined by the underlying dynamics. Nine of these amplitudes are purely transverse and describe photoproduction. The remaining four appear in electroproduction in addition, describing charge and longitudinal current contributions. Furthermore, a reduction of these amplitudes to operators acting in non-relativistic spin space is given. Received September 30, 1998; accepted for publication October 22, 1998     

Hard exclusive meson production and nonforward parton distributions

We present an analysis of twist-2, leading order QCD amplitudes for hard exclusive leptoproduction of mesons in terms of double/nonforward parton distribution functions. After reviewing some general features of nonforward nucleon matrix elements of twist-2 QCD string operators, we propose a phenomenological model for quark and gluon nonforward distribution functions. The corresponding QCD evolution equations are solved in the leading logarithmic approximation for flavor nonsinglet distributions. We derive explicit expressions for hard exclusive , , and neutral vector meson production amplitudes and discuss general features of the corresponding cross sections. Received: 12 November 1997 / Published online: 26 February 1998     

The space-time picture of the Wee partons and the AGK cutting rules in perturbative QCD

We discuss the space-time picture of scattering amplitudes with single and double ladder exchange in perturbative QCD. Particular emphasis is given to the Abramovsky Gribov Kanchelli (AGK) rules which describe the relative contributions of the diffractive dissociation and processes with other multiplicities to the elastic scattering amplitude. Inside the Pomeron Pomeron interaction vertices we find a new matrix which describes the transition from one s-cut to another and which goes beyond the original AGK rules.     

Heavy quarkonium production in double pomeron exchange processes in perturbative QCD

We calculate the heavy quarkonium production in double pomeron exchange processes in perturbative QCD by using two-gluon exchange model. For the P-wave χ_J productions, we find χ₁ and χ₂ production amplitudes which vanish in the forward scattering limit. We also calculate direct J/ψ()+γ production in the same approach, and these direct contributions are much smaller than the feeddown contributions from the P-wave states.     

(Quasi)elastic large-angle electron-muon scattering in the two-loop approximation: Contributions of the eikonal type

A part of the eikonal-type contributions to the eμ large-angle high-energy scattering cross section is considered in a quasielastic experimental setup. In addition to virtual corrections, we examine inelastic processes with emission of one and two soft real photons and soft lepton and pion pairs. Virtual photon contributions are given within a logarithmic accuracy. Box-type Feynman amplitudes with leptonic and a hadronic vacuum polarization insertion and double-box ones are considered explicitly. Wherever appropriate, the analytic expressions obtained are compared with those predicted by the structure function approach.     

Double Regge exchange phenomenology

We construct a double Regge exchange amplitude which has the proper analytic structure and which is phenomenologically viable. The various couplings involved can be estimated using pole extrapolation techniques which are successful in two-body scattering. We explicitly calculate the double Regge exchange contributions to the well-measured, and related, processes K^±p → K⁰π^±p and π^?p → K^?K⁰p. In this way the observed features of the dimeson partial-wave production amplitudes are used to text the double-exchange approach.     

Low-energy limit of parity-violating amplitudes and anomaly cancellations in type-I superstrings

The low-energy limit of parity-violating one-loop amplitudes with external six gauge bosons is studied in type-I superstring theory. The leading contributions come from the integration region near the boundaries of moduli space and give the same anomaly as in the effective particle field theory.     

Inclusive single particle density in configuration space from the QCD-cascade in DLA approximation

The structure of the QCD gluonic cascade in configuration space is investigated. The explicit form of the inclusive single particle density matrix and single particle density in configuration space transverse coordinates is derived in the double logarithmic approximation (DLA) of QCD. The possible simplification of the multiparton density matrix formalism for DLA approach is found and discussed. Received: 18 November 1997 / Published online: 26 February 1998     

Two-dimensional integrodifferential equations for unequal mass particle systems

The two-variable Integrodifferential Equation Approach (IDEA) valid for A nucleons is generalized to describe quantum mechanical systems consisting of A, unequal mass, particles. The method is based on an expansion of the wave function in Faddeev amplitudes for the various particle pairs and a subsequent expansion of them in terms of Potential Harmonics. Projecting the resulting Faddeev-type equations on a specific two-body space and spin-isospin channel one obtains coupled, two-variable, integrodifferential equations describing the system. These equations can be readily applied, for example, to hypernuclear systems such as the double hypernucleus ΛΛα which can be handled either as a three- or as a six-body problem. We demonstrate our approach by applying it to various single and double hypernuclei and compare the results to those obtained by other methods.     

An update on the evolution of double parton distributions

We consider double parton distributions in the general case in which the virtualities of the interacting partons are different. We elaborate the corresponding evolution equations and their extension to next-to-leading logarithmic accuracy.     

The \gamma \gamma \to \gamma \gamma process in the standard and SUSY models at high energies

We study the helicity amplitudes of the process at high energy, which in the standard and SUSY models first arise at the one-loop order. In the standard model (SM), the diagrams involve , charged-quark, and lepton loops, while in SUSY, we also have contributions from chargino-, charged-sfermion, and Higgs-loop diagrams. The SUSY contributions are most important in the region above the threshold for producing the supersymmetric partners; there, they interfere most effectively with the primarily imaginary SM amplitudes. Simple expressions for the relevant one-loop functions are given which provide a direct overview of the behaviour of the helicity amplitudes in the whole parameter space at high energies. The various characteristics of a large set of observables are studied in detail. Received: 3 February 1999 / Pulished online: 30 June 1999     

The Hilbert-Schmidt method for nucleon-deuteron scattering

The Hilbert-Schmidt technique is used for computing the divergent multiple-scattering series for scattering of nucleons by deuterons at energies above the deuteron breakup. We have found that for each partial amplitude a series ofs-channel resonances diverges because of the logarithmic singularities which reflect thet-channel singularities of the total amplitude. However, the convergence of the Hilbert-Schmidt series may be improved by iterating the Faddeev equations thereby extracting the most strong logarithmic singularities. We show that the series for the amplitudes with the first two iteration subtracted converges rapidly. Our final results are in excelent agreement with exact results obtained by a direct matrix technique.     

On the equations of state in quantum statistical mechanics

By extending methods previously used to study the equations of state at low temperature, it is shown that the entropy density and the statistical average of a conserved, non-spontaneously violated, charge density can be expanded in terms of integrals over products of many body n-point amplitudes defined for real, continuous frequencies. The general structure of the expansions is described, and it is demonstrated that essentially the same spectral function determines the entropy density and the average charge densities. Certain classes of terms are worked out in detail, and the formal sum of one such class is shown to provide the contributions to the equations of state arising from composite quasiparticles associated with the poles of the n-point amplitudes. [Another term, discussed in many previous works, involves the logarithms of the elementary propagators and yields the contributions to the equations of state coming from elementary quasiparticles.]The Appendices include an extensive study of the analytic properties of many body amplitudes in the frequencies of the external and internal lines. Specialized to zero temperature, these considerations apply to the Feynman diagrams for elementary particle amplitudes.     

Finite fermion mass effects in pseudoscalar Higgs production via gluon–gluon fusion

We compute the leading logarithmic behaviour of the cross-section for the production of a pseudoscalar Higgs boson in gluon–gluon fusion to all-orders in perturbation theory, in the limit of large partonic centre of mass energy. We also calculate the Higgs rapidity distribution to the same accuracy. We include the contributions of top and bottom quarks, together with their interference. Our results are given in terms of single and double integrals, evaluated explicitly up to next-to next-to leading order (NNLO). We use our results to improve the known NNLO inclusive cross-section computed in the effective theory where the fermions in the loop are integrated out. The size of finite fermion mass effects on the inclusive cross-section is found to be small, reaching a few percent only for large values of the pseudoscalar mass.