M.G. Schmidt

Worldline Green functions for multiloop diagrams

Abstract We propose a multiloop generalization of the Bern-Kosower formalism, based on Strasslers approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop graph, and for a loop with an arbitrary number of propagator insertions. For scalar and abelian gauge theories, the resulting integral representations allow to combine whole classes of Feynman diagrams into compact expressions.

Hadron scattering in two-dimensional QCD: (II). Second-order calculations, multi-Regge and inclusive reactions

Hadron scattering is studied in higher orders of the 1/Nc expansion for quantum chromodynamics in two dimensions. In order 1/Nc2, individual pomeron-like cylinder graphs give a forward amplitude growing as s, but cancellations in their sum remove this embryonic pomeron. The cancellations reflect colour gauge invariance in a way specific to two dimensions. Otherwise, 1/Nc2 diagrams yield the expected “Regge” pole renormalizations and “cut” singularities. Factorizing multi-Regge behaviour is demonstrated for higher point functions. Final-state hadron distributions in hadronic and deep inelastic collisions are closely related.

Hadron scattering in two-dimensional QCD I Formalism and leading order calculations

Abstract Two-dimensional quantum chromodynamics in the 1/Nc expansion is explored as a model for hadronic interactions. In meson-meson scattering, order 1/Nc terms exhibit embryonic “Regge” behaviour, with the crossed channel factorization, signature and exchange degeneracy properties found in dual Regge models. “Regge” intercepts are additive in the quark quantum numbers exchanged, and have a lower limit for large quark masses. Residues also factorize in the direct channel. An analogue for fixed angle scattering is presented which has deviations from dimensional counting rules related to form factors and Regge intercepts.

The instanton-induced vacuum structure of SQCD

Abstract The vacuum condensates of supersymmetric QCD with an arbitrary number of flavors (below the asymptotic freedom bound) are calculated by extending previous instanton methods. The outcome is in complete agreement with large-distance clustering and with the effective lagrangian results.

High-energy scattering in a two-dimensional gauge theory

Abstract 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.

Structure of hadron in Migdal's regularization scheme for QCD

Abstract Migdals approach to the spectrum of QCD is generalized to three-point (hadron) amplitudes. This procedure is shown to be unique once the two-point functions are known. In particular, meson form factors and structure functions are discussed including hard gluon and Regge contributions. Quark mass effects turn out to be very important.

Threshold behaviour of pion structure functions probed in inclusive e+e− annihilation

Abstract The inclusive e + e − annihilation cross-section is analyzed with respect to the threshold behaviour of the (short distance) pion structure functions, taking proper account of anomalous threshold contributions. The threshold behaviour is found to be (1 − x ) rather than (1 − x ) 2 as one might infer from the SPEAR data.

Narrow baryonium states in QCD

Abstract The unconventional states of qqqq, qq and pure gluon type, appearing in BB dual diagrams with nonplanar baryons are discussed, treating their interpolating fields in a confinement approach to QCD due to Migdal. The mass spectrum is given to lowest order and the quantum numbers are discussed. It is argued that some of the resonances should have narrow width and hence could be identified with the narrow resonances in pp scattering.

Lepton pair production in two-dimensional QCD

Abstract Large q2 lepton pair production is calculated in leading order in 1/Nc in two-dimensional quantum chromodynamics (QCD). From this confinement model the (Drell-Yan) parton model result is recovered.

How asymptotic freedom predictions for R = σ(e+e− → hadrons)/σ(e+e− → μ+μ−) lead to a paradox

Abstract Describing the total cross-section via the one-hadron inclusive distribution e + e − → h + X, we are led into a contradiction to the asymptotic freedom (naive quark-parton model) result R = ΣQ j 2 .