QED in a Strong External Magnetic Field: Beyond the Constant Mass Approximation

We solve the Schwinger-Dyson equations for QED in 2+1 or 3+1 dimensions in the presence of a strong homogeneous external magnetic field. The magnetic field is assumed strong enough, so that the lowest Landau level approximation holds, but the usual assumption of a momentum-independent self-energy is not made. In 2+1 dimensions, the scaling with logarithm changes to a square root dependence on the magnetic field, but the most spectacular result takes place in 3+1 dimensions, where the constant mass approximation turns out to be unreliable and the (momentum-dependent) dynamical mass is larger by several orders of magnitude compared to what has been found till now using the constant mass approximation.Comment: 21 pages, 8 figures, plain latex, references adde

Multiplicity Distribution and Mechanisms of the High-Energy Hadron Collisions

We discuss the multiplicity distribution for highest accessible energies of $pp$- and $\bar pp$- interactions from the point of view of the multiparton collisions. The inelastic cross sections for the single, $\sigma_1$, and multiple (double and, presumably, triple, $\sigma_{2+3}$) parton collisions are extracted from the analysis of the experimental data on the multiplicity distribution up to the Tevatron energies. It follows that $\sigma_1$ becomes energy independent while $\sigma_{2+3}$ increases with $\sqrt{s}$ for $\sqrt{s}\ge$ 200 GeV. The observed growth of $$ with multiplicity is attributed to the increasing role of multiparton collisions for the high energy $\bar pp(pp)$- inelastic interactions.Comment: Revtex file, 17 pages, 5 figure