Euler potentials for the MHD Kamchatnov-Hopf soliton solution

In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf invariant of the mapping of a 3D sphere into a 2D sphere; it can have arbitrary helicity depending on control parameters. It is shown how to define Euler potentials globally. The singular curve of the Euler potential plays the key role in computing helicity. With the introduction of Euler potentials, the helicity can be calculated as an integral over the surface bounded by this singular curve. A special programme for visualization is worked out. Helicity coordinates are introduced which can be useful for numerical simulations where helicity control is needed.Comment: 15 pages, 12 figure

Point-form quantum field theory and meson form factors

We shortly review point-form quantum field theory, i.e. the canonical quantization of a relativistic field theory on a Lorentz-invariant surface of the form $x_\mu x^\mu = \tau^2$. As an example of how point-form quantum field theory may enter the framework of relativistic quantum mechanics we discuss the calculation of the electromagnetic form factor of a confined quark-antiquark pair (e.g. the pion).Comment: 3 pages, 2 figures. Based on a talk presented by W. Schweiger at the 20th European Conference on Few-Body Problems in Physics, September 10-14 2007, Pisa, Ital

Reggeon and pion contributions in semi-exclusive diffractive processes at HERA

A detailed analysis of semi-exclusive diffractive processes in e-p DIS at HERA, with the diffractive final states in the forward direction is presented. The contributions of the subleading f_2, \omega, a_2, \rho reggeons and the pion exchanges to the diffractive structure function with the forward proton or neutron are estimated. It is found that the (a_2,\rho) reggeons are entirely responsible for the forward neutron production at x_P < 10^{-3}. The \pi N production in the forward region is estimated using the Deck mechanism. The significance of this reaction for the processes measured at HERA, especially with the leading neutron, is discussed.Comment: Strongly revised version accepted for publication in Phys.Rev.D. Latex, 14 pages with 5 eps figures include

Solving QCD evolution equations in rapidity space with Markovian Monte Carlo

This work covers methodology of solving QCD evolution equation of the parton distribution using Markovian Monte Carlo (MMC) algorithms in a class of models ranging from DGLAP to CCFM. One of the purposes of the above MMCs is to test the other more sophisticated Monte Carlo programs, the so-called Constrained Monte Carlo (CMC) programs, which will be used as a building block in the parton shower MC. This is why the mapping of the evolution variables (eikonal variable and evolution time) into four-momenta is also defined and tested. The evolution time is identified with the rapidity variable of the emitted parton. The presented MMCs are tested independently, with ~0.1% precision, against the non-MC program APCheb especially devised for this purpose.Comment: version compatible with with the erratum in Acta Physica Polonic

Electromagnetic meson form factor from a relativistic coupled-channel approach

Point-form relativistic quantum mechanics is used to derive an expression for the electromagnetic form factor of a pseudoscalar meson for space-like momentum transfers. The elastic scattering of an electron by a confined quark-antiquark pair is treated as a relativistic two-channel problem for the $q\bar{q}e$ and $q\bar{q}e\gamma$ states. With the approximation that the total velocity of the $q\bar{q}e$ system is conserved at (electromagnetic) interaction vertices this simplifies to an eigenvalue problem for a Bakamjian-Thomas type mass operator. After elimination of the $q\bar{q}e\gamma$ channel the electromagnetic meson current and form factor can be directly read off from the one-photon-exchange optical potential. By choosing the invariant mass of the electron-meson system large enough, cluster separability violations become negligible. An equivalence with the usual front-form expression, resulting from a spectator current in the $q^+=0$ reference frame, is established. The generalization of this multichannel approach to electroweak form factors for an arbitrary bound few-body system is quite obvious. By an appropriate extension of the Hilbert space this approach is also able to accommodate exchange-current effects.Comment: 30 pages, 5 figure

Shrinkers, expanders, and the unique continuation beyond generic blowup in the heat flow for harmonic maps between spheres

Using mixed analytical and numerical methods we investigate the development of singularities in the heat flow for corotational harmonic maps from the $d$-dimensional sphere to itself for $3\leq d\leq 6$. By gluing together shrinking and expanding asymptotically self-similar solutions we construct global weak solutions which are smooth everywhere except for a sequence of times $T_1<T_2<...<T_k<\infty$ at which there occurs the type I blow-up at one of the poles of the sphere. We show that in the generic case the continuation beyond blow-up is unique, the topological degree of the map changes by one at each blow-up time $T_i$, and eventually the solution comes to rest at the zero energy constant map.Comment: 24 pages, 8 figures, minor corrections, matches published versio

Cronin Effect in Hadron Production off Nuclei

Recent data from RHIC for high-$p_T$ hadrons in gold-gold collisions raised again the long standing problem of quantitatively understanding the Cronin effect, i.e. nuclear enhancement of high-$p_T$ hadrons due to multiple interactions in nuclear matter. In nucleus-nucleus collisions this effect has to be reliably calculated as baseline for a signal of new physics in high-$p_T$ hadron production. The only possibility to test models is to compare with available data for $pA$ collisions, however, all existing models for the Cronin effect rely on a fit to the data to be explained. We develop a phenomenological description based on the light-cone QCD-dipole approach which allows to explain available data without fitting to them and to provide predictions for $pA$ collisions at RHIC and LHC. We point out that the mechanism causing Cronin effect drastically changes between the energies of fixed target experiments and RHIC-LHC. High-$p_T$ hadrons are produced incoherently on different nucleons at low energies, whereas the production amplitudes interfere if the energy is sufficiently high.Comment: the final version to appear in Phys. Rev. Let

Self-similar solution of fast magnetic reconnection: Semi-analytic study of inflow region

An evolutionary process of the fast magnetic reconnection in ``free space'' which is free from any influence of outer circumstance has been studied semi-analytically, and a self-similarly expanding solution has been obtained. The semi-analytic solution is consistent with the results of our numerical simulations performed in our previous paper (see Nitta et al. 2001). This semi-analytic study confirms the existence of self-similar growth. On the other hand, the numerical study by time dependent computer simulation clarifies the stability of the self-similar growth with respect to any MHD mode. These results confirm the stable self-similar evolution of the fast magnetic reconnection system.Comment: 15 pages, 7 figure

γ∗γ∗→ρρ\gamma ^* \gamma ^* \to \rho \rho at very high energy

The next generation of $e^+e^-$-colliders will offer a possibility of clean testing of QCD dynamics in the Regge limit. Recent progress in the theoretical description of exclusive processes permits for many of them a consistent use of the perturbative QCD methods. We advocate that the exclusive diffractive production of two $\rho$ mesons from virtual photons at very high energies should be measurable at the future linear collider (LC).Comment: 4 pages, 2 figures, talk given at the conference Baryon 0