Coulomb effects in the spin-dependent contribution to the intra-beam scattering rate

Coulomb effects in the intra-beam scattering are taken into account in a way providing correct description of the spin-dependent contribution to the beam loss rate. It allows one to calculate this rate for polarized $e^{\pm}$ beams at arbitrarily small values of the ratio $\delta \varepsilon/\varepsilon$, characterizing relative change of the electron energy in the laboratory system during scattering event.Comment: 8 pages, 2 figure

Averages of shifted convolutions of d3(n)d_3(n)

We investigate the first and second moments of shifted convolutions of the generalised divisor function $d_3(n)$.Comment: 22 page

Photon Splitting in a Very Strong Magnetic Field

Photon splitting in a very strong magnetic field is analyzed for energy $\omega < 2m$. The amplitude obtained on the base of operator-diagram technique is used. It is shown that in a magnetic field much higher than critical one the splitting amplitude is independent on the field. Our calculation is in a good agreement with previous results of Adler and in a strong contradiction with recent paper of Mentzel et al.Comment: 5 pages,Revtex , 4 figure

Angular Dependence of the Radiative Gluon Spectrum and the Energy Loss of Hard Jets in QCD Media

The induced momentum spectrum of soft gluons radiated from a high energy quark propagating through a QCD medium is derived in the BDMPS formalism. A calorimetric measurement for the medium dependent energy lost by a jet with opening angle $\theta_{{\rm cone}}$ is proposed.The fraction of this energy loss with respect to the integrated one appears to be the relevant observable.It exhibits a universal behaviour in terms of the variable $\theta^2_{{\rm cone}} L^3 \hat q$ where $L$ is the size of the medium and $\hat q$ the transport coefficient. Phenomenological implications for the differences between cold and hot QCD matter are discussed.Comment: 13 pages and 7 figures, RevTe

Medium-induced gluon radiation and jet quenching in heavy ion collisions

In this brief review, I summarize the new developments on the description of gluon radiation by energetic quarks traversing a medium as well as the observable consequences in high-energy heavy ion collisions. Information about the initial state is essential for a reliable interpretation of the experimental results and will also be reviewed. Comparison with experimental data from RHIC and expectation for the future LHC will be given.Comment: 16 pages, 9 postscript figures. Invited brief review for Modern Physics Letters

Remarks on transient photon production in heavy ion collisions

In this note, we discuss the derivation of a formula that has been used in the literature in order to compute the number of photons emitted by a hot or dense system during a finite time. Our derivation is based on a variation of the standard operator-based $S$-matrix approach. The shortcomings of this formula are then emphasized, which leads to a negative conclusion concerning the possibility of using it to predict transient effects for the photon rate.Comment: 13 page

Multi-photon effects in energy losses spectra

Effect of radiation of many photons by a single electron traversing a target is discussed. When the summary energy of emitted photons (the energy losses spectrum) is measured only, the photon spectrum is distorted comparing with the photon spectrum in one interaction. Influence of this effect is discussed for the cases (1) bremsstrahlung (described by Bethe-Heitler formula), (2) the strong Landau-Pomeranchuk-Migdal effect and (3) transition radiation. Qualitative picture of the phenomenon is discussed in detail. Comparison with the recent SLAC experiment in relatively thick target (2.7% of the radiation length), where the effect of emission of many photons by a projectile is very essential, shows perfect agreement of the theory and data.Comment: LaTeX2.09, 19 pages, 5 PostScript figure

Zero-Reachability in Probabilistic Multi-Counter Automata

We study the qualitative and quantitative zero-reachability problem in probabilistic multi-counter systems. We identify the undecidable variants of the problems, and then we concentrate on the remaining two cases. In the first case, when we are interested in the probability of all runs that visit zero in some counter, we show that the qualitative zero-reachability is decidable in time which is polynomial in the size of a given pMC and doubly exponential in the number of counters. Further, we show that the probability of all zero-reaching runs can be effectively approximated up to an arbitrarily small given error epsilon > 0 in time which is polynomial in log(epsilon), exponential in the size of a given pMC, and doubly exponential in the number of counters. In the second case, we are interested in the probability of all runs that visit zero in some counter different from the last counter. Here we show that the qualitative zero-reachability is decidable and SquareRootSum-hard, and the probability of all zero-reaching runs can be effectively approximated up to an arbitrarily small given error epsilon > 0 (these result applies to pMC satisfying a suitable technical condition that can be verified in polynomial time). The proof techniques invented in the second case allow to construct counterexamples for some classical results about ergodicity in stochastic Petri nets.Comment: 20 page

Abelian Landau-Pomeranchuk-Migdal effects

It is shown that the high-energy expansion of the scattering amplitude calculated from Feynman diagrams factorizes in such a way that it can be reduced to the eikonalized form up to the terms of inverse power in energy in accordance with results obtained by solving the Klein-Gordon equation. Therefore the two approaches when applied to the suppression of the emission of soft photons by fast charged particles in dense matter should give rise to the same results. A particular limit of thin targets is briefly discussed.Comment: 14 pages, LATEX, 1 Fig. ps, submitted to Mod. Phys. Lett.

Induced Gluon Radiation in a QCD Medium

Soft gluon radiation induced by multiple scattering of a fast quark or gluon propagating through QCD matter is discussed. After revisiting the Landau-Pomeranchuk-Migdal effect in QED we show that large formation times of bremsstrahlung quanta determine the QCD radiation intensity (in analogy to QED) and derive the gluon energy spectrum. Coherent suppression takes place as compared to the Bethe-Heitler situation of independent emissions. As a result the energy loss of fast partons in a QCD medium depends on the incident energy $E$ similarly to QED, $-dE/dz \propto \sqrt{E}$.Comment: 13 pages, 3 included figures, latex fil