Average formation length in string model

The space-time scales of the hadronization process in the framework of string model are investigated. It is shown that the average formation lengths of pseudoscalar mesons, produced in semi-inclusive deep inelastic scattering (DIS) of leptons on different targets, depend from their electrical charges. In particular the average formation lengths of positively charged hadrons are larger than of negatively charged ones. This statement is fulfiled for all using scaling functions, for $z$ (the fraction of the virtual photon energy transferred to the detected hadron) larger than 0.15, for all nuclear targets and any value of the Bjorken scaling variable $x_{Bj}$. In all cases, the main mechanism is direct production of pseudoscalar mesons. Including in consideration additional mechanism of production in result of decay of resonances, leads to decrease of average formation lengths. It is shown that the average formation lengths of positively (negatively) charged mesons are slowly rising (decreasing) functions of $x_{Bj}$. The obtained results can be important, in particular, for the understanding of the hadronization process in nuclear environment

Concept of Formation Length in Radiation Theory

The features of electromagnetic processes are considered which connected with finite size of space region in which final particles (photon, electron-positron pair) are formed. The longitudinal dimension of the region is known as the formation length. If some external agent is acting on an electron while traveling this distance the emission process can be disrupted. There are different agents: multiple scattering of projectile, polarization of a medium, action of external fields, etc. The theory of radiation under influence of the multiple scattering, the Landau-Pomeranchuk-Migdal (LPM) effect, is presented. The probability of radiation is calculated with an accuracy up to "next to leading logarithm" and with the Coulomb corrections taken into account. The integral characteristics of bremsstrahlung are given, it is shown that the effective radiation length increases due to the LPM effect at high energy. The LPM effect for pair creation is also presented. The multiple scattering influences also on radiative corrections in a medium (and an external field too) including the anomalous magnetic moment of an electron and the polarization tensor as well as coherent scattering of a photon in a Coulomb field. The polarization of a medium alters the radiation probability in soft part of spectrum. Specific features of radiation from a target of finite thickness include: the boundary photon emission, interference effects for thin target, multi-photon radiation. The experimental study of LPM effect is described. For electron-positron colliding beams following items are discussed: the separation of coherent and incoherent mechanisms of radiation, the beam-size effect in bremsstrahlung, coherent radiation and mechanisms of electron-positron creation.Comment: Revised review paper, 96 pages, 28 figures. Description of SLAC E-146 experiment removed, discussion of CERN SPS experiment adde

Lorentz Invariance Violation and the QED Formation Length

It was recently suggested that possible small volations of Lorentz invariance could explain the existence of UHECR beyond the GZK cutoff and the observations of multi-TeV gamma-rays from Mkn 501. Our analysis of Lorentz-violating kinematics shows that in addition to the modified threshold conditions solving cosmic ray puzzles we should expect a strong suppression of electromagnetic processes like bremsstrahlung and pair creation. This leads to drastic effects in electron-photon cascade development in the atmosphere and in detectors.Comment: 9 pages, some new comments and references adde

Anomalous mass dependence of radiative quark energy loss in a finite-size quark-gluon plasma

We demonstrate that for a finite-size quark-gluon plasma the induced gluon radiation from heavy quarks is stronger than that for light quarks when the gluon formation length becomes comparable with (or exceeds) the size of the plasma. The effect is due to oscillations of the light-cone wave function for the in-medium $q\to gq$ transition. The dead cone model by Dokshitzer and Kharzeev neglecting quantum finite-size effects is not valid in this regime. The finite-size effects also enhance the photon emission from heavy quarks.Comment: 8 pages, 3 figure

On the Energy Loss of High Energy Quarks in a Finite-Size Quark-Gluon Plasma

We study within the light-cone path integral approach the induced gluon emission from a fast quark passing through a finite-size QCD plasma. We show that the leading log approximation used in previous studies fails when the gluon formation length becomes of the order of the length of the medium traversed by the quark. Calculation of the energy loss beyond the leading log approximation gives the energy loss which grows logarithmically with quark energy contrary to the energy independent prediction of the leading log approximation.Comment: 7 pages, 0 figure