Multiple electromagnetic electron positron pair production in relativistic heavy ion collisions

We calculate the cross sections for the production of one and more electron-positron pairs due to the strong electromagnetic fields in relativistic heavy ion collisions. Using the generating functional of fermions in an external field we derive the N-pair amplitude. Neglecting the antisymmetrisation in the final state we find that the total probability to produce N pairs is a Poisson distribution. We calculate total cross sections for the production of one pair in lowest order and also include higher-order corrections from the Poisson distribution up to third order. Furthermore we calculate cross sections for the production of up to five pairs including corrections from the Poisson distribution.Comment: 13 pages REVTeX, 4 Postscript figures, This and related papers may also be obtained from http://www.phys.washington.edu/~hencken

Biomechanical comparison of the track start and the modified one-handed track start in competitive swimming: an intervention study

This study compared the conventional track and a new one-handed track start in elite age group swimmers to determine if the new technique had biomechanical implications on dive performance. Five male and seven female GB national qualifiers participated (mean ± SD: age 16.7 ± 1.9 years, stretched stature 1.76 ± 0.8 m, body mass 67.4 ± 7.9 kg) and were assigned to a control group (n = 6) or an intervention group (n = 6) that learned the new onehanded dive technique. All swimmers underwent a 4-week intervention comprising 12 ± 3 thirty-minute training sessions. Video cameras synchronized with an audible signal and timing suite captured temporal and kinematic data. A portable force plate and load cell handrail mounted to a swim starting block collected force data over 3 trials of each technique. A MANCOVA identified Block Time (BT), Flight Time (FT), Peak Horizontal Force of the lower limbs (PHF) and Horizontal Velocity at Take-off (Vx) as covariates. During the 10-m swim trial, significant differences were found in Time to 10 m (TT10m), Total Time (TT), Peak Vertical Force (PVF), Flight Distance (FD), and Horizontal Velocity at Take-off (Vx) (p < .05). Results indicated that the conventional track start method was faster over 10 m, and therefore may be seen as a superior start after a short intervention. During training, swimmers and coaches should focus on the most statistically significant dive performance variables: peak horizontal force and velocity at take-off, block and flight time

Equivalent Photon Approach to Simultaneous Excitation in Heavy Ion Collision

We apply the Equivalent Photon Approximation to calculate cross sections for the simultaneous excitation of two heavy ions in relativistic collisions. We study especially the excitation of two nuclei to a 1- - state and show that the equations are symmetric with respect to both ions. We also examine the limit in which the excitation energy of one of the nuclei goes to zero, which gives the elastic case. Finally a few remarks about the limits of this approach are made.Comment: 9 pages REVTex, 4 Figures included, see also http://www.phys.washington.edu/~hencken

QCD and QED dynamics of the EMC effect

Applying exact QCD sum rules for the baryon charge and energy-momentum we demonstrate that if nucleons are the only degrees of freedom of nuclear wave function, the structure function of a nucleus would be the additive sum of the nucleon distributions at the same Bjorken x = AQ^2/2(p_Aq)< 0.5 up to very small Fermi motion corrections if x>0.05. Thus the difference of the EMC ratio from one reveals the presence of non-nucleonic degrees of freedom in nuclei. Using exact QCD sum rules we show that the ratio R_A(x_p,Q^2) used in experimental studies, where x_p = Q^2/2q_0 m_p deviates from one even if a nucleus consists of nucleons with small momenta only. Use of the Bjorken x leads to additional decrease of R_A(x,Q^2) as compared to the x_p plots. Coherent contribution of equivalent photons into photon component of parton wave function of a nucleus unambiguously follows from Lorentz transformation of the rest frame nucleus Coulomb field. For A~200 photons carry ~0.0065 fraction of the light momentum of nucleus almost compensates the difference between data analysis in terms of Bjorken x and x_p. Different role of higher twist effects for Q^2 probed at electron and muon beams is emphasized. Direct observations of large and predominantly nucleonic short-range correlations in nuclei pose a serious challenge for most of the models of the EMC effect for x>0.6. The data are consistent with a scenario in which the hadronic EMC effect reflects fluctuations of inter nucleon interaction due to fluctuations of color distribution in the interacting nucleons. The dynamic realization of this scenario is the model in which the 3q (3qg) configurations with x > 0.5 parton have a weaker interaction with nearby nucleons, leading to suppression of such configurations giving a right magnitude of the EMC effect. The directions for the future studies and challenging questions are outlined.Comment: The sign in the relation of x_Bj and x_p is corrected and the following discussion is adjusted accordingly. Discussion of the higher twist effects is adde

Production of QED pairs at small impact parameter in relativistic heavy ion collisions

The STAR collaboration at RHIC is measuring the production of electron-positron pairs at small impact parameters, larger than but already close to the range, where the ions interact strongly with each other. We calculate the total cross section, as well as, differential distributions of the pair production process with the electromagnetic excitation of both ions in a semiclassical approach and within a lowest order QED calculation. We compare the distribution of electron and positron with the one coming from the cross section calculation without restriction on impact parameter. Finally we give an outlook of possible results at the LHC.Comment: 15 pages, 8 figure

Structure of the Coulomb and unitarity corrections to the cross section of e+e−e^+e^- pair production in ultra-relativistic nuclear collisions

We analyze the structure of the Coulomb and unitarity corrections to the single pair production as well as the cross section for the multiple pair production. In the external field approximation we consider the probability of $e^+e^-$ pair production at fixed impact parameter $\rho$ between colliding ultra-relativistic heavy nuclei. We obtain the analytical result for this probability at large $\rho$ as compared to the electron Compton wavelength. We estimate also the unitary corrections to the total cross section of the process.Comment: 10 pages, 2 figures, RevTeX, references correcte

Coherent Vector Meson Photoproduction with Nuclear Breakup in Relativistic Heavy Ion Collisions

Relativistic heavy ions are copious sources of virtual photons. The large photon flux gives rise to a substantial photonuclear interaction probability at impact parameters where no hadronic interactions can occur. Multiple photonuclear interactions in a single collision are possible. In this letter, we use mutual Coulomb excitation of both nuclei as a tag for moderate impact parameter collisions. We calculate the cross section for coherent vector meson production accompanied by mutual excitation, and show that the median impact parameter is much smaller than for untagged production. The vector meson rapidity and transverse momentum distribution are very different from untagged exclusive vector meson production.Comment: 14 pages, including 4 figure

Strong suppression of Coulomb corrections to the cross section of e+e- pair production in ultrarelativistic nuclear collisions

The Coulomb corrections to the cross section of $e^+e^-$ pair production in ultrarelativistic nuclear collisions are calculated in the next-to-leading approximation with respect to the parameter $L=\ln \gamma_A\gamma_B$ ($\gamma_{A,B}$ are the Lorentz factors of colliding nuclei). We found considerable reduction of the Coulomb corrections even for large $\gamma_A\gamma_B$ due to the suppression of the production of $e^+e^-$ pair with the total energy of the order of a few electron masses in the rest frame of one of the nuclei. Our result explains why the deviation from the Born result were not observed in the experiment at SPS.Comment: 4 pages, RevTe

Coherent and incoherent atomic scattering: Formalism and application to pionium interacting with matter

The experimental determination of the lifetime of pionium provides a very important test on chiral perturbation theory. This quantity is determined in the DIRAC experiment at CERN. In the analysis of this experiment, the breakup probabilities of of pionium in matter are needed to high accuracy as a theoretical input. We study in detail the influence of the target electrons. They contribute through screening and incoherent effects. We use Dirac-Hartree- Fock-Slater wavefunctions in order to determine the corresponding form factors. We find that the inner-shell electrons contribute less than the weakly bound outer electrons. Furthermore, we establish a more rigorous estimate for the magnitude of the contributions form the transverse current (magnetic terms thus far neglected in the calculations).Comment: Journal of Physics B: Atomic, Molecular and Optical Physics; (accepted; 22 pages, 6 figures, 26 references) Revised version: more detailed description of DIRAC experiment; failure of simplest models for incoherent scattering demonstrated by example

Hot Topics in Ultra-Peripheral Collisions

Ultra-peripheral collisions of relativistic heavy ions involve long-ranged electromagnetic interactions at impact parameters too large for hadronic interactions to occur. The nuclear charges are large; with the coherent enhancement, the cross sections are also large. Many types of photonuclear and purely electromagnetic interactions are possible. We present here an introduction to ultra-peripheral collisions, and present four of the most compelling physics topics. This note developed from a discussion at a workshop on ``Electromagnetic Probes of Fundamental Physics,'' in Erice, Italy, Oct. 16-21, 2001.Comment: 7 pages, with 3 figures. This developed from a discussion at the workshop on "Electromagnetic Probes of Fundamental Physics," Oct. 16-21, Erice, Ital