Impact parameter

Abstract: We compute initial conditions in heavy ion collisions within the color glass condensate framework by combining the impact parameter dependent saturation model with the classical Yang-Mills description of initial Glasma fields. In addition to fluctuations of nucleon positions, this impact parameter dependent Glasma description includes quantum fluctuations of color charges on the length scale determined by the inverse nuclear saturation scale ${Q}_{s}$. The model naturally produces initial energy fluctuations that are described by a negative binomial distribution. The ratio of triangularity to eccentricity ${\ensuremath{\epsilon}}_{3}/{\ensuremath{\epsilon}}_{2}$ is close to that in a model tuned to reproduce experimental flow data. We compare transverse momentum spectra and ${v}_{2,3,4}({p}_{T})$ of pions from different models of initial conditions using relativistic viscous hydrodynamic evolution.

Abstract: The Fourier transform of generalized parton distribution functions at ξ = 0 describes the distribution of partons in the transverse plane. The physical significance of these impact parameter dependent parton distribution functions is discussed. In particular, it is shown that they satisfy positivity constraints which justify their physical interpretation as a probability density. The generalized parton distribution H is related to impact parameter distribution of unpolarized quarks for an unpolarized nucleon, $\tilde{H}$ is related to the distribution of longitudinally polarized quarks in a longitudinally polarized nucleon, and E is related to the distortion of the unpolarized quark distribution in the transverse plane when the nucleon has transverse polarization. The magnitude of the resulting transverse flavor dipole moment can be related to the anomalous magnetic moment for that flavor in a model independent way.

Abstract: We develop a dipole model for DESY HERA deep inelastic scattering data which incorporates the impact parameter distribution of the proton. The model describes the inclusive total ${\ensuremath{\gamma}}^{*}p$ cross sections as well as the diffractive $J/\ensuremath{\psi}$ differential cross sections. We compare the model with previous approaches and show that the t distributions are sensitive to saturation phenomena. We estimate the boundary of the saturation region and show that it dominates the data in the low-${Q}^{2}$ region where the total ${\ensuremath{\gamma}}^{*}p$ cross section exhibits the same universal rise as hadronic cross sections. The model is then extended to nuclei and shows good agreement with the nuclear shadowing data at small x. Finally, we estimate the saturation scale in nuclei.

Abstract: We use (3+1)-dimensional hydrodynamics with exact longitudinal boost-invariance to study the influence of collision centrality and initial energy density on the transverse flow pattern and the angular distributions of particles emitted near midrapidity in ultrarelativistic heavy-ion collisions. We concentrate on radial flow and the elliptic flow coefficientv2 as functions of the impact parameter and of the collision energy. We demonstrate that the finally observed elliptic flow is established earlier in the collision than the observed radial flow and thus probes the equation of state at higher energy densities. We point out that a phase transition from hadronic matter to a color-deconfined quark-gluon plasma leads to nonmonotonic behaviour in both beam energy and impact parameter dependences which, if observed, can be used to identify such a phase transition. Our calculations span collision energies from the Brookhaven AGS (Alternating Gradient Synchrotron) to beyond the LHC (Large Hadron Collider); the QGP phase transition signature is predicted between the lowest available SPS (CERN Super Proton Synchrotron) and the highest RHIC (Brookhaven Relativistic Heavy Ion Collider) energies. To optimize the chances for applicability of hydrodynamics we suggest to study the excitation function of flow anisotropies in central uranium-uranium collisions in the sideon-side collision geometry.