Quasi-linear response theory of statistical heavy-ion collisions: (II). Analysis of the friction tensor and the energy transport

We apply the recently proposed quasi-linear response theory to the study of energy transport in deep inelastic heavy-ion collisions. By solving a master equation, we show how quickly the canonical distribution function becomes a good representation of the intrinsic state in the case of the random intrinsic excitations proposed by Weidenmüller and co-workers. We numerically analyze the properties of the corresponding friction tensor. In addition, we demonstrate that the known fluctuation dissipation theorem in the linear response theory is considerably violated for large part of deep inelastic collisions. We then calculate the double differential cross section for three typical examples. The results agree well with the experimental data if we phenomenologically introduce a time-dependent potential. We remark on the difference of the present calculation from that of the linear response theory. We comment also on the validity of a time-dependent theory, which derives the basic equations from time-independent equations by assuming a one-to-one correspondence between the time and the relative distance.     

A quasi-linear response theory of statistical heavy-ion collisions: (I). Basic formulation : Transport equations and roles of Green functions

We develop a time-dependent theory of heavy-ion collisions which consistently treats the relative and the intrinsic motions by coupled equations derived from the many-body von Neumann equation. The structure of the equations determining the mean trajectory and the fluctuations of the relative motion is the same as that of the corresponding equations in the known linear response theory. The present theory differs, however, from the linear response theory, in that it presumes neither weak coupling between the relative motion and the intrinsic excitations, nor the canonical distribution function for the density operator of the intrinsic motions. We apply the theory especially to deep inelastic collisions, where the relative motion couples to intrinsic excitations through a stochastic hamiltonian. Based on the stochastic assumption, we study the properties of the Green functions that take into account the higher order effects of the coupling hamiltonian. We then discuss, in particular, the effects of the Green functions on the time evolution of the intrinsic state, which is described in terms of a coarse-grained master equation, the friction tensor and fluctuation dissipation theorems.     

Measuring the photon fragmentation function at HERA

The production of final state photons in deep inelastic scattering originates from photon radiation off leptons or quarks involved in the scattering process. Photon radiation off quarks involves a contribution from the quark-to-photon fragmentation function, corresponding to the non-perturbative transition of a hadronic jet into a single, highly energetic photon accompanied by some limited hadronic activity. Up to now, this fragmentation function was measured only in electron–positron annihilation at LEP. We demonstrate by a dedicated parton-level calculation that a competitive measurement of the quark-to-photon fragmentation function can be obtained in deep inelastic scattering at HERA. Such a measurement can be obtained by studying the photon energy spectra in γ+(0+1)-jet events, where γ denotes a hadronic jet containing a highly energetic photon (the photon jet). Isolated photons are then defined from the photon jet by imposing a minimal photon energy fraction. For this so-called democratic clustering approach, we study the cross sections for isolated γ+(0+1)-jet and γ+(1+1)-jet production as well as for the inclusive isolated photon production in deep inelastic scattering.     

Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards.     

Inelastic shadowing effects in multiple scattering

The projectile-nucleon scattering amplitudes used as input into multiple scattering theories of projectile-nucleus scattering naturally include the effects of coupling to inelastic (i.e., production) channels. We employ a multichannel separable potential to describe the projectile-nucleon interaction and show that within the fixed nucleon framework we can obtain the nuclear elastic scattering amplitude. This includes terms outside the conventional formalisms, corresponding to intermediate propagation in the inelastic channels both above and below inelastic threshold. We refer to this as inelastic shadowing. In a two-channel approximation, we show that knowledge of the projectile-nucleon elastic scattering phase shifts plus specification of the inelastic threshold energy are sufficient to determine the off-shell coupled-channel transition matrix, implying that the nuclear amplitude can be calculated within this model without any detailed information about the inelastic channels. We study this solution quantitatively for some model problems and for pion scattering, with the general result that inelastic shadowing can be significant whenever the elementary interaction has important channel coupling. For pion scattering in the energy regime characterized by strongly absorptive resonances, we find, for example, that the effect of inelastic shadowing is much more important than that due to two-nucleon correlations.     

Inelastic intermediate states in proton-deuteron and deuteron-deuteron elastic collisions at the ISR

We present experimental results on proton-deuteron and deuteron-deuteron elastic scattering measured at the two highest ISR energies, √s = 53 GeV and √s = 63 GeV. The data cover the single- and multiple-scattering regions over a wide interval of four-momentum transfer t. In both reactions we find clear evidence for a substantial t-dependent contribution of inelastic intermediate states in the multiple-scattering region, as well as in single scattering. In the analysis we use the Glauber multiple-scattering theory extended to include inelastic shadow effects. This extension of the basic theory contains as input a triple-Regge parametrization describing the high-mass inclusive spectrum. The analysis of inelastic corrections to multiple scattering on deuterons at high energies is shown to provide a sensitive test of different parametrization of inclusive production in proton-proton collisions.     

Dynamical properties of a dissipative hybrid Fermi-Ulam-bouncer model

Some consequences of dissipation are studied for a classical particle suffering inelastic collisions in the hybrid Fermi-Ulam bouncer model. The dynamics of the model is described by a two-dimensional nonlinear area-contracting map. In the limit of weak and moderate dissipation we report the occurrence of crisis and in the limit of high dissipation the model presents doubling bifurcation cascades. Moreover, we show a phenomena of annihilation by pairs of fixed points as the dissipation varies.     

The strange-sea quark spin distribution in the nucleon from inclusive and semi-inclusive deep-inelastic scattering

We propose new method which allows determination of the strange-sea quark spin distribution in the nucleon through measurement of various inclusive and semi-inclusive polarized deep inelastic electron–proton or muon–proton reactions. It is shown, that using combinations of inclusive data and semi-inclusive data containing neutral pions in the final state, it is possible to extract the strange-sea quark spin distribution. Similar result can be obtained for charged pions and some other hadrons also.     

Testing QCD scaling violations in the HERA energy range

High energy electron-proton colliders open new kinematical domains for the investigation of scaling violations in nucleon structure functions. Focussing on HERA as a definite study case we explore the precision which can be expected in determinations of the QCD scale parameter Λ and the running coupling constant α _s (Q ²). Our results provide a quantitative basis for discussions of the possibilities and requirements of QCD tests in inclusive deep inelastic scattering at HERA energies.     

Microscopic,quantal theory of Brownian motion applied to deep inelastic heavy-ion collisions

The present understanding of the statistical features of deep inelastic heavy ion collisions can be improved considerably by following the lines of modern molecular theory of Brownian motion. Only a few assumptions are necessary, which are direct consequences of the underlying physical picture. The physical interpretation of these assumptions leads to simple estimates of their validity. The theory is a quantum mechanical, strong coupling, transport theory. Collective vibrations can be included in a simple and straightforward manner.     

Ultracold inelastic collisions in two dimensions

We show that cross sections for inelastic collisions of ultracold atoms or molecules confined by a harmonic potential have the same energy dependence as in pure 2D geometry. This indicates that chemical reactions and inelastic collisions may be suppressed in an ultracold gas under strong confinement in one dimension. We present a numerical proof of the threshold collision laws in 2D. Our results indicate that inelastic collisions in weak electromagnetic fields may be controlled by varying the orientation of the external field axis with respect to the plane of confinement.     

A family of crisis in a dissipative Fermi accelerator model

The Fermi accelerator model is studied in the framework of inelastic collisions. The dynamics of this problem is obtained by use of a two-dimensional nonlinear area-contracting map. We consider that the collisions of the particle with both periodically time varying and fixed walls are inelastic. We have shown that the dissipation destroys the mixed phase space structure of the nondissipative case and in special, we have obtained and characterized in this problem a family of two damping coefficients for which a boundary crisis occurs.     

Large corrections to high-pT hadron-hadron scattering in QCD

We have computed the first non-trivial QCD corrections to the quark-quark scattering process which contributes to the production of hadrons at large p_T in hadron-hadron collisions. Using quark distribution functions defined in deep inelastic scattering and fragmentation functions defined in one particle inclusive e⁺e^? annihilation, we find that the corrections are large. This implies that QCD perturbation theory may not be reliable for large-p_T haron physics.     

Inelastic processes in the interaction of an atom with an ultrashort electromagnetic pulse

Electron transitions occurring during the interaction of a heavy relativistic atom with a spatially inhomogeneous ultrashort electromagnetic pulse are considered by solving the Dirac equation. The corresponding transition probabilities are expressed in terms of known inelastic atomic form factors, which are widely used in the theory of relativistic collisions between charged particles and atoms. By way of example, the inelastic processes accompanying the interaction of ultrashort pulses with hydrogen-like atoms are considered. The probabilities of ionization and production of a bound-free electron-positron pair on a bare nucleus, which are accompanied by the formation of a hydrogen-like atom in the final state and a positron in the continuum, are calculated. The developed technique makes it possible to take into account exactly not only the spatial inhomogeneity of an ultrashort electromagnetic pulse, but also the magnetic interaction.     

Structure of final states with a high transverse momentum π0 in proton-proton collisions

We present a study of the final state structure in proton-proton collisions (√s = 53 GeV) where a large transverse momentum π⁰ (p_t > 2 GeV/c) is produced at an angle of 90°. Charged secondaries have been detected and momentum analysed in the split field magnet detector at the CERN Intersecting Storage Rings. The large angular coverage of this detector extends over ±2.5 units of rapidity and ±30° of azimuth with respect to the trigger π⁰, both towards and away from it. In each of these directions, where we observe similar strong correlations, we present charged particle distributions, in rapidity and momentum. In the hemisphere containing the trigger π⁰ we have measured the cross section for inclusive production of large transverse momentum ?^± mesons. In the opposite hemisphere the data exhibit several features predicted by hard scattering quark-parton models: coplanarity and short-range rapidity correlation for the large transverse momentum secondaries as well as a transverse momentum sharing distribution similar to that observed in deep inelastic electro-production and in e⁺e^? collisions.     

Signals for intrinsic charm in high energy interactions

The prospects to test the hypothesis of intrinsic charm quarks in the proton are investigated. We consider how this component can be directly or indirectly probed in deep inelastic scattering at HERA and in fixed target experiments and find that an overlooked signal might be present in existing NMC data. Applying the intrinsic charm model to hadron collisions we compare the resulting charm production cross-sections with those based on standard perturbative QCD and available data. Extrapolating to higher energies we obtain predictions for charm production at the Tevatron and LHC.     

Two particle correlations: Saturation and issues with universality

We study the universality issue of the transverse momentum dependent parton distributions at small-x, by comparing the initial/final state interaction effects in di-jet correlation in pA collisions with those in deep inelastic lepton–nucleus scattering. We demonstrate the non-universality by performing an explicit calculation in a particular model where the multiple gauge boson exchange contributions are summed up to all orders. In addition, we generalize the model calculation to the CGC formalism, and find the non-universality for quark distributions in CGC.     

The effects of forcing and dissipation on phase transitions in thin granular layers

Recent experimental and computational studies of vibrated thin layers of identical spheres have shown transitions to ordered phases similar to those seen in equilibrium systems. Motivated by these results, we carry out simulations of hard inelastic spheres forced by homogenous white noise. We find a transition to an ordered state of the same symmetry as that seen in the experiments, but the clear phase separation observed in the vibrated system is absent. Simulations of purely elastic spheres also show no evidence for phase separation. We show that the energy injection in the vibrated system is dramatically different in the different phases, and suggest that this creates an effective surface tension not present in the equilibrium or randomly forced systems. We do find, however, that inelasticity suppresses the onset of the ordered phase with random forcing, as is observed in the vibrating system, and that the amount of the suppression is proportional to the degree of inelasticity. The suppression depends on the details of the energy injection mechanism, but is completely eliminated when inelastic collisions are replaced by uniform system-wide energy dissipation.