Effects of the quantum interference in collisions of particles have a twofold nature: they arise because of the auto-correlation of a complex scattering amplitude and due to spatial coherence of the incoming wave packets. Both these effects are neglected in a conventional scattering theory dealing with the delocalized plane waves, although they sometimes must be taken into account in particle and atomic physics. Here, we study the role of a transverse coherence length of the packets, putting special emphasis on the case in which one of the particles is twisted, that is, it carries an orbital angular momentum $\ell\hbar$. In $ee, ep$, and $pp$ collisions the interference results in corrections to the plane-wave cross sections, usually negligible at the energies $\sqrt{s} \gg 1$ GeV but noticeable for smaller ones, especially if there is a twisted hadron with $|\ell| > 10^3$ in initial state. Beyond the perturbative QCD, these corrections become only moderately attenuated allowing one to probe a phase of the hadronic amplitude as a function of $s$ and $t$. In this regime, the coherence effects can compete with the loop corrections in QED and facilitate testing the phenomenological models of the strong interaction at intermediate and low energies.
We study nuclear shadowing for transverse and longitudinal photons. The coherence length, which controls the onset of nuclear shadowing at small Bjorken-x is longer for longitudinal than for transverse photons. The light-cone Green function technique properly treats the finite coherence length in all multiple scattering terms. This is especially important in the region x>0.01, where most of the data exist. NMC data on shadowing in deep inelastic scattering are well reproduced in this approach. We also incorporate nonperturbative effects, in order to extrapolate this approach to small photon vi…
Large transverse momentum distributions of identified particles observed at RHIC are analyzed by a relativistic stochastic model in the three dimensional rapidity space. Temperature for inclusive reactions is estimated.
Motivated by the recent results for DIS off nuclei from the HERMES experiment we have performed a systematic study of shadowing for transverse and longitudinal photons. We found that the coherence length which controls the onset of nuclear shadowing at small x_{Bj} is much longer for longitudinal than transverse photons, and is much shorter for shadowing of gluons. The light-cone Green function approach we apply properly treats shadowing in the transition region x_{Bj}>0.01. It also incorporates the nonperturbative effects and is legitimate at small Q^2. We calculate nuclear shadowing and comp…
Transverse momentum spectra of the reaction products from proton-proton and nucleus-nucleus collisions are discussed within the phenomenological frameworks of statistical phase-space and string fragmentation models. It will be shown that a string fragmentation model can accommodate all of the observations discussed here and consequently it is claimed that no conclusion about the thermal nature or collective expansion of the created system may be derived from observed transverse momentum spectra.
Longitudinal and transverse parton distributions for pion and nucleon are calculated from hadron vertexes obtained by a study of form factors within relativistic quark models. The relevance of the one-gluon-exchange dominance at short range for the behavior of the form factors at large momentum transfer and of the parton distributions at the end points is stressed.
We revisit the relation between the asymmetries $A_{FB}$ and $A_{FB}^\ell$ in $t \bar t$ production at the Tevatron, using as new physics benchmark a colour octet. We find that $A_{FB}^\ell$ receives large contributions from the interference between $λ= \pm 1/2$ top helicity states, which has been ignored in some of the previous literature on the subject. The omission of these contributions results in a severe underestimation of the asymmetry, around $1/2$ and $1/50$ of the true value for right-handed and left-handed top couplings to the octet, respectively. Interference effects are closely re…
We present a simple gluon production picture which is based on the McLerran-Venugopalan model and gluon BFKL evolution in relativistic heavy ion collision. Results for the multiplicity and transverse energy distribution in both the central and forward rapidity regions for gluon production in early stages of heavy ion collisions at the LHC are given. Finally, we provide a general qualitative discussion of the consequences of the forward rapidity behavior of produced gluons.
Transverse momentum distributions measured by the STAR and PHENIX collaborations at the Relativistic Heavy Ion Collider and by the ALICE, ATLAS and CMS collaborations at the Large Hadron Collider can be considered in the framework of relativistic thermodynamics using the Tsallis distribution. Theoretical issues are clarified concerning the thermodynamic consistency in the case of relativistic high energy quantum distributions. An improved form is proposed for describing the transverse momentum distribution and fits are presented together with estimates of the parameter q and the temperature T.
We obtain an extension of Bjorken's 1+1 dimensional scaling relativistic flow solution to relativistic transverse velocities with cylindrical symmetry in 1+3 dimensions at constant, homogeneous pressure (vanishing sound velocity). This can be the situation during a first order phase transition converting quark matter into hadron matter in relativistic heavy ion collisions.
A new method for solving relativistic ideal hydrodynamics in (1+3)D is developed. Longitudinal and transverse radial flows are explicitly embedded and the hydrodynamic equations are reduced to a single equation for the transverse velocity field only, which is much more tractable. As an application we use the method to find analytically all possible solutions with power dependence on proper time and transverse radius. Possible application to the Relativistic Heavy Ion Collisions and possible generalizations of the method are discussed.
Using a coherence time extracted from high precision proton-nucleus Drell-Yan measurements and a nuclear absorption cross section extracted from pA charmonium production experiments, we study J/psi production and absorption in nucleus-nucleus collisions. We find that coherence time effects are large enough to affect the measured J/psi-to-Drell-Yan ratio. The S+U data at 200A GeV/c measured by NA38 are reproduced quantitatively without the introduction of any new parameters. However, when compared with recent NA50 measurements for Pb+Pb at 158A GeV/c, the data is not reproduced in trend or in m…
By the sample generated by the AMPT with string melting model, we compare the azimuthal distributions of multiplicity, total transverse rapidity, and mean transverse rapidity. It is demonstrated that the azimuthal distribution of mean transverse rapidity is a good probe of the radial kinetic expansion. The anisotropic part of the distribution characterizes the anisotropic nature of the radial expansion, and isotropic part is combinations of thermal motion and isotropic radial expansion.
From the correlation structure of transverse momentum $p_t$ in relativistic nuclear collisions we observe for the first time temperature/velocity structure resulting from low-$Q^2$ partons. Our novel analysis technique does not invoke an {\em a priori} jet hypothesis. $p_t$ autocorrelations derived from the scale dependence of $<p_t>$ fluctuations reveal a complex parton dissipation process in RHIC heavy ion collisions. We also observe structure which may result from collective bulk-medium recoil in response to parton stopping.
We incorporate the effect of lattice thermal vibrations into the Glauber theory description of particle- and nucleus-crystal Coulomb interactions at high-energy. The allowance for the lattice thermal vibrations is shown to produce strong absorption effect: the phase shift function of the multiple-diffraction scattering on a chain of $N$ identical atoms acquires large imaginary part and the radius of the absorption region in the impact parameter plane grows logarithmically with $N$. Consequences of this observation for the elastic and quasi-elastic Coulomb scattering are discussed. Practically …
Large transverse momentum distributions of identified particles observed at RHIC are analyzed by a relativistic stochastic model in the three dimensional (non-Euclidean) rapidity space. A distribution function obtained from the model is Gaussian-like in radial rapidity. It can well describe observed transverse momentum $p_T$ distributions. Estimation of radial flow is made from the analysis of $p_T$ distributions for $\bar{p}$ in Au + Au Collisions. Temperatures are estimated from observed large $p_T$ distributions under the assumption that the distribution function approaches to the Maxwell-B…
We discuss coherent QCD radiation from space-like parton branching and its effects on multi-jet final states at high-energy hadron colliders. Coherence effects for small longitudinal momentum fractions x are not included in the branching algorithms of standard shower Monte Carlo event generators. On the other hand, they are taken into account only partially in perturbative next-to-leading-order calculations for multi-jets. Such effects are present to all orders in alpha_s and can become logarithmically enhanced with \sqrt{s} / E_T, where E_T is the hardest jet transverse energy. We present res…
In this study, we investigate the impact of the magnetic field on the evolution of the transverse flow of QGP matter in the magneto-hydrodynamic (MHD) framework. We assume that the magnetic field is perpendicular to the reaction plane and then we solve the coupled Maxwell and conservation equations in (1+1D) transverse flow, within the Bjorken scenario. We consider a QGP with infinite electrical conductivity. First, the magnetic effects on the QGP medium at mid-rapidity are investigated at leading order; then the time and space dependence of the energy density, velocity and magnetic field in t…
A classical calculation, modified by Compton-recoil kinematics, of the radiation emitted by a relativistic neutrino with mass and a magnetic moment passing through a transverse magnetic field. The calculation is performed in the neutrinos rest frame by the method of virtual quanta. The total number N of virtual quanta scattered by the neutrino is determined. The semi-classical result for the analog of the Klein-Nishina formula is compared with a QED calculation of the photon scattering cross section. The different angular distributions, both strongly peaked, lead to a factor of two difference …
In order to describe large transverse momentum ($p_T$) distributions observed in high energy nucleus-nucleus collisions, a stochastic model in the three dimensional rapidity space is introduced. The fundamental solution of the radial symmetric diffusion equation is Gaussian-like in radial rapidity. We can also derive a $p_T$ or radial rapidity distribution function, where a distribution of emission center is taken into account. It is applied to the analysis of observed large $p_T$ distributions of charged particles. It is shown that our model approaches to a power function of $p_T$ in the high…
We argue that the transverse mass spectra of identified hadrons as measured in gold-gold collisions at BNL's Relativistic Heavy-Ion Collider (RHIC) follows a generalized scaling law. Such a scaling behavior is motivated by the idea of a Color Glass Condensate, or more generally, saturation of the gluon density. In particular, we describe the shapes of transverse mass spectra as a function of centrality. This scaling of the transverse mass spectrum is shown to be consistent with previously observed scaling of multiplicity with centrality.
Using the relativistic Eikonal approximation, we study the one and two photon exchange amplitudes in elastic electron-nucleon scattering for the case of transversely polarized nucleons with unpolarized electrons beam. In our approach, we utilize the convolution theory of Fourier transforms and the transverse charge density in transverse momentum space to evaluate the one and two photon exchange Eikonal amplitudes. The results obtained for the $2γ$ amplitude in impact parameter space are compared to the corresponding 4D case. We show that while the one and two photon cross sections are azimutha…
The correlation between the transverse momentum and the azimuthal asymmetry the flow is studied. A correlation coefficient is defined between the average transverse momentum of hadrons emitted in an event and the square of the elliptic or triangular flow coefficient. The hydrodynamic model predicts a positive correlation of the transverse momentum with the elliptic flow, and almost no correlation with the triangular flow in Pb-Pb collisions at LHC energies. In p-Pb collisions the new correlation observable is very sensitive to the mechanism of energy deposition in the first stage of the collis…
We study the transverse momentum distribution of vector mesons produced in ultraperipheral relativistic heavy ion collisions (UPCs). In UPCs there is no strong interaction between the nuclei and the vector mesons are produced in photon-nucleus collisions where the (quasireal) photon is emitted from the other nucleus. Exchanging the role of both ions leads to interference effects. A detailed study of the transverse momentum distribution which is determined by the transverse momentum of the emitted photon, the production process on the target and the interference effect is done. We study the tot…
Transverse hadron spectra from proton-proton, proton-nucleus and nucleus-nucleus collisions from 2 AGeV to 21.3 ATeV are investigated within two independent transport approaches (HSD and UrQMD). For central Au+Au (Pb+Pb) collisions at energies above $E_{\rm lab}\sim$ 5 AGeV, the measured $K^{\pm}$ transverse mass spectra have a larger inverse slope parameter than expected from the default calculations. The additional pressure - as suggested by lattice QCD calculations at finite quark chemical potential $μ_q$ and temperature $T$ - might be generated by strong interactions in the early pre-hadro…
Transverse energy and charged particle pseudorapidity densities at midrapidity and their ratio, $dE_{T}/dη\mid_{mid} / dN_{ch}/dη|_{mid}$, are evaluated in a statistical model with longitudinal and transverse flows for the wide range of colliders, from AGS to RHIC at $\sqrt{s_{NN}}=200$ GeV. Evaluations are done at freeze-out parameters established independently from fits to observed particle yields and $p_{T}$ spectra. Decays of hadron resonances are treated thoroughly and are included in derivations of $dE_{T}/dη|_{mid}$ and $dN_{ch}/dη|_{mid}$. The predictions of the model agree well with t…
Hydrodynamic model simulations of Au-Au collisions at RHIC have indicated recently, that with improved simulations in the coming years, it may be feasible to quantify the viscosity of the matter produced in heavy ion collisions. To this end, a consistent fluid dynamic description of viscous effects is clearly needed. In this note, we observe that a recently used, approximate form of the 2nd order Israel-Stewart viscous hydrodynamic equations of motion cannot account consistently for the transverse flow fields, which are expected to develop in heavy ion collisions. We identify the appropriate e…
We analyze the transverse momentum distribution of $J/ψ$ mesons produced in Au + Au collisions at the top RHIC energy within a blast-wave model that accounts for a possible inhomogeneity of the charmonium distribution and/or flow fluctuations. The results imply that the transverse momentum spectra of$J/ψ$, $ϕ$ and $Ω$ hadrons measured at the RHIC can be described well if kinetic freeze-out takes place just after chemical freeze-out for these particles.
We show that the event-by-event fluctuations of the transverse size of the initial source, which follow directly from the Glauber treatment of the earliest stage of relativistic heavy-ion collisions, cause, after hydrodynamic evolution, fluctuations of the transverse flow velocity at hadronic freeze-out. This in turn leads to event-by-event fluctuations of the average transverse momentum, p_T. Simulations with GLISSANDO for the Glauber phase, followed by a realistic hydrodynamic evolution and statistical hadronization carried out with THERMINATOR, lead to agreement with the RHIC data. In parti…
We study the production of the D and J/psi mesons from deconfined quark matter at CERN SPS energy. Using the MICOR microscopical coalescence model we determine the transverse momentum spectra of these charm mesons. We predict the slopes of their transverse momentum spectra in Pb+Pb collision at 158 GeV/nucleon beam energy.
We investigate the impact parameter dependent parton distributions for a relativistic composite system in light-front framework. We express them in terms of overlaps of light-cone wave functions for a self consistent two-body spin-1/2 state, namely an electron dressed with a photon in QED. The pdfs are distorted in the transverse space for transverse polarization of the state at one loop level.
Transverse-mass spectra, their inverse slopes and mean transverse masses in relativistic collisions of heavy nuclei are analyzed in a wide range of incident energies 2.7 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The analysis is performed within the three-fluid model employing three different equations of state (EoS's): a purely hadronic EoS, an EoS with the first-order phase transition and that with a smooth crossover transition into deconfined state. Calculations show that inverse slopes and mean transverse masses of all the species (with the exception of antibaryons within the hadronic scenario) ex…
The photon-photon interaction in ultra-relativistic heavy-ion collision is a source of the $(e^+,e^-)$ pairs. The photon-photon fusion leads the lepton creation in the broad configuration space around "collision" point. Those created close to heavy nuclei may undergo strong interaction with them. The impact parameter space distribution of electrons and positrons are calculated within the b-space EPA model of such collisions. The evolution due to the electromagnetic interaction of $(e^+,e^-)$ with nuclei is studied, and the distortion of rapidity and transverse momentum distributions are shown.…
We investigate the impact of three-body forces on the transverse-momentum distribution of partons inside the proton. This is achieved by considering the three-body problem in a class of hyper-central quark potential models. Solving the corresponding Schrödinger equation, we determine the quark wave function in the proton and with appropriate transformations and projections we find the transverse-momentum distribution of a single quark. In each case the parameters of the quark potentials are adjusted in order to sufficiently describe observable properties of the proton. Using a factorization an…
Dijet, dihadron, hadron-jet angular correlations have been reckoned as important probes of the transverse momentum broadening effects in relativistic nuclear collisions. When a pair of high-energy jets created in hard collisions traverse the quark-gluon plasma produced in heavy-ion collisions, they become de-correlated due to the vacuum soft gluon radiation associated with the Sudakov logarithms and the medium-induced transverse momentum broadening. For the first time, we employ the systematical resummation formalism and establish a baseline calculation to describe the dihadron and hadron-jet …
We investigate the Generalized Parton Distributions (GPDs) in impact parameter space using the explicit light front wave functions (LFWFs) for the two-particle Fock state of the electron in QED. The Fourier transform (FT) of the GPDs gives the distribution of quarks in the transverse plane for zero longitudinal momentum transfer ($ξ=0$). We study the relationship of the spin flip GPD $E(x,0,-\vecΔ_\perp^2)$ with the distortion of unpolarized quark distribution in the transverse plane when the target nucleon is transversely polarized and also determine the sign of distortion from the sign of an…
We show that non-conventional statistical effects (due to the presence of long range forces, memory effects, correlations and fluctuations) can be very relevant in the interpretation of the experimental observables in relativistic heavy-ions collisions. Transverse mass spectrum, transverse momentum fluctuations and rapidity spectra are analysed in the framework of the non-extensive statistical mechanics.
We investigate the impact parameter dependent parton distributions for a relativistic composite system in light-front framework. We take an effective two-body spin-1/2 state, namely an electron dressed with a photon in QED. We express the impact parameter dependent parton distributions in terms of overlaps of light-cone wave functions. We obtain the scale dependence of both fermion and gauge boson distributions and show the distortion of the pdfs in the transverse space for transverse polarization of the state at one loop level.
We show that an event-shape engineering based on the mean transverse momentum of charged hadrons, $[p_t]$, provides an optimal handle on the strength of the magnetic field created in central heavy-ion collisions at high energy. This is established through quantitative evaluations of the correlation existing between the event-by-event magnetic field produced by the spectator protons in 5.02 TeV Pb+Pb collisions and the event-by-event $[p_t]$ at a given collision centrality. We argue that the event selection based on $[p_t]$ provides a better handle on the magnetic field than the more traditiona…
We calculate transverse momentum distribution of direct photons from various sources by taking into account the initial state momentum anisotropy of {\em Quark-Gluon-Plasma} (QGP) and late stage transverse flow effects. The total photon yield, calculated for various combinations of initial conditions, transition temperatures, is then compared with the recent measurement of photon transverse momentum distribution by the PHENIX collaboration. It is shown that the presence of such an anisotropy can describe the PHENIX photon data better than the isotropic case. We show that the isotropization tim…
The formalism for describing hadrons using a light-cone Hamiltonian of SU(N) gauge theory on a coarse transverse lattice is reviewed. Physical gauge degrees of freedom are represented by disordered flux fields on the links of the lattice. A renormalised light-cone Hamiltonian is obtained by making a colour-dielectric expansion for the link-field interactions. Parameters in the Hamiltonian are renormalised non-perturbatively by seeking regions in parameter space with enhanced Lorentz symmetry. In the case of pure gauge theories to lowest non-trivial order of the colour-dielectric expansion, thi…
The Tsallis distribution has been used recently to fit the transverse momentum distributions of identified particles by the STAR collaboration \cite{Abelev:2006cs} at the Relativistic Heavy Ion Collider and by the ALICE \cite{Aamodt:2011zj} and CMS \cite{Khachatryan:2011tm} collaborations at the Large Hadron Collider. Theoretical issues are clarified concerning the thermodynamic consistency of the Tsallis distribution in the particular case of relativistic high energy quantum distributions. An improved form is proposed for describing the transverse momentum distribution and fits are presented …
We derive field-theoretic local quantum transport equations which can describe quantum coherence. Our methods are based on Kadanoff--Baym equations derived in the Schwinger--Keldysh closed time path formalism of non-equilibrium quantum field theory. We focus on spatially homogeneous and isotropic systems and mixing fermions with a time-dependent mass and a weak coupling to a thermal plasma. We introduce a new local approximation (LA) method and use it to derive quantum kinetic equations which can describe coherence and also include effects of the spectral width. The method is based on a local …
Using a viscosity-based survival scale for geometrical perturbations formed in the early stages of relativistic heavy-ion collisions, we model the radial flow velocity during freeze-out. Subsequently, we employ the Cooper-Frye freeze-out prescription, with first-order viscous corrections to the distribution function, to obtain the transverse momentum distribution of particle yields and flow harmonics. For initial eccentricities, we use the results of Monte Carlo Glauber model. We fix the blast-wave model parameters by fitting the transverse momentum spectra of identified particles at the Large…
A new iteration method is proposed for analyzing both the multiplicities and the transverse momentum spectra measured only within a small rapidity interval and with low momentum limit without any inconsistency or ad hoc assumptions and applied to the hadron data by the ALICE collaboration in Pb+Pb collisions at 2.76 TeV/A. In order to correctly consider the resonance contribution only to the small rapidity interval, ratios involving only those hadrons whose transverse momentum spectrum is available are considered. In spite of the small number of ratios considered, the fittings of both the rati…
The transverse profile of the chromoelectric field generated by a quark-antiquark pair in the SU(3) vacuum is analysed within the dual superconductor scenario, then the London penetration depth and coherence length are extracted. The color field is determined on the lattice through a connected correlator of two Polyakov loops measured on smeared configurations.
Effective Fermion-Photon Vertex in a Rotating Relativistic Medium: Tree-Level Structure
Universidad del Valle（德爾瓦列大學）；Universidad Nacional Autónoma de México（墨西哥國立自治大學）；Universidad del Quindío（金迪奧大學）；Pontificia Universidad Católica de Chile（智利天主教pontifical大學）；Center for Nanotechnology and Advanced Materials CIEN-UC（納米技術與先進材料中心CIEN-UC）
We investigate pseudorapidity correlations of the average transverse flow of particles emitted in relativistic heavy-ion collisions. We employ 3+1 dimensional viscous relativistic hydrodynamics with initial conditions from the quark Glauber Monte Carlo model to confront the recent measurements on the pseudorapidity correlations of the transverse momentum fluctuations in Pb+Pb collisions at $\sqrt{s_{NN}}=2760$GeV. We find good agreement between the model predictions and data. Further, we study two other observables build with the covariance of the average transverse momentum in different rapid…
