We examine numerically different zero-dimensional reaction-diffusion processes as candidate toy models for high-energy QCD evolution. Of the models examined -- Reggeon Field Theory, Directed Percolation and Reversible Processes -- only the latter shows the behaviour commonly expected, namely an increase of the scattering amplitude with increasing rapidity. Further, we find that increasing recombination terms, quantum loops and the heuristic inclusion of a running of the couplings, generically slow down the evolution.
In the present work, Monte-Carlo toy model with repulsing quark-gluon strings in hadron-hadron collisions is described. String repulsion creates transverse boosts for the string decay products, giving modifications of observables. As an example, long-range correlations between mean transverse momenta of particles in two observation windows are studied in MC toy simulation of the heavy-ion collisions.
As a toy model for QED in strong background fields, we consider the impact of back-reaction and loop effects on scattering processes in quantum optics. We show that neglecting back-reaction misses qualitative and quantitative features of strong-field physics. We are able to study an analogue of the Narozhny-Ritus conjecture on the scaling of higher loop diagrams with intensity: we prove that there is no corresponding behaviour in our model. Implications for QED are identified and discussed.
We explore possible extensions of the $t$-channel and $s$-channel unitary model of high energy evolution in zero transverse dimensions appropriate to very high energy/atomic number where the dipole density in a toy hadron is parametrically high.We suggest that the appropriate generalization is to allow emission of more than one dipole in a single step of energy evolution. We construct explicitly such a model that preserves the $t$-channel and s-channel unitarity and have the correct low density limit, and study the particle multiplicity distribution resulting from this evolution. We consider i…
We analyze a toy model which has a structure similar to that of the recently found QCD evolution equations, but without transverse dimensions. We develop two different but equivalent methods in order to compute the leading-order and next-to-leading order Pomeron loop diagrams. In addition to the leading-order result which has been derived from Mueller's toy model~\cite% {Mueller:1994gb}, we can also calculate the next-to-leading order contribution which provides the $(α_{s}^{2}αY)$ correction. We interpret this result and discuss its possible implications for the four-dimensional QCD evolution…
We will give convincing arguments to view transverse spin asymmetries in inclusive reactions, as very exciting observables, although there were considered as irrelevant for a long time. We look forward to new high energy data in the near future.
We develop general formalism of how to relate cross-section for exclusive processes to spatial image of reaction area. More precisely we show how to determine the spatial distribution of outgoing particles in the space of so-called nearest approach parameter. This parameter characterizes the position in the coordinate space the place where the final particle is produced.
Hadron-nucleus amplitudes at high energies are studied in the "toy" Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and looses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprizing result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite wel…
The Reggeon field theory in zero transverse dimensions is investigated. Two versions of the theory are considered: one that allows at most triple pomeron interactions and the other that embodies an additional 2-->2 quartic Reggeon coupling. The behavior of the scattering amplitude at asymptotic rapidities is obtained in both cases. In an s-channel picture of the high energy scattering both models can be viewed as reaction-diffusion processes. We derive known results in Reggeon field theory rather easily using the reaction-diffusion formalism. We find that some results which are surprising from…
Intrinsic transverse parton momenta pT play an important role in the understanding of azimuthal/spin asymmetries in semi-inclusive deep-inelastic scattering (SIDIS) and the Drell-Yan process (DY). We review and update what is presently known about pT from these processes. In particular, we address the question to which extent data support the popular Gauss model for the pT-distributions. We find that the Gauss model works very well, and observe that the intrinsic transverse momenta in SIDIS and DY are compatible, which is a support for the factorization approach. As a byproduct we recover a si…
Toy models of interacting Pomerons with triple and quaternary Pomeron vertices in zero transverse dimension are investigated. Numerical solutions for eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained, providing the quantum solution for the scattering amplitude in both models. The equations of motion for the Lagrangians of the theories are also considered and the classical solutions of the equations are found. Full two-point Green functions ("effective" Pomeron propagator) and amplitude of diffractive dissociation process are calculated in the framework of RFT-0 appr…
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…
Data for Drell-Yan (DY) processes on nuclei are currently available from fixed target experiments up to the highest energy of $\sqrt{s}=40\GeV$. The bulk of the data cover the range of short coherence length, where the amplitudes of the DY reaction on different nucleons do not interfere. In this regime, DY processes provide direct information about broadening of the transverse momentum of the projectile parton experiencing initial-state multiple interactions. We revise a previous analysis of data from the E772 experiment and perform a new analysis of broadening including data from the E866 exp…
The nature of invariant cross-sections and multiplicities in some $^{208}Pb$-induced reactions and some important ratio-behaviours of the invariant multiplicities for various centralities of the collision will here be dealt with in the light of a combinational approach which has been built up in the recent past by the present authors. Next, the results would be compared with the outcome of some of the simulation-based standard models for multiple production in nuclear collisions at high energies. Finally, the implications of all this would be discussed.
We point out that the $s$-channel unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun's Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a "black disk limit" as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature.
A model for the $p(e,e'π^+)n$ reaction which combines an improved treatment of gauge invariant meson--exchange currents and hard deep--inelastic scattering (DIS) of virtual photons off nucleons is proposed. It is shown that DIS dominates and explains the transverse response at moderate and high photon virtualities $Q^2$ whereas the longitudinal response is dominated by hadronic degrees of freedom and the pion electromagnetic form factor. This leads to a combined description of the longitudinal and transverse components of the cross section in a wide range of photon virtuality $Q^2$ and momentu…
In the present work, we investigate the effects of magnetic field on expanding hot and dense nuclear matter as an ideal fluid. We consider QGP, on the particular case of a (1 + 2) dimensional longitudinally boost-invariant fluid expansion, in the background of an inhomogeneous magnetic field that is generated by external sources. We assume the magnetic field points in the direction perpendicular to the reaction plane, follows the power-law decay in proper time, and has two components on the transverse plane. To simplify the calculation, we suppose the investigated fluid has azimuthal symmetry,…
Experimental data on the polarization of hyperons, inclusively produced in hadron-hadron collisions, have been analyzed. It is shown that the existing data can be described by a function of transverse momentum (Pt) and two scaling variables Xa+-=(Xr +- Xf)/2: P_H=A^alpha*F(Pt)[G(Xa+ -x2) -sigma*G(Xa- +x2)]. The function G(x) is proportional to sin[omega*(x -x1)]/omega, which results for some reactions in an oscillation of P_H as a function of Xf. The "omega", as well as the magnitude and the sign of the hyperon polarization depend on quark composition of hadrons participating in a reaction. Th…
Accurate measurements of the p(e,e?p)pi0 reaction were performed at Q^2=0.127(GeV/c)^2 in the Delta resonance energy region. The experiments at the MIT-Bates Linear Accelerator used an 820 MeV polarized electron beam with the out of plane magnetic spectrometer system (OOPS). In this paper we report the first simultaneous determination of both the TL and TL? (``fifth" or polarized) cross sections at low Q^{2} where the pion cloud contribution dominates the quadrupole amplitudes (E2 and C2). The real and imaginary parts of the transverse-longitudinal cross section provide both a sensitive determ…
Rescattering following a neutrino-nucleus reaction changes the number, energy, and direction of detectable hadrons. In turn, this affects the selection and kinematic distributions of subsamples of neutrino events used for interaction or oscillation analysis. This technical note focuses on three forms of two-body rescattering. Elastic hadron+nucleus scattering primarily changes the direction of the hadron with very little energy transfer. Secondly, a hadron+nucleon quasi-elastic process leads to the knockout of a single struck nucleon, possibly with charge exchange between the two hadrons. Also…
We explore the mechanism of transverse momentum broadening of fast quarks propagating in nuclei, using Drell-Yan (DY) transverse momentum distributions measured in the experiment E866 at FermiLab with beams of 800 GeV protons. Our theoretical analysis is based on the color dipole approach in the target rest frame, which has provided a successful phenomenological description of a variety of hadronic reactions. The present application is relevant to the regime of short coherence length (SCL), where the spatial extent of the fluctuations of the projectile responsible for the Drell-Yan reaction is…
We present a short overview on the studies of transverse momentum dependent parton distribution functions of the nucleon. The aim of such studies is to provide a three dimensional imagining of the nucleon and a comprehensive description of semi-inclusive high energy reactions. By comparing with the theoretical framework that we have for the inclusive deep inelastic lepton-nucleon scattering and the one-dimensional imaging of the nucleon, we summarize what we need to do in order to construct such a comprehensive theoretical framework for semi-inclusive processes in terms of three dimensional ga…
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.
We extend the Gyulassy-Levai-Vitev reaction operator approach to multiple elastic scattering of fast partons traversing dense nuclear matter to take into account the leading power corrections due to the medium recoil and to derive the change in the partons' longitudinal momentum.We employ a boost-invariant formalism to generalize previous treatments of the problem, which were specific to the target rest frame. We apply the transverse momentum diffusion results in a simple analytic model to evaluate the broadening of the back-to-back di-hadron correlation function in $d+Au$ reactions.
I discuss a number of novel phenomenological features of QCD in high transverse momentum reactions. The presence of direct higher-twist processes, where a proton is produced directly in the hard subprocess, can explain the "baryon anomaly" -- the large proton-to-pion ratio seen at RHIC in high centrality heavy ion collisions. Direct hadronic processes can also account for the deviation from leading-twist PQCD scaling at fixed x_T = 2p_T/\sqrt s. I suggest that the "ridge" -- the same-side long-range rapidity correlation observed at RHIC in high centrality heavy ion collisions is due to the imp…
The state of the art concerning transverse-spin and transverse-momentum phenomena in hard hadronic reactions is reviewed. An account is given of single-spin and azimuthal asymmetries in semiinclusive deep inelastic scattering, e^+ e^- annihilation, Drell-Yan production, and hadroproduction. The ongoing experiments and the main theoretical frameworks are described in the first part of the paper. The second part is devoted to the experimental findings and their phenomenological interpretations. A brief discussion of the perspectives of future measurements is finally presented.
Transverse single-spin asymmetries (SSA) in inclusive reactions are now considered to be directly related to the transverse momentum $k_{T}$ of the fundamental partons involved in the process. Several possible leading-twist QCD mechanisms have been proposed to explain the available data, in particular the Sivers effect which was resurrected recently. We show that from the measurement of transverse SSA in inclusive production of gauge bosons, one can learn more about the Sivers functions and possibly to achieve a reliable flavor separation.
We study the resummation of large logarithmic QCD corrections for the process pp ->H+ X when the Higgs boson H is produced at high transverse momentum. The corrections arise near the threshold for partonic reaction and originate from soft gluon emission. We perform the all-order resummation at next-to-leading logarithmic accuracy and match the resummed result with the next-to-leading order perturbative predictions. The effect of resummation on the Higgs transverse momentum distribution at the LHC is discussed.
The transverse polarization of $Λ^0$ hyperons produced in the inclusive $ep$ reaction at the 27.6 GeV beam energy is assumed to appear mostly via scattering of the strange quark in a color field. Results of application of such an idea to the preliminary data of HERMES are presented. Contributions of $Σ^0$, $Ξ$, and $Σ^*$ resonances to the polarization are taken into account.
The scale factor $σ_{eff}$, which characterizes double parton collisions in high energy hadron interactions, is a direct manifestation of the distribution of the interacting partons in transverse space, in such a way that different distributions give rise to different values of $σ_{eff}$ in different double parton collision processes. We work out the value of the scale factor in a few reactions of interest, in a correlated model of the multi-parton density of the proton recently proposed.
Jefferson Lab (JLab) 12 GeV energy upgrade provides a golden opportunity to perform precision studies of the transverse spin and transverse-momentum-dependent structure in the valence quark region for both the proton and the neutron. In this paper, we focus our discussion on a recently approved experiment on the neutron as an example of the precision studies planned at JLab. The new experiment will perform precision measurements of target Single Spin Asymmetries (SSA) from semi-inclusive electro-production of charged pions from a 40-cm long transversely polarized $^3$He target in Deep-Inelasti…
We apply the $k_T$-factorization approach to the production of $ϕ$ meson in deep-inelastic scattering. The helicity-conserving $γ^*(T,L) \to ϕ$ impact factor is calculated for longitudinal and transverse photon polarization using $ϕ$ meson distribution amplitudes. Different unintegrated gluon distributions are used in the calculations. The formalism for massless quarks/antiquarks gives too large transverse and longitudinal cross sections for photon virtualities below $Q^2\sim 8 \, \rm{GeV}^2$. We suggest how to improve the description of the HERA data by introducing effective strange quark mas…
We calculate the yields of quarkonia in heavy ion collisions at RHIC and the LHC as a function of their transverse momentum. Based upon non-relativistic quantum chromodynamics, our results include both color-singlet and color-octet contributions and feed-down effects from excited states. In reactions with ultra-relativistic nuclei, we focus on the consistent implementation of dynamically calculated nuclear matter effects, such as coherent power corrections, cold nuclear matter energy loss, and the Cronin effect in the initial state. In the final state, we consider radiative energy loss for the…
The influence of the nuclear Coulomb field on transverse spectra of $π^+$ and $π^-$ measured in $Pb+Pb$ reactions at 158 A GeV has been investigated. Pion trajectories are calculated in the field of an expanding fireball. The observed enhancement of the $π^-/π^+$ ratio at small momenta depends on the temperature and transverse expansion velocity of the source, the rapidity distribution of the net positive charge, and mainly the time of the freeze-out.
We employ the Monte-Carlo PYTHIA to calculate the transverse mass spectra of various hadrons and their inverse slopes T* at m_T-m=1.5-2 GeV in p+p reactions at sqrt(s)=200 GeV. Due to (multiple) minijet production T* increases as a function of the hadron mass. Moreover, the T*(m) systematics has a ``discontinuity'' at the charm threshold, i.e. the inverse slope of D-mesons is much higher than that of non-charmed hadrons and even of the heavier Lambda_C baryon. The experimental observation of this characteristic behaviour in Au+Au collisions would indicate the absence of c-quark rescattering. I…
Partonic intrinsic transverse momentum can be essential for the explanation of large single spin asymmetries in hadronic reactions in the framework of perturbative QCD. The status of an ongoing program investigating in a consistent way the role of intrinsic transverse momentum both in unpolarized and polarized processes is discussed. We compute inclusive cross sections for hadron and photon production in hadronic collisions and for Drell-Yan processes; the results are compared with available experimental data in several different kinematical situations.
The transverse polarization observed in the inclusive production of Lambda hyperons in the high energy collisions of unpolarized hadrons is tackled by considering a new set of spin and kT dependent quark fragmentation functions. Simple phenomenological expressions for these new ``polarizing fragmentation functions'' are obtained by a fit of the data on Lambda's and Lambdabar's produced in p-N processes.
Since the $ν_τ(\barν_τ) A_Z \to τ^\mp X$ reaction is notoriously difficult to be directly measured, the information on the dynamics of this nuclear process should be extracted from the analysis of the energy and angular distributions of the tau decay visible products. These distributions depend on the components of the tau-polarization vector. We give, for the first time, the general expression for the outgoing hadron (pion or rho meson) energy and angular differential cross section for the sequential $ν_τA_Z \to τ^-(π^- ν_τ, ρ^-ν_τ) X$ and $\barν_τA_Z \to τ^+(π^+ \barν_τ, ρ^+ \barν_τ) X$ reac…
The effective reggeon field theory in zero transverse dimension ("the toy model") is studied. The transcendental equation for eigenvalues of the Hamiltonian of this theory is derived and solved numerically. The found eigenvalues are used for the calculation of the pomeron propagator.
