Hadron Dynamics Research Articles

Composite superstring model for hadron amplitudes

Hadron dynamics is formulated in terms of interacting composite strings. These composite string amplitudes give other possible solution of duality equations for crossing channels in addition to classical string amplitudes. The composite strings carry quark flavour and spin degrees of freedom on edging two-dimensional surfaces. Consistent composite string models with extended N = 3 Virasoro superconformal symmetry are found. Simple amplitudes for interaction of π and K-mesons in this model are represented.

Relativistic corrections of one-nucleon current in low-energy three-nucleon photonuclear reactions

Proton-deuteron radiative capture and two- and three-body photodisintegration of 3He at low energy are described using realistic hadronic dynamics and including the Coulomb force. The sensitivity of the observables to the relativistic corrections of one-nucleon electromagnetic current operator is studied. Significant effects of the relativistic spin-orbit charge are found for the vector analyzing powers in the proton-deuteron radiative capture and for the beam-target parallel-antiparallel spin asymmetry in the three-body photodisintegration of 3He.

Slow-proton production in semi-inclusive deep inelastic scattering off the deuteron and complex nuclei: Hadronization and final-state interaction effects

The effects of the final-state interaction in slow-proton production in semi-inclusive deep inelastic scattering processes off nuclei, $A(e,{e}^{'}p)X$, are investigated in detail using the spectator and target-fragmentation mechanisms. In the former mechanism, a hard interaction on a nucleon of a correlated pair leads, by recoil, to the emission of the partner nucleon, whereas in the latter mechanism a proton is produced when the diquark, which is formed right after the ${\ensuremath{\gamma}}^{*}$-quark interaction, captures a quark from the vacuum. Unlike previous papers on the subject, particular attention is paid to the effects of the final-state interaction of the hadronizing quark with the nuclear medium using an approach based on an effective time-dependent cross section that combines the soft and hard parts of hadronization dynamics in terms of the string model and perturbative QCD, respectively. It is shown that the final-state interaction of the hadronizing quark with the medium plays a relevant role in both deuterons and complex nuclei. Nonetheless, kinematical regions where final-state interaction effects are minimized can be selected experimentally, which would allow one to investigate the structure functions of nucleons embedded in the nuclear medium. Likewise, regions where the interaction of the struck hadronizing quark with the nuclear medium is maximized can be found, which would make it possible to study nonperturbative hadronization mechanisms.

Parton–hadron–string dynamics: An off-shell transport approach for relativistic energies

The dynamics of partons, hadrons and strings in relativistic nucleus–nucleus collisions is analyzed within the novel Parton–Hadron–String Dynamics (PHSD) transport approach, which is based on a Dynamical QuasiParticle Model (DQPM) for partons matched to reproduce recent lattice-QCD results – including the partonic equation of state – in thermodynamic equilibrium. Scalar- and vector-interaction densities are extracted from the DQPM as well as effective scalar- and vector-mean fields for the partons. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark–antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energy–momentum conservation. Since the dynamical quarks and antiquarks become very massive close to the phase transition, the formed resonant ‘pre-hadronic’ color-dipole states ( q q ¯ or qqq) are of high invariant mass, too, and sequentially decay to the groundstate meson and baryon octets increasing the total entropy. The PHSD approach is applied to nucleus–nucleus collisions from 20 to 160 A GeV in order to explore the space–time regions of ‘partonic matter’. We find that even central collisions at the top-SPS energy of 158 A GeV show a large fraction of non-partonic, i.e. hadronic or string-like matter, which can be viewed as a hadronic corona. This finding implies that neither hadronic nor only partonic ‘models’ can be employed to extract physical conclusions in comparing model results with data. On the other hand – studying in detail Pb + Pb reactions from 40 to 158 A GeV – we observe that the partonic phase has a very low impact on rapidity distributions of hadrons but a sizeable influence on the transverse mass distribution of final kaons due to the repulsive partonic mean fields. Furthermore, we find a significant effect on the production of multi-strange antibaryons due to a slightly enhanced s s ¯ pair production in the partonic phase from massive time-like gluon decay and a larger formation of antibaryons in the hadronization process.

Elliptic flow and incomplete equilibration

The dependence of eccentricity scaled elliptic flow on the partonic cross section in $\mathrm{Au}+\mathrm{Au}$ collisions at relativistic heavy ion collider (RHIC) energy $\sqrt{{s}_{\mathit{NN}}}=200 \mathrm{GeV}$ with impact parameter $b=8 \mathrm{fm}$ is analyzed using a multiphase transport (AMPT) model. It is shown that the dependence of eccentricity scaled elliptic flow on the partonic cross section could be described well by a formula suggested by Bhalerao et al. The eccentricity scaled elliptic flow of the parton is $19%~27%$ lower than its `hydrodynamic limit.' The hadronization of the parton through coalescence and hadronic dynamics (decay, collision) could influence the obtained deviation of eccentricity scaled elliptic flow of the hadron from its `hydrodynamic limit.' The hadronic final state interactions and hadronization reduce the extracted `hydrodynamic limit' by 20% and also reduce the deviation from the `hydrodynamic limit' by 26%.

QCD critical point and experimental observables

The presence of a critical point in the QCD phase diagram can deform the trajectories describing the evolution of the expanding fireball in the μB–T phase diagram. If the average emission time of hadrons is a function of transverse velocity, as microscopic simulations of the hadronic freeze-out dynamics suggest, the deformation of the hydrodynamic trajectories will change the transverse velocity (βT) dependence of the proton–antiproton ratio when the fireball passes in the vicinity of the critical point. An unusual βT-dependence of the ratio in a narrow beam energy window would thus signal the presence of the critical point.

Transverse Velocity Dependence of the Proton-Antiproton Ratio as a Signature of the QCD Critical Point

The presence of a critical point in the QCD phase diagram can deform the trajectories describing the evolution of the expanding fireball in the mu_B-T phase diagram. If the average emission time of hadrons is a function of transverse velocity, as microscopic simulations of the hadronic freeze-out dynamics suggest, the deformation of the hydrodynamic trajectories will change the transverse velocity (beta_T) dependence of the proton-antiproton ratio when the fireball passes in the vicinity of the critical point. An unusual beta_T dependence of the [over]p/p ratio in a narrow beam energy window would thus signal the presence of the critical point.

OPEN AND HIDDEN CHARM IN PROTON–NUCLEUS AND HEAVY-ION COLLISIONS

We review dynamical and thermal models for the collectivity and the suppression pattern of charmed mesons — produced in proton–nucleus and nucleus–nucleus collisions at SPS (~158 A GeV) and RHIC energies (~21 A TeV). In particular, we examine the charmonium "melting" and the "comover dissociation" scenarios — implemented in a microscopic transport approach — in comparison to the available data from the SPS and RHIC. The analysis shows that the dynamics of c and [Formula: see text] quarks. quarks at RHIC are dominated by partonic or "pre-hadronic" interactions in the strongly coupled plasma stage and can neither be modeled by "hadronic" interactions nor described appropriately by color screening alone. Both the "charmonium melting" and the hadronic "comover absorption and recreation model" are found, however, to be compatible with the experimental observation at SPS energies; the experimental ratio of Ψ′/J/Ψ versus centrality clearly favors the "hadronic comover" scenario. We find that the collective flow of charm in the purely hadronic Hadron-String Dynamics (HSD) transport appears compatible with the data at SPS energies, but the data at top RHIC energies are substantially underestimated. Thus, the large elliptic flow v2 of D-mesons and the low RAA(pT) of J/Ψ seen experimentally have to be attributed to early interactions of non-hadronic degrees of freedom. Simultaneously, we observe that non-hadronic interactions are mandatory in order to describe the narrowing of the J/Ψ rapidity distribution from pp to central Au + Au collisions at the top RHIC energy of [Formula: see text]. Additionally we demonstrate that the strong quenching of high-pTJ/Ψ's in central Au + Au collisions indicates that a large fraction of final J/Ψ mesons is created by a coalescence mechanism close to the phase boundary. Throughout this review we, furthermore, provide predictions for charm observables from Au + Au collisions at FAIR energies of 25–35 A GeV.

Mass ordering of differential elliptic flow and its violation for ϕ mesons

We simulate the dynamics of Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC) with a hybrid model that treats the dense early quark-gluon plasma (QGP) stage macroscopically as an ideal fluid but models the dilute late hadron resonance gas (HG) microscopically using a hadronic cascade. By comparing with a pure hydrodynamic approach we identify effects of hadronic viscosity on the transverse momentum spectra and differential elliptic flow v{sub 2}(p{sub T}). We investigate the dynamical origins of the observed mass ordering of v{sub 2}(p{sub T}) for identified hadrons, focusing on dissipative effects during the late hadronic stage. Within our approach, we find that, at RHIC energies, much of the finally observed mass splitting is generated during the hadronic stage, due to buildup of additional radial flow. The {phi} meson, having a small interaction cross section, does not fully participate in this additional flow. As a result, it violates the mass-ordering pattern for v{sub 2}(p{sub T}) that is observed for other hadron species. We also show that the early decoupling of the {phi} meson from the hadronic rescattering dynamics leads to interesting and unambiguous features in the p{sub T} dependence of the nuclear suppression factor R{sub AA} and of the {phi}/pmore » ratio.« less

Strangeness at the threshold of phase change

We explore entropy and strangeness as the signature of quark–gluon plasma (QGP) for the top AGS and the energy scan at SPS. We find that the hadronization dynamics changes between 20 and 30 A GeV projectile energy. The high-energy results are consistent with the QGP.

Recent developments in chiral dynamics of hadrons and hadrons in a nuclear medium

In this talk I present recent developments in chiral dynamics of hadrons and hadrons in a medium addressing the following points: interaction of the octet of pseudoscalar mesons with the octet of baryons of the nucleon, showing recent experimental evidence on the existence of two Λ(1405) states, the interaction of the octet of pseudoscalar mesons with the decuplet of baryons of the Δ, with particular emphasis on the Λ(1520) resonance, dynamically generated by this interaction. Then I review the interaction of kaons in a nuclear medium and briefly discuss the situation around the claims of deeply bound states in nuclei. The large renormalization of the Λ(1520) in the nuclear medium is shown as another example of successful application of the chiral unitary techniques.

Parton degrees of freedom and hadronization dynamics at RHIC

Most observables measured at RHIC involve strongly interacting particles from the final hadronic stage. They carry, however, useful information on the properties of the partonic matter produced during the initial stage and its hadronization dynamics. For example, observed large elliptic flow of hadrons and their scaling according to the number of valence quarks in a hadron have provided strong evidence for the formation of an initial partonic matter that is strongly interacting and hadronizes via coalescence or recombination of quarks. In this paper, the relation between hadron anisotropic flow and that of produced partons is illustrated in terms of a multiphase transport model that includes interactions both in initial partonic and final hadronic matters as well as the transition between these two phases of matter.

Chiral Dynamics of Hadrons in Nuclei

In this talk I report on selected topics of hadron modification in the nuclear medium using the chiral unitary approach to describe the dynamics of the problems. I shall mention how antikaons, $\eta$, and $\phi$ are modified in the medium and will report upon different experiments done or planned to measure the $\phi$ width in the medium.

Momentum-space description of three-nucleon breakup reactions including the Coulomb interaction

The Coulomb interaction between two protons is included in the calculation of proton-deuteron breakup and of three-body electromagnetic disintegration of $^{3}\mathrm{He}$. The hadron dynamics is based on the purely nucleonic charge-dependent (CD) Bonn potential and its realistic extension, CD Bonn + \ensuremath{\Delta}, to a coupled-channel two-baryon potential, allowing for single virtual \ensuremath{\Delta}-isobar excitation. Calculations are done using integral equations in momentum space. The screening and renormalization approach is employed for including the Coulomb interaction. Convergence of the procedure is found at moderate screening radii. The reliability of the method is demonstrated. The Coulomb effect on breakup observables is seen at all energies in particular kinematic regimes.

Dynamics and decay of heavy-light hadrons

Recent signals for narrow hadrons containing heavy and light flavors are compared with quark model predictions for spectroscopy, strong decays, and radiative transitions. In particular, the production and identification of excited charmed and $c\overline{s}$ states are examined with emphasis on elucidating the nature of ${0}^{+}$ and ${1}^{+}$ states. Roughly 200 strong decay amplitudes of $D$ and ${D}_{s}$ states up to 3.3 GeV are presented. Applications include determining flavor content in $\ensuremath{\eta}$ mesons and the mixing angle in $P$ and $D$ wave states and probes of putative molecular states. We advocate searching for radially excited ${D}_{s}^{*}$ states in $B$ decays.

Quantum Systems on Linear Groups

Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in nuclear and hadronic dynamics. They differ from traditional Bohr–Mottelson models where SL(n,ℝ) is used as a so-called non-invariance group. There is an interesting relationship between classical and quantized integrable lattices.

Calculation of Proton-Deuteron Breakup Reactions including the Coulomb Interaction between the Two Protons

The Coulomb interaction between the two protons is fully included in the calculation of proton-deuteron breakup with realistic interactions for the first time. The hadron dynamics is based on the purely nucleonic charge-dependent (CD) Bonn potential and its realistic extension CD Bonn +Delta to a coupled-channel two-baryon potential, allowing for single virtual Delta-isobar excitation. Calculations are done using integral equations in momentum space. The screening and renormalization approach is employed for including the Coulomb interaction. The Coulomb effect on breakup observables is seen at all energies in particular kinematic regimes.

Polarizations in decaysBu,d→VVand possible implications forR-parity violating supersymmetry

Recently BABAR and Belle have measured anomalous large transverse polarizations in some pure penguin $B\ensuremath{\rightarrow}VV$ decays, which might be inconsistent with the standard model expectations. We try to explore its implications for $R$-parity violating (RPV) supersymmetry. The QCD factorization approach is employed for the hadronic dynamics of $B$ decays. We find that it is possible to have parameter spaces solving the anomaly. Furthermore, we have derived stringent bounds on relevant $R$-parity violating couplings from the experimental data, which is useful for further studies of RPV phenomena.

Atomic mass dependence of hadron production in deep inelastic scattering on nuclei

Hadron production in lepton–nucleus deep inelastic scattering is studied in an absorption model. In the proposed model, the early stage of hadronization in the nuclear medium is dominated by prehadron formation and absorption, controlled by flavor-dependent formation lengths and absorption cross sections. Computations for hadron multiplicity ratios are presented and compared with the HERMES experimental data for pions, kaons, protons and antiprotons. The mass-number dependence of hadron attenuation is shown to be sensitive to the underlying hadronization dynamics. Contrary to common expectations for absorption models, a leading term proportional to A 2 / 3 is found. Deviations from the leading behavior arise at large mass-numbers and large hadron fractional momenta.

Benchmark calculation for proton-deuteron elastic scattering observables including the Coulomb interaction

Two independent calculations of proton-deuteron elastic scattering observables including Coulomb repulsion between the two protons are compared in the proton laboratory energy region between 3 and 65 MeV. The hadron dynamics is based on the purely nucleonic charge-dependent AV18 potential. Calculations are done in both coordinate space and momentum space. The coordinate-space calculations are based on a variational solution of the three-body Schr\"odinger equation using a correlated hyperspherical expansion for the wave function. The momentum-space calculations proceed via the solution of the Alt-Grassberger-Sandhas equation using the screened Coulomb potential and the renormalization approach. Both methods agree to the order of 1% on all observables, showing the reliability of both numerical techniques in that energy domain. At energies below the three-body breakup threshold, the coordinate-space method remains favored; at energies higher than 65 MeV, the momentum-space approach seems to be more efficient.