Quark Rearrangement Model Research Articles

Baryon-antibaryon dynamics in relativistic heavy-ion collisions

The dynamics of baryon-antibaryon annihilation and reproduction ($B{\bar B} \leftrightarrow 3 M$) is studied within the Parton-Hadron-String Dynamics (PHSD) transport approach for Pb+Pb and Au+Au collisions as a function of centrality from lower Super Proton Synchrotron (SPS) up to Large Hadron Collider (LHC) energies on the basis of the quark rearrangement model (QRM). At Relativistic Heavy-Ion Collider (RHIC) energies we find a small net reduction of baryon-antibaryon ($B {\bar B}$) pairs while for the LHC energy of $\sqrt{s_{NN}}$ = 2.76 GeV a small net enhancement is found relative to calculations without annihilation (and reproduction) channels. Accordingly, the sizeable difference between data and statistical calculations in Pb+Pb collisions at $\sqrt{s_{NN}}$= 2.76 TeV for proton and antiproton yields \cite{53}, where a deviation of 2.7 $\sigma$ was claimed by the ALICE Collaboration, should not be attributed to a net antiproton annihilation. This is in line with the observation that no substantial deviation between the data and statistical hadronization model (SHM) calculations is seen for antihyperons, since according to the PHSD analysis the antihyperons should be modified by the same amount as antiprotons. As the PHSD results for particle ratios are in line with the ALICE data (within error bars) this might point towards a deviation from statistical equilibrium in the hadronization (at least for protons/antiprotons). Furthermore, we find that the $B {\bar B} \leftrightarrow 3 M$ reactions are more effective at lower SPS energies where a net suppression for antiprotons and antihyperons up to a factor of 2 -- 2.5 can be extracted from the PHSD calculations for central Au+Au collisions.

Baryon-antibaryon annihilation and reproduction in relativistic heavy-ion collisions

The quark rearrangement model for baryon-antibaryon annihilation and reproduction ($B\bar B\leftrightarrow 3M$) - incorporated in the Parton-Hadron-String Dynamics (PHSD) transport approach - is extended to the strangeness sector. A derivation of the transition probabilities for the three-body processes is presented and a strangeness suppression factor for the invariant matrix element squared is introduced to account for the higher mass of the strange quark compared to the light up and down quarks. In simulations of the baryon-antibaryon annihilation and reformation in a box with periodic boundary conditions we demonstrate that our numerical implementation fulfills detailed balance on a channel-by-channel basis for more than 2000 individual $2 \leftrightarrow 3$ channels. Furthermore, we study central Pb+Pb collisions within PHSD from 11.7$A$ GeV to 158$A$ GeV and investigate the impact of the additionally implemented reaction channels in the strangeness sector. We find that the new reaction channels have a visible impact essentially only on the rapidity spectra of antibaryons. The spectra with the additional channels in the strangeness sector are closer to the experimental data than without for all antihyperons. Due to the chemical redistribution between baryons/antibaryons and mesons we find a slightly larger production of antiprotons thus moderately overestimating the available experimental data. We additionally address the question if the antibaryon spectra (with strangeness) from central heavy-ion reactions at these energies provide further information on the issue of chiral symmetry restoration and deconfinement. However, by comparing transport results with/without partonic phase as well as including/excluding effects from chiral symmetry restoration we find no convincing signals in the strange antibaryon sector for either transition due to the strong final-state interactions.

Spin physics in the high energy hadron productions. A systematic study of the spin asymmetries induced by pp, γp, ep and λp collisions

The spin polarizations of hadrons inclusively produced by pp, γp and νp collisions are studied by the quark rearrangement model. The present model is a phenomenological one based on the relativistic spin equations of motion and using the quark distribution functions in hadrons and photon. A general success of the model is demonstrated. We find usefulness of the present formulation for studying the dynamics producing spin asymmetry distributions and the statics determining signs and magnitudes of the spin polarization by reflecting the characteristic quark structure in hadrons.

NN̄ annihilation into two mesons: Effect of final-state interactions

An extension of the usual quark rearrangement model is made in such a way that the transition NN̄(S) into two s-wave mesons takes place with the 3P 0 vertex acting only once. However, this is at the expense of introducing, into the final state, meson-meson rescattering. The result is a partial understanding of several S-wave branching ratios but does not explain the so-called πρ puzzle.

P� p annihilation into two mesons in the quark rearrangement model and the quark annihilation model

The relativistic3P0 model is applied to the\(p\bar p\) annihilation into twoS-wave mesons. We calculate the branching ratios of the\(p\bar p\) annihilation at rest into two mesons in the quark rearrangement model and in the quark annihilation model. In the annihilation model, we project the intermediate\(cq\bar q\) state to eigenstates ofSU (4) with the relative angular momentum of\(cq\bar q\) equals orp. In the rearrangement model, no annihilation occurs from theS-wave\(p\bar p\) and certain branching ratios conflict with the experimental data. Detailed comparison with the experiment needs inclusion ofP-wave mesons in the final state, nevertheless we find that the annihilation model gives qualitatively better results than the rearrangement model. The effect of initial state interaction through\(N\bar \Delta \pm \Delta \bar {\rm N}\) or\(\Delta \bar \Delta \) channels is discussed.

P�p Annihilation into two mesons in the quark rearrangement model and the quark annihilation model

The relativistic3P0 model is applied to the\(p\bar p\) annihilation into twoS-wave mesons. We calculate the branching ratios of the\(p\bar p\) annihilation at rest into two mesons in the quark rearrangement model and in the quark annihilation model. In the annihilation model, we project the intermediate\(cq\bar q\) state to eigenstates ofSU (4) with the relative angular momentum of\(cq\bar q\) equals orp. In the rearrangement model, no annihilation occurs from theS-wave\(p\bar p\) and certain branching ratios conflict with the experimental data. Detailed comparison with the experiment needs inclusion ofP-wave mesons in the final state, nevertheless we find that the annihilation model gives qualitatively better results than the rearrangement model. The effect of initial state interaction through\(N\bar \Delta \pm \Delta \bar {\rm N}\) or\(\Delta \bar \Delta \) channels is discussed.

NN̄ annihilation — the effect of one- and two-meson intermediate states

Earlier work describing NN̄ annihilation in terms of three-meson intermediate states with the quark rearrangement model is now extended to include one- and two-meson states. The latter are incorporated using the 13P 0 quark-antiquark annihilation mechanism. In addition an estimate is made of the strength of the rearrangement interaction, and also the effect of treating the annihilation into two mesons as a two-step process.

Annihilation branching ratios into three mesons in the S-wave quark rearrangement model

The branching ratios of the p p annihilation “at rest” into three s-wave mesons have been calculated in the quark rearrangement model. The strength of the annihilation potential — basically the only parameter adjusted — most favoured in comparison with the sparse data is found to be approximately the same which maximizes the annihilation cross section at a laboratory energy of 100 MeV. The effect of the meson-exchange initial interaction is studied in some detail and found to be strong.

FormulaN Bound and Scattering States Due to the Quark-Rearrangement Annihilation and the One-Boson Exchange

A microscopic NN potential is presented where the annihilation contribution is described by the quark rearrangement model and the one-boson-exchange contribution is further added. Gross features of PP scattering observables are described by the potential with modification by a phenomenological repulsion at short distances. The NN potential has the remarkable features: the strong dependence on energy and quantum-numbers, the node effects and the tensor-force dominance. These properties create several narrow-width bound and resonance states in the mass region 1900\gtrsimMNN≳1360 MeV. The nature of the phenomenological repulsion is discussed.

Quark Rearrangement and Annihilation Model for Formula N Annihilation at 0 300 MeV

Quark Rearrangement and Annihilation Model for Formula N Annihilation at 0 300 MeV

Formula omitted] scattering below 300 MeV due to quark rearrangement annihilation and one-boson exchange

A microscopic NN potential is presented where the annihilation effect is described by the quark rearrangement model and the one-boson-exchange contribution is further added. Gross features of pp scattering observables are described by the potential with modification by a phenomenological repulsion at short distances.

Pp̄ Annihilation in a quark rearrangement model including S- and P-waves

A quark-antiquark rearrangement mechanism is applied to S- plus P-wave pp̄ annihilation. Including the effect of N Δ ± Δ and Δ Δ configurations enables the model to account for up to 70% of the observed annihilation cross section. This is achieved only by including the widths of the mesons.

The pp̄ interaction with an annihilation potential derived from the quark rearrangement model

Abstract The s-wave pp annihilation potential is derived from the quark rearrangement model. Combining the G -parity transformed OBEP of Bryan and Phillips and the derived s-wave annihilation potential we solve the multichannel N / D equation by the Pade approximant method. For the p- and d-waves we introduce a phenomenological annihilation potential from a few-meson decay mode. We can reproduce the annihilation cross section by choosing two parameters: the strength of the s-wave annihilation potential and the strength of the p- and d-wave annihilation potential. We find p-wave quasi-bound states near the threshold but their energy and width are sensitive to the energy dependence of the effective phase-space function x ( E ).

Pp̄ Annihilation at rest into mesons in the quark rearrangement model and the quark annihilation modelt

Abstract pp annihilation at rest into mesons is calculated in the quark rearrangement model in which 3 quarks and 3 antiquarks rearrange into 3 mesons and in the quark annihilation model in which one or two quark-antiquark pairs are annihilated and a quark-antiquark pair is created to form two or three mesons. The constants of the quark-meson coupling are adjusted such that the meson-nucleon interactions agree with experiment. The radial dependences of the quark-meson couplings are all assumed to be the same. This is determined by the vector-meson-quark interaction derived from the charge form factor of the proton. In the case of the decay into three mesons both rearrangement and annihilation models explain with similar reliability the branching ratio of the decay products. In the case of the decay into two-meson annihilation gives a better agreement with experiment than rearrangement.

A quark rearrangement model with spatial overlap function for low energy N [formula omitted] annihilation

The major part of the branching ratios for the N N annihilation at rest is explained by the quark rearrangement in the N and N into three SU(6) mesons. This is shown by using the spin, isospin, and spatial overlap function derived theoretically from quark dynamics.

Quark Rearrangement Model for Nucleon-Antinucleon Annihilation at Low Energies

Nucleon·antinucleon annihilation process at low energies has been explained by the quark rearrangement model with parameters ga, where ga describes the strength for a quark·antiquark pair to combine into a meson (Jr, lJ, P, w). This parameter has strong dependence on the kind of the meson and is in the order of the meson mass. It is shown that these properties originate from the overlapping of quark wave functions of hadrons. The relation to the potential model for NN interaction is also discussed.

N̄N annihilation at low energies in a quark rearrangement model and decay widths of N̄N bound states

Using N̄N annihilation data at rest, we make a quark rearrangement model for annihilation into three mesons. This model describes the decay branching ratios of the p̄p and p̄n annihilations at rest satisfactorily. With this model we find considerable dependence of the annihilation on the isospin and spin of the initial N̄N system. By calculating the energy dependence due to the phase space of three mesons, we extend the model in the energy range E c.m.. = 1400 MeV–2300 MeV where E c.m. is the total energy in the c.m.s. We find the strong energy dependence of the annihilation, with the annihilation probability below the N̄N threshold reduced drastically, compared to that at threshold. Based on the result for the quantum number and energy dependence, we discuss the possibility of the existence of N̄N bound states with narrow decay widths.

Simple picture of the annihilation process

We propose a simple geometrical picture for $\overline{B}B$ annihilations, which is motivated by the electric-flux-tube model and is consistent with the quark-rearrangement model, as well as the nonplanar multiperipheral quark-exchange model. Within its framework we are able to explain all the salient features of the experimental annihilation data.

Electroproduction of a Meson and Correlating Quark Rearrangement Model

n is the total number of quark lines with large momentum transfer in the respective diagrams. A virtual photon must not be countecl as "two" like a meson, but as "unity" in the power counting. ii) The angular distribution and Q' dependence on the differential cross section are predicted and they are in good agreement with experiments. iii) The valence quark contribution is dominant in the large Q 2 region. The correspondence between the parton model and correlating quark rearrangement model is discussed.

Large pT Jet Production and Hard Rearrangement of Quarks

Productions of large pT meson-, baryon- and antibaryon-jets are investigated on the basis of correlating quark rearrangement (CQR) model. In meson-jet productions the main contribution arises from the quark rearrangements (QR) with two hard quarks which are scattered to each other with large momentum transfer, while in baryon- and antibaryon-jet productions QR's with three hard quarks dominate. Antibaryon-jet production in BB collisions is, however, forbidden in CQR model. The power behaviors, the xT(=2pT/√s)-dependence, the angular dependence and the relative magnitudes for various types of jet productions are obtained. It is shown that these features of the jet cross sections are closely linked to the patterns of QR. The predicted power behaviors of large pT hadron productions are ∼pT-8 for (M, B, ̄B)B→MX and BB→̄BX and ∼pT-12 for (M, B, ̄B)→BX and (M, ̄B)B→̄BX in the FNAL region. Above that energy and pT, we have ∼pT-8 for all the large pT hadron production processes.