Reaction πN Research Articles

Roles of NΔ → NN and πN → Δ Reactions in Heavy-Ion Collisions at Intermediate Energies**Supported by the National Natural Science Foundation of China under Grant No. 11505150; the Yuncheng University Research Project under Grant No. YQ-2014014; the National Natural Science Foundation of China under Grant No. 11405278

Within the framework of the isospin-dependent transport model, the roles of the reactions NΔ → NN and πN → Δ are investigated through simulating heavy-ion collisions at 1000 MeV/nucleon. The absorption process NΔ → NN plays an important role for heavy impact systems and small impact parameters than for light impact systems and large impact parameters. The resorption process πN → Δ is of importance for heavy impact systems and large impact parameters than for light impact systems and small impact parameters. Thus the influences of the reaction NΔ → NN (πN → Δ) on pion production dynamics can be neglected in heavy-ion collisions for smaller (larger) impact parameters and light systems. It is the reaction πN → Δ that causes the anti-correlation of pions and nucleons in the rapidity dependence of the directed flow.

Chiral dynamics of/with unstable particles

We review the achievements of the project C.9 . Topics addressed include the magnetic moment of the ρ -meson, elastic pion-nucleon scattering in various settings of chiral perturbation theory, the reaction πN → ππN as well as new directions in chiral perturbation theory.

The reaction πN → ππN in a meson-exchange approach

A resonance model for two-pion production in the pion-nucleon reaction is developed that includes information obtained in the analysis of pion-nucleon scattering in a meson-exchange model. The baryonic resonances Δ(1232), N*(1440), N*(1520), N*(1535), and N*(1650) are included. The model reproduces the total cross-sections up to kinetic energies of the incident pion of 400MeV and obtains the shapes of the differential cross-sections in reasonable agreement with the data.

Baryon resonance dynamics in πN → NV reactions near threshold

The ϱ − ω interference in the exclusive reaction πN → N′ e + e − is studied within a schematic model including the established baryon resonances up to 1720 MeV. Near threshold the interference can be used to separate the isoscalar part of the electromagnetic current. The role of various baryon resonances is highlighted.

One-loop analysis of the reaction πN→ ππN

Single pion production off nucleons is studied in the framework of heavy baryon chiral perturbation theory to third order in the chiral expansion. Using total and some older differential cross section data to pin down the low-energy constants, most of the recent differential cross sections and angular correlation functions can be described as well as total cross sections at higher energies. We show that the contributions from the one loop graphs are essentially negligible and that the dominant terms at second and third order are related to pion–nucleon scattering graphs with one pion added. We also discuss the possibility of extracting the pion–pion S-wave scattering lengths from the unpolarized data.

ωN final state interactions and ω-meson production from heavy-ion collisions

We calculate the elastic and inelastic ωN→ωN, →πN, →ρN, →ρπN, →ππN, →σN reactions within a boson exchange approximation where the ωρπ coupling constant and form factor are fixed by the reaction πN→ωN in comparison to the experimental data. We find rather large ωN cross sections at low relative momenta of the ω-meson which leads to a substantial broadening of the ω-meson width in nuclear matter. The implications of the ωN final state interactions are studied for ω production in 12C +12C, 40Ca +40Ca and 58Ni +58Ni reactions at about 2 · A GeV within the HSD transport approach; the drastic changes of the transverse mass spectra relative to a general m T-scaling (for π0 and η mesons) might be controlled experimentally by the TAPS Collaboration.

Phenomenological πN→ππN amplitude and the modelling of the Olsson–Turner and Chew–Low approaches

The phenomenological amplitude for the reaction πN→ππN fixed by fittings to the experimental data in the energy region 0.300 ≤PLab≤ 500 MeV/c is used for modelling the Chew–Low extrapolation and Olsson–Turner threshold approach. It is shown that the uncritical application of the former results in enermous theoretical errors, the extracted values being in fact random numbers. The results of the Olsson–Turner method are characterized by significant systematic errors coming from unknown details of the isobar physics.

The reaction πN → ππN above threshold in chiral perturbation theory

Single pion production off nucleons is studied in the framework of relativistic baryon chiral perturbation theory at tree level with the inclusion of the terms from the dimension two effective pion-nucleon Lagrangian. The five appearing low-energy constants are fixed from pion-nucleon scattering data. Despite the simplicity of the approach, most of the existing data for total and differential cross sections as well as for the angular correlation functions for incoming pion kinetic energies up to 400 MeV can be satisfactorily described.

Phi meson production cross sections in pion-baryon and baryon-baryon interactions

Phi meson production in pion-baryon and baryon-baryon interactions near the production threshold is studied in a boson-exchange model. Parameters in this model are either taken from the Bonn model for the nucleon-nucleon potential or determined from the measured phi meson decay width and the experimental data for the reactions π − p→ φn and pp→ ppφ. The isospin-averaged cross sections for the reactions πN→ φN, πΔ→ φN, NN→ NNφ, which are needed in transport models to study phi meson production in heavy-ion collisions at subthreshold energies, have been evaluated. For the reactions NΔ→ NNφ and ΔΔ→ NNφ, which become singular when the exchanged pion is on-shell, the Peierls method is used to calculate their cross sections. We find that the cross section for the reaction πN→ φN is much larger than the other cross sections.

The reaction πN → ππN at threshold in chiral perturbation theory

In the framework of heavy baryon chiral perturbation theory, we give the chiral expansion for the πN → ππN threshold amplitudes D 1 and D 2 to quadratic order in the pion mass. The theoretical results agree within one standard deviation with the empirical values. We also derive a relation between the two threshold amplitudes of the reaction πN → ππN and the ππ S-wave scattering lengths, a 0 0 and a 2 0, respectively, to order ( M 2 π ). We show that there are uncertainties mostly related to resonance excitation which make an accurate determination of the ππ scattering length a 0 0 from the ππN threshold amplitudes at present very difficult. The situation is different in the ππ isospin two final state. Here, the chiral series converges and one finds a 2 0 = −0.031 ± 0.007 consistent with the one-loop chiral perturbation theory prediction.

The reaction πN→ ππN at threshold

We consider the chiral expansion for the reaction πN → ππN in heavy baryon chiral perturbation theory. To order M π we derive novel low-energy theorems that compare favorably with recent determinations of the total cross sections for π + p → π + π + n and π − p → π 0 π 0 n.

Chiral symmetry and the near threshold pion-induced 2π production on the nucleon: (III). Perturbative estimate of initial and final state interactions

We investigate initial and final state interactions in the exclusive reaction πN → π πN near the 2π-threshold. Based on a diagrammatical expansion of the transition amplitude we estimate the leading loop and triangle diagrams in lowest order. We find, that for monopole cutoff masses Λ ⩽ 800 MeV (corresponding to radii of R ⩾ 0.7 fm in the cloudy bag model) at the different vertices, both contributions are at least one order of magnitude suppressed compared to the leading non-loop contributions to the total πN → π πN cross section.

A study of meson-baryon couplings in the constituent quark model

Within the framework of the constituent quark model we discuss the effects of different types of meson-baryon-baryon vertex operators on the form factors and the coupling strengths of the lowest-lying positive and negative parity non-strange baryons. We compare the quark pair creation model (3P0-model) with the SU(6)-model in which mesons are treated as elementary fields that directly couple to the quarks. The latter model is employed both in the so-called static limit and in a modification motivated by Galilei invariance. It is demonstrated that the inclusion of non-static effects simulates some features of the3P0 vertex. Especially the reaction πN→ππN is found to be very sensitive to the different assumptions on the dynamics of theq¯q pair creation process. More indirect hints for the internal structure of the mesons might be obtained from the predicted asymmetry for the two form factors ofN→Δ+π andΔ→N+π, which occurs in the3P0-model, only.

Duality and the reaction πN to πΔ

Finite energy sum rules applies to the reaction pi N to pi Delta are shown to discriminate in favour of one low-energy partial wave solution. The Adler-Weisberger sum rule is re-evaluated to estimate the required pi - Delta coupling constant. Local duality and the superconvergence of the exotic amplitudes are tested. The two-component duality hypothesis and the t dependence of the FESRS are also discussed.

Model-independent amplitude analysis for the reaction πN → ρΔ

A method is proposed for determining the amplitudes for the reaction πN → ϱΔ using only those moments of the joint decay angular distribution 〈 Y L 1 M 1 Y L 2 M 2 〉 with both L 1 and L 2 even. The solution is not unique; both continuous and discrete ambiguities exist. The conditions under which an analysis is possible are studied in detail; in addition to certain positivity conditions on the joint density matrix, a complicated inequality involving the experimental moments must be satisfied. This condition defines a non-convex domain in the space of the moments. We apply our methods to the high-statistics experimental data at 3.7 GeV/ c.

ω Production in the reaction π−p → π+π−π0n at 8 and 12 GeV/c

The reaction π −p → ωn has been studied at 8 and 12 GeV/ c incident momenta with the CERN Omega spectrometer using a neutron time of flight trigger. The differential cross sections and the ω-decay density matrix elements are presented as functions of the momentum transfer squared − t in the range of 0.02 to 0.80 GeV 2. The data are used to evaluate the intercept and slope of both the natural and unnatural parity exchange trajectories. Regge exchange amplitude factorisation tests involving the reaction πN → ωN are investigated.

A comparison of the reaction pp→ ΔϱN at 19 GeV/ c with the reaction πN→ ϱN′

The ratios between the cross sections of the reactions pp→Δ ☆☆ϱ 0 n, pp→Δ ☆☆ϱ − p, pp→Δ ☆ϱ 0 p and pp→Δ 0ϱ ☆ p , all at 19 GeV/ c incoming momentum, are calculated with the aid of the known cross sections at various energies for reactions of the type πN→ ϱN′. The results are in good agreement with experimental data and give evidence for dominance of a one-pion exchange mechanism in the reaction pp→ Δ( ϱN). The procedure also gives rough estimates of cross sections for the reactions pp→ ΔA 2N and pp→ ΔfN which are consistent with experimental observations.

N * resonance parameters and K-matrix fits to the reactions πN→Δπ+ϱN+ɛN

From a partial wave analysis of the reaction πN→ππN we extract 50 cuoplings and partial widths for N * resonance decaying into Δπ, ϱN and εN. Three different methods of determining the resonance parameters are compared. The signs of the πΔ couplings are found to be consistent with the predictions of l-broken SU(6) w, if one assigns P′ 11(1415), P″ 11(1730) and P 33(1700) to [56, L=0 +] supermultiplets. The signs of the ϱN couplings are inconsistent with SU(6) w symmetry in its l-broken form, but in good agreement with the observed photon couplings.

One‐Pion Exchange Model in the Vector Theory for the Reaction πN → πN. The Present Status. Connection with the Absorption

AbstractIn the present paper it is shown that the Born diagram model with an overall phenomenological form factor suggested in papers [2, 3] on the basis of the ideas of universal interaction of Q‐meson with hadrons describes well the experimental data on the reaction π−p → Q°n in a wide range of energies 2.7 GeV/c ≦ QL ≦ 17 GeV/c at small momentum transfers |t| ≦ 0.2 (GeV/c)2. The connection of the Born diagram model with the other high energy models is considered. On one hand, we show that the absorption account in many respects, though not literally, comes to forming an overall form factor. On the other hand, the normalization of amplitudes of the traditional absorptive one‐pion exchange models to the Born diagrams at t = 0 lays on the absorptive parameters the condition σtotC/8πA = 1 corresponding to the total absorption of the low partial waves. In this case the one‐pion exchange models with absorption coincide at all t with the Born diagram model with absorption and the reaction aplitudes are independent of a choice of the initial vector theory Lagrangian.

The dynamics of the D 13 wave in πN scattering

In earlier papers we have studied the interactions in the ϱN and πΔ systems. These analyses include predictions about the forces in those partial waves which couple to the πN D 13 wave. Although the many channels and strong forces which are involved in this wave make a quantitative prediction difficult we show in this paper that the qualitative predictions are in good agreement with πN elastic phase-shift analyses and with the Berkeley-SLAC analysis of the reaction πN → ππN. The interactions in the πN and ϱN systems combine to give the resonance D 13(1520) whereas the attraction in the πΔ D-wave system produces a resonance around 1700 MeV which however does not couple strongly to the πN system.