Process πN Research Articles

GTMDs and the factorization of exclusive double Drell-Yan

Different exclusive processes have been proposed to access the generalized transverse momentum dependent distributions (GTMDs) with no proof of factorization, which allows to rigorously define the GTMDs. Using Soft Collinear Effective Theory we derive for the first time the factorization of the differential cross section for the exclusive double Drell-Yan process πN→N′γ⁎γ⁎→N′(ℓ+ℓ−)(ℓ+ℓ−), for small transverse momenta of the photons in terms of a perturbatively calculable hard factor, GTMDs and light-cone wave functions (LCWFs). We find that the hard factor of the process can be obtained from single inclusive Drell-Yan production so that one can resum logarithms at high orders in QCD. We also discuss the evolution of the GTMDs and the LCWFs.

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.

Relativistic interactions for meson-nucleon systems in the clothed particle representation

The method of unitary clothing transformations (see [1–3] and references therein) enables one to represent the initial Hamiltonian H for interacting fields in terms of the creation (destruction) operators for the so-called clothed (physical) particles and their relativistic interactions. Using this clothed particle representation (CPR) of H and starting from the Yukawa-type couplings between fermions (nucleons and antinucleons) and bosons (π-, η-, ρ-, ω-mesons, etc.), we have derived a new family of the Hermitian and energy-independent interactions for physical processes πN → πN, NN → NN, NN ↔ πNN and NNN → NNN. Each of the obtained analytic expressions in momentum space is the sum of a Feynman-like part and some off-energy-shell correction term. The latter cannot appear when calculating the corresponding S-matrix elements by Feynman rules.

A microscopic quark model of πN → KΣ reactions for heavy-ion collisions

We investigate the process πN → KΣ in a microscopic quark model for heavy-ion collisions. In the model the effective 3 P 0 quark-antiquark creation and annihilation vertex is applied. The relative motion of the meson and baryon in the initial (and final) state is taken as plane waves, while the internal quark wave functions of the hadrons are described by harmonic oscillator wave functions. Predictions of the model are reasonably in agreement with the available experimental data.

Higher-twist effects in the Drell-Yan angular distribution

We study the Drell-Yan process πN → μ + μ − X at large x F using perturbative QCD. A higher-twist mechanism suggested by Berger and Brodsky is known to qualitatively explain the observed x F dependence of the muon angular distribution, but the predicted large x F behavior differs quantitatively from observations. We have repeated the model calculation taking into account the effects of nonasymptotic kinematics. At fixed-target energies we find important corrections which improve the agreement with data. The asymptotic result of Berger and Brodsky is recovered only at much higher energies. We discuss the generic reasons for the large corrections at high x F . A proper understanding of the x F → 1 data would give important information on the pion distribution amplitude and exclusive form factor.

Description of πp→Δ(1232)π and πp→Δ(1232)ρ(770) reaction proceeding via baryon exchange mechanism

We analyze the available experimental data on the backward production processes πN→Δπ and πN→ Δπ in the framework of the strong-cut Reggeized absorption model, which is based on the exchange of the baryon Regge trajectoriesNα and Δδ with the associated cuts. The model describes rather well the data on the differential cross sections at incident π momenta ranging from 2.15 to 20 GeV/c. An essential contribution of Δδ exchange even at small energies (Elab of the order of a few GeV) is found. A model-independent analysis of data confirms this fenomena.

Subthreshold K +-production in proton-nucleus reactions

The production of positively charged kaons in proton-nucleus reactions is analysed with respect to primary nucleon-nucleon and two-step proton-nucleon→pion plus pion-nucleon production processes on the basis of Hartree-Fock ground state momentum distributions and free on-shell production processes. Clear evidence is found for the dominance of secondary processes πN→ ΛK + below 1 GeV. Estimates for the production of hypernuclei in p+ 12C and p+U reactions up to 1 GeV are given.

What is the correct propagator for a spin-3/2 particle?

Recently a form for the propagator of a spin-3/2 particle has been proposed, which differs from the one normally used in the literature. We show that the new propagator gives unique predictions for the contributions to the processes πN → πN, γN → πN, γd → pn from tree diagrams with a Δ(1231) intermediate state, whereas the old propagator gives results which depend on unknown parametersy, z arising from off-mass-shell γNΔ, πNΔ couplings. We show further that, with the new propagator, one obtains a very simple model of low-energy pion-nucleon scattering, while the contributions to pion photoproduction and deuteron photodisintegration fit very well into models for these processes. These properties of the new propagator lead to the conclusion that it should be used in an effective treatment of Δ exchange, in preference to the usual treatment.

Are some π−N resonances a manifestation of coupling to the π−Δ(1232) channel?

Using separable potentials for the processes πN → πN, πN → πΔ, and πΔ → πΔ, we investigate the possibility that some of the low lying resonances seen in π−N elastic scattering may be due to the opening of the threshold for π− Δ production. We find excellent fits to the P 11, D 13, D 15, and S 31 phase shifts and inelasticities without the need for introducing the P 11(1440), D 13(1520), D 15(1675), and S 31(1620) resonances explicitly. While not claiming that true particle resonances do not exist, our results indicate that coupling to the π − Δ channel should not be ignored.

Pion-nucleon scattering: The P 11 channel

A simple model is presented for the πN scattering in the P 11 channel from the threshold to the Roper resonance N(1470). The model starts with the πBB′ coupling of the Yukawa type where B (and B') stands for N, R or Δ. A unitarized scattering amplitude is constructed from the K-matrix which is obtained perturbatively. With appropriate coupling constants and form factors for the πBB′ interactions, which conform to the quark model, the P 11 scattering can be well reproduced. It is emphasized that the process πN → ππΔ → πN, which has been ignored hitherto, plays a crucial role in the energy region considered.

Partial-wave analysis including π exchange for πN → N ππ in the c.m. energy range 1.65–1.97 GeV

We study the inelastic scattering processes πN → N ππ from c.m. energies 1.65–1.97 GeV using an isobar model. The effect of including a non-zero high partial wave contribution on the determination of low partial wave scattering amplitudes is analysed in detail. The proper formulation of a high partial wave input due to the π-exchange process πN → ϱN is presented. The major improvements due to including the π-exchange high partial wave input in the analysis of low-energy πN → N ππ scattering are found to be the elimination of the overall phase ambiguity in the scattering matrix and improvement in the representation of the angular scattering distribution by the fit parametrization for c.m. energies above 1.8 GeV. We find that our analysis and the previous major isobar analysis of these reactions at these energies share serious deficiencies (such as the failure to properly satisfy partial-wave unitarity and the poor representation of various single-particle distributions), but certain strong features of the data are well determined by both analyses.

A simple Regge-pole model for pp → pp ω

The process pp → pp ω is analyzed in terms of the Reggeized Deck model. Diagrams with π-ϱ, π-B, ω-pom, and p-pom exchange are found to be the important contributors. Extensive use is made of experimental data on the two-body processes πN → ωN, pp → pp, and γp → ωp. Vector dominance is used to obtain ωp → ωp from γp → ωp. The large amount of experimental data, including the prominent peak in the total cross section, is well accounted for. It is pointed out that interference effects cannot be neglected on phase-space arguments alone, and may be important in this process.

Backward dispersion relations for πN→ πΔ scattering and NΔγ couplings

Using unsubtracted dispersion relations for the invariant amplitudes of the process πN→ πΔ in forward and backward direction we derive sum rules relating t channel to s and u channel resonances. We saturate these sum rules by ϱ, N, and Δ and obtain for the ϱ coupling constants C 3m= 5 3 ; C 4m 2 =C 5m 2 = 5 4 3 where m is the average mass of N and Δ. Assuming vector meson dominance of the electromagnetic vertex NΔγ these become the values of the Gourdin-Salin coupling constants in reasonable agreement with experiment.

Effective lagrangians in pion-production process πN → 2 πN

Chiral Dynamics is applied to study the pion-production process πN → 2 πN and comparison is made with the results of current algebra. The isobar production process πN → πN ∗(1236) is also examined and the production parameters are determined.

Effective lagrangians in pion-production process πN → 2πN: Ghulam Murtaza and A. M. Harun-Ar-Rashid. Institute of Physics, University of Inslamabad, Rawalpindi, Pakistan

Effective lagrangians in pion-production process πN → 2πN: Ghulam Murtaza and A. M. Harun-Ar-Rashid. Institute of Physics, University of Inslamabad, Rawalpindi, Pakistan

Treatment of πN → K Λ and πN → K Σ with a Veneziano type model

We study the processes πN → K Λ and πN → K Σ and the corresponding crossed reactions KN → πΛ and KN → πΣ simultaneously. We make a simple Veneziano type ansatz for the invariant amplitudes of these processes with only three free parameters in each case. In each isospin channel, there is at most one (possibly degenerate) trajectory, together with its daughters. Veneziano terms for which there is no allowed duality diagram are omitted. The parameters can be chosen such that the high-energy data (magnitude and slope of forward and backward peak) fit well. With these parameters the resonance spectrum in all channels is described satisfactorily. Parity doubling of baryon resonances occurs. However, the parity partners which are not seen so far turn out to have very small widths as a result of kinematic suppression. The products of partial widths of the well-known Y o, Y 1 and Δ-resonances are found to be in good agreement with experimental data.