Self-consistent Gaussian model of nonperturbative QCD vacuum

We show that the minimal Gaussian model of nonlocal vacuum quark and quark-gluon condensates in QCD violates the transverse character of the correlator of two vector currents. We suggest the improved Gaussian model of the nonperturbative QCD vacuum, which respects QCD equations of motion and minimizes the revealed gauge-invariance breakdown. We obtain the refined values of pion distribution amplitude (DA) conformal moments 〈ξ^2N 〉_π (N = 1, ..., 5) using the improved QCD vacuum model, including the inverse moment 〈x ^?1〉_π, being inaccessible if one uses the standard QCD SR. We construct the allowed region for Gegenbauer coefficients a ₂ and a ₄ of the pion DA for two values of the QCD vacuum nonlocality parameter, λ _q ² = 0.4 and 0.5 GeV².     

Analysis of pion electroproduction data in terms of a pion distribution function of the proton

Experimental data on the longitudinal π⁺ electroproduction on hydrogen have been analyzed in terms of a pion distribution function of the proton. This interpretation is based on the assumption that the pion can be considered as a parton in the nucleon for low momentum transfer Q². For the kinematical conditions photon mass Q² < 1 GeV² and electron energy loss ν > 2.2 GeV the pion electroproduction in the direction of the virtual photon can be viewed upon as quasielastic eπ⁺ → e′π⁺ scattering. Using the impulse approximation the pion distribution function of the proton can be deduced. According to the distribution function evaluated from pion electroproduction in the infinite momentum frame, the physical proton has a 3% admixture of the nπ⁺ state and the π⁺ in the nπ⁺ state carries 0.6% of the proton momentum.     

High-pT pion production in ππ interactions

Charged pion production in high energy π^-π^- interactions is studied in the p_T region of 1–2 GeV/c. The characteristics of pion production in π^-π^- interactions are compared with those in π^-p and pp interactions. The p_T dependence of pion production in these reactions follows a systematic trend which indicates that high-p_T pion production for ππ interactions as well as for πp and pp interactions proceeds via quark-quark scattering as predicted by QCD.     

Coherent π0 photoproduction near threshold on closed-shell nuclei

Coherent π⁰ photoproduction is considered on closed-shell nuclei in the DWIA frame from threshold up to pion energies of 50 MeV. The elementary photoproduction operator is taken from Blomqvist and Laget and treated in the coordinate-space representation. It includes, besides the negligible Born terms, delta formation in the s-channel and ω⁰ exchange in the t-channel, two mechanisms which have comparable importance even near threshold. The emerging pion wave is distorted by optical-model potentials which give equally good fits both to pionic atom data and pion scattering data. In the considered energy range the DWIA cross section is enhanced with respect to the plane-wave case by an amount between 50% and 100% depending on the particular optical-model potential. Distortion is necessary to gain a satisfactory agreement with the available data.     

Possibilities of revealing collective pion degrees of freedomin nuclei by means of quasielastic pion knockout by high-energy electrons

The kinematics of quasielastic pion knockout by longitudinal virtual photons in the electroproduction process is presented. The possibility of directly investigating pion momentum distributions in specific channels owing to pole-amplitude dominance is considered. It is shown that, taking into account the final-state interaction of the knock-on pion and the nucleus involved, one can reveal the existence of a pion condensate in nuclei, since the momentum distribution of collective pions has a pronounced maximum at a momentum in excess of 0.3 GeV/c and since the excitation spectrum of the final recoil nucleus is concentrated in the low-energy region E* ≈ K ²/(2AM _N ) ≤ 1 MeV. The picture of pion knockout from meson clouds of individual nucleons is totally different. The analogous rho-mesonmomentum distributions for the process ρ + γT* → π are also presented.     

Branching ratio for radiative pion capture in 6Li and 12C

The radiative pion capture rate in ¹²C and ⁶Li leading to bound final states is calculated using the impulse approximation. The T-matrix is obtained from the time-reversed pion photo-production amplitude and initial-state distortion of the bound pion is taken into account. Using recently published capture schedules for pionic atoms the branching ratio R is calculated and compared to experimental values. The agreement is excellent if those experimental values are used that have been obtained by direct observation of the emitted γ-ray and if an optical-model value for the total 2P absorption width in ¹²C is used.     

pi-Mesonic decay of hypernuclei and pion wavefunction

The pi-mesonic decay of hypernuclei is studied by using the pion distorted waves which are the solutions of the Klein-Gordon equation with the optical potential. The distortions of the pion waves give rise to significant enhancement of theπ-decay rate compared with the pion free-wave case. Theπ-decay rates are very sensitive to the behavior of the pion wave deep inside the nucleus and therefore to the chosen pion optical potentials. There is a tendency that the enhancement is larger for theπ ^?-decay than for theπ ⁰-decay due to the combined effects of the Coulomb and optical potentials.     

Production of positive pions by neutron-proton collisions

Spectra of positive pions from the processn+p→π ⁺+n+n have been measured for incident neutron energies from 470 MeV to 590 MeV and for laboratory angles up to 20°. The rather broad pion energy spectra and the pronounced anisotropy of the differential cross sections, both indicate an appreciable non-resonant, isoscalar (T=0) contribution to the pion production.     

The structure function of the pion

The data on muon-pair production in pion interactions on a nuclear target are reanalysed in the light of what we know about nucleon structure functions in a nuclear environment. A consistent picture of the pion structure function is obtained, which is compatible with the evolution of a hard valence quark distribution atQ ²=2.5 GeV². Vector dominance is used to estimate the hadronic component of the photon structure function atQ ²=2.5 GeV² and it is found to saturate the data there.     

Pion chemical potentials in heavy-ion collisions: relativistic quantum molecular dynamic analysis

In the framework of relativistic quantum molecular dynamics we analyse pion chemical potentials in the hadron system produced in central heavy-ion collisions at the bombarding energiesE _lab/A=(1–2) GeV/nucl. We find that the equilibrium relations hold for chemical potentials of π^?, of π⁰, of π⁺ and pion energy spectra reach local thermal equilibrium. However, there is no chemical equilibrium. The pion chemical potentials are very large and decrease during the expansion stage.     

Evaluation of fully integrated γ v p → π+π− p cross sections in the resonance region at photon virtualities 5 < Q 2 < 12 GeV2

Evaluation of fully integrated double pion electroproduction cross sections of protons was carried out at 1.4 < W < 2.0 GeV, 5 < Q ² < 12 GeV². The cross-section evaluation was obtained from an approach based on extrapolation of the double pion component of inclusive structure functions F ₁ and F ₂ from photon virtualities Q ² < 5 GeV² towards 5 < Q ² < 12 GeV². Q ²-parameterization compatible with restrictions from the Operator Product Expansion was used to conduct the extrapolation. The results will be used to extract double pion electroproduction cross sections of protons in future experiments with the new CLAS12 detector.     

Isovector kaon form factor in the dispersion theory and S-wave π K-scattering lengths

A one-dimensional integral representation for isovector kaon form factor is constructed within the dispersion theory in terms of the pion form factor and the backwardπK-scattering amplitude. The normalization condition for isovector kaon form factor at zero momentum transfer gives a sum rule for theπK-scattering amplitude, with the use of which difference between thes-waveπK-scattering lengths in triplet and singlet isospin states is estimated to bea ₀ ^3/2 - a ₀ ^1/2 ≈μ ^{? 1} whereμ is the pion mass. In agreement with the vector-meson-dominance model, deviations of the isovector kaon form factor from half of the pion form factor are found to be small.     

A unitary isobar model for pion photo- and electroproduction on the proton up to 1 GeV

A new operator for pion photo- and electroproduction has been developed for nuclear applications at photon equivalent energies up to 1 GeV. The model contains Born terms, vector mesons and nucleon resonances (P₃₃(1232), P₁₁(1440), D₁₃(1520), S₁₁(1535), F₁₅(1680), and D₃₃(1700)). The resonance contributions are included taking into account unitarity to provide the correct phases of the pion photoproduction multipoles. The Q² dependence of electromagnetic resonance vertices is described with appropriate form factors in the electromagnetic helicity amplitudes. Within this model we have obtained good agreement with the experimental data for pion photo- and electroproduction on the nucleon for both differential cross sections and polarization observables. The model can be used as a starting point to predict and analyze forthcoming data.     

Pion condensation in symmetric nuclear matter

The problem of pion condensation in isospin symmetric nuclear matter is investigated in the framework of the σ-model with a residual nucleon-nucleon interaction (g′σ₁ · σ₂τ₁ · τ₂δ(x)) and Δ-isobars. The equation of state for the pion condensed phase is calculated and applied to a low-energy heavy-ion collision in the TDHF approximation. The effective particle-hole interaction and the response to spin-isospin excitation are used to determine the magnitude of the Landau-Migdal parameter g′. For a reasonable range of g′(0.5 < g′ ≦ in units of g²/4m²_N = 410 MeV · fm³) pion condensation occurs at densities above normal nuclear matter density and leads to an equation of state with no stable density isomer.     

Pion electroproduction in the 3He(e,é π+)3H reaction at intermediate energies

The differential coincident pion electroproduction cross section in the ³He(e,é π⁺)³H reaction has been measured with high resolution with the three-spectrometer set-up at the Mainz Microtron (MAMI) electron accelerator. Measurements were performed at the four incident energies E₀ = 855, 675, 600, and 555 MeV at fixed four-momentum transfer Q² = 0.045 GeV², with the pions detected in parallel kinematics. This enables a separation of the measured cross section into the transverse and longitudinal structure functions by means of the Rosenbluth method. The experimental data are compared to model calculations, in which the elementary pion production amplitude includes the standard Born-amplitudes and also delta and higher resonance terms. Three-body Fadeev wave functions are used and the final state interaction of the outgoing pion is taken into account. The calculation describes the data only after medium modifications of the delta and of the pion are included.     

Study of the R meson produced in 13 GeV/cπ+p interactions

The missing mass spectrum opposite the proton in a 750 000 picture exposure, 13 GeV/cπ⁺p bubble chamber experiment, is investigated in two and four pion channels for structures observed or denied by boson spectrometers at the same energy in the reaction π^?p→X^?p.In the four pion final state the R⁺ enhancement is observed clearly and the possibility of multi-component mass structure is considered. Treating the phenomenon as one object, cross sections and branching ratios are derived for intermediate quasi two and three body decay modes (ωπ, ??, A₂π, ?ππ). The signals in the two pion state and for the neutral state produced opposite Δ⁺⁺(1231) are also presented and an elasticity is calculated.     

Scale of corrections to the t-channel pole approximation in quasielastic pion knockout from a nucleon by high-energy electrons

An investigation of a dominant role of the simplest t-channel pole diagrams in pion electroproduction on nucleons for quasielastic-knockout kinematics at an electron energy of a few GeV is completed-namely, the competition between the t-channel pion and rho-meson pole amplitudes, on one hand, and the s-channel pole amplitude (tree diagram), on the other hand, is considered. When the virtual-photon mass is sufficiently large [Q ²>2(GeV/c)²], the last amplitude does not make significant contributions to relevant cross sections, either the longitudinal (dσ _L/dt) or the transverse (dσ _T/dt) one. At Q ²=0.7(GeV/c)², the term associated with the interference between the t-channel pion-pole amplitude and the s-channel pole amplitude is still noticeable in the longitudinal cross section. The vertex functions g _ρ NN(t) as obtained from the cross section for the quasielastic knockout of rho mesons and from the cross section for pion photoproduction are compared. Their disagreement must give impetus to a further development of the gauge-invariant theory of pion photoproduction.     

Pion-production in heavy-ion collisions at SIS energies

We investigate the production of pions in heavyion collisions in the energy range of 1–2 GeV/A. The dynamics of the nucleus-nucleus collisions is described by a set of coupled transport equations of the Boltzmann-Uehling-Uhlenbeck type for baryons and mesons. Besides theN(938) and theΔ(1232) we also take into account nucleon resonances up to masses of 1.95 GeV/c² as well asπ-,η- andρ-mesons. We study in detail the influence of the higher baryonic resonances and the 2π-production channels (NN→NNππ) on the pion spectra in comparison toπ ^? data fromAr+KCl collisions at 1.8 GeV/A andπ ⁰-data forAu+Au at 1.0GeV/A. We, furthermore, present a detailed comparison of differential pion angular distributions with the BEVALAC data forAr+KCl at 1.8 GeV/A. The general agreement obtained indicates that the overall reaction dynamics is well described by our novel transport approach.     

High energy pion photoproduction amplitudes from fixed-t dispersion relations and duality

Contributions to the high energy imaginary parts of the charged and neutral pion photoproduction amplitudes from degenerate ? and A₂ exchanges and ω and B exchanges are parametrized similarly to the dual absorptive model. These contributions together with the imaginary parts of the amplitudes found at low energies from partial-wave analyses are then used to evaluate the high energy real parts of the photoproduction amplitudes from fixed-t dispersion relations. A fit is made to data on pion photoproduction at 3.4 and 16 GeV incident photon energies, for momentum transfers up to ?1(GeV/c)². It is shown that much of the data is reproduced both qualitatively and quantitatively by our model. The high energy imaginary parts of the photoproduction amplitudes given by the fit are shown to be in accord with their average low energy behaviour.