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.     

1/N calculation of structure functions

We calculate the quark and pion structure functions in CP^n?1 models with quarks using 1/N expansions. We find that the quark structure function, in the lowest order in 1/N, is just the free parton result with a modified coupling constant. The pion structure function resembles the phenomelogically successful fit but contains correction terms which modulate the function.     

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.     

Scaling violation in the pion structure function

TheQ ²-dependence of the pion structure function extracted from high transverse momentum π⁰ production cross sections is examined. We find, in thex→1 region, that this dependence can be parametrized by a power of (1?x) increasing as ln lnQ ². This is in agreement with the expectations of asymptotic freedom and also seen in the structure function extracted from dilepton production. It is not possible to fit all of theQ ²-dependence with a simple power law term.     

Photoproduction of neutral pions at backward angles in the resonance region and the η-cusp

At the Bonn 2.5 GeV electron synchrotron we have measured the differential cross section of the reaction γp→π⁰ p at a pion CM angle of 170° and at photon energiesK _γ between 0.6 and 1.8 GeV. In comparison to previous measurements the accuracy of the data was improved substantially. For the first time in neutral pion photoproduction a cusp structure at the η-threshold has been confirmed [1].     

A Combined Study of the Pion’s Static Properties and form Factors

We study consistently the pion’s static observables and the elastic and γ* γ → π ⁰ transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adjusted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the γ* γ → π ⁰ form factor at large q ², yet the BaBar data on this transition form factor resists a sensible comparison. We relax the initial constraint on the bound-state wave function and show the BaBar data can partially be accommodated. This, however, comes at the cost of a hard elastic form factor not in agreement with experiment. Moreover, the pion charge radius is about 40 % smaller than its experimentally determined value. It is argued that a decreasing charge radius produces an ever harder form factor with a bound-state amplitude difficultly reconcilable with soft QCD. We also discuss why vector dominance type models for the photon-quark vertex, based on analyticity and crossing symmetry, are unlikely to reproduce the litigious transition form factor data.     

Charged pion production in 70 GeV/cK + p interactions

Inclusive charged pion production is studied in an exposure of BEBC, filled with hydrogen, to an incidentK ⁺ beam of 70 GeV/c. Total cross sections for pion production and inclusive longitudinal and transverse momentum distributions of π^?'s and of positive particles are presented and compared with data at lower energies. Earlier evidence for scaling in the fragmentation regions is confirmed. The central region π^? cross section increases proportionally top _LAB ^?1/4 ; positive particles show almost no energy dependence atx=0. Particle ratios π⁺/π^? are studied as a function ofx andy ^* and a comparison with 70 GeV/cK ^? p data is made. Analysis of structure functions for (ππ) pairs and of particle production associated with π^± triggers at large |x| in the context of quark/parton models, provides qualitative evidence for the diquark-quark structure of the proton.     

Dynamics of pion double-charge-exchange reactions

The (π⁺, π^?) reactions leading to the double isobaric analog state are studied at pion energies 50 to 300 MeV, with¹⁴C as an example. Effects of nuclear structure, nuclear recoil, the reaction pathway and off-shell πN interactions are examined in detail. Our study reveals a very strong dependence of calculated cross sections on off-shell πN dynamics. Consequently, use of a self-consistent off-shell πN theory is essential to studying short-range nucleon-nucleon correlations from double-charge-exchange data. The present study further shows that reaction dynamics other than two successive pion single charge exchanges is needed to account for the experimental data.     

Prediction of the one pion exchange contribution to the processπ − p→π − pω with the help of the Veneziano model

The one pion exchange contribution to the differentialπ ^? p→π ^? pω cross-section is calculated assuming that theπ→πω amplitude associated with one of the vertices is described by the Veneziano formula, and that only a trivial dependence of the latter on the mass of the exchanged pion needs to be taken into account. The remaining unknown overall constant is then fixed by considering the decayω→3π. A rough comparison with preliminary data from a 16 GeV/cπ ^? p experiment shows that the one pion exchange model could possibly describe the reactionπ ^? p→π ^? pω forπω masses above 1.4 GeV.     

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.     

Spin structure of the pion in a light-cone representation

The spin structure of the pion is discussed by transforming the wave function for the pion in the naive quark model into a light-cone representation. It is shown that there are higher helicity (λ ₁+λ ₂=±1) states in the full light-cone wave function for the pion besides the ordinary helicity (λ ₁+λ ₂=0) component wave functions as a consequence from the Melosh rotation relating spin states in light-front dynamics and those in instantform dynamics. Some low energy properties of the pion, such as the electromagnetic form factor, the charged mean square radius, and the weak decay constant, could be interrelated in this representation with reasonable parameters.     

On the strength of absorption in single pion production reactions

From data on the reactions π^?p → π^?π⁺n and K⁺n → K⁺π^?p we determine the strength of absorptive corrections to the pion exchange Bornterm as a function of the ππ and Kπ mass and angular momentum.     

Coincidence π electroproduction in the second resonance region

The reaction e⁻ + p → e⁻ + p + π^o has been studied in the region of the second pion nucleon resonance. Two sets of data have been taken and analysed at nominal values of the squared four momentum transfer to the pion nucleon system of 0.4 and 0.6 (GeV/c)². A phenomenological interpretation of the data is presented. Our results are compared with the predictions of fixed-t dispersion relation calculations and with the symmetric quark model.     

The decay of theτ lepton to six pions

We present the branching ratio predictions of an isospin statistical model forτ decays to four, five and six pions. Limits on the branching ratios of the three possible six pionτ decay modes using the Conserved Vector Current (CVC) Hypothesis and thee ⁺ e ^?→6π cross section data are also presented. We find that the isospin model prediction is in good agreement with the well-measured four pion decay modes and consistent with the five pion decay modes. However, we find that some of the recent six pionτ measurements do not agree with the isospin model and the CVC prediction.     

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.     

A relativistic model of the composite π meson

The pion is treated as a fermion-antifermion composite state, described by the Euclidean Bethe-Salpeter equation. The kernel of the equation is a local potential having an exponentially infinite spectral function, connected with the empirical mass spectrum of resonances. For the simplest potential U(r) = f²(r²?a²)^?1 the equation for the massless pion is solved by using WKBJ method, and the parameters f, a and the fermion mass M are estimated.     

Quark-hadron duality in electron-pion scattering

We explore the relationship between exclusive and inclusive electromagnetic scattering from the pion, focusing on the transition region at intermediate Q². Combining Drell-Yan data on the leading twist quark distribution in the pion with a model for the resonance region at large x, we calculate QCD moments of the pion structure function over a range of Q², and quantify the role of higher twist corrections. Using a parameterization of the pion elastic form factor and phenomenological models for the π↦ρ transition form factor, we further test the extent to which local duality may be valid for the pion. Received: 10 February 2003 / Accepted: 12 March 2003 / Published online: 27 May 2003     

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.     

Experimental study of the photoemission of protons off12C using tagged photons in the energy range 200–385 MeV

Data are presented for proton emission off¹²C using tagged photons in the energy range 200–385 MeV. The protons are detected in a magnetic spectrometer. In addition, charged or neutral particles can be measured with a scintillation counter setup. Contributions to the proton energy spectra from primary pion production and quasideuteron reactions are separated using the coincidence data. The total¹²C(γ, p)X cross section is derived as a function of the photon energy. The data are compared to the predictions of an intranuclear cascade calculation. Final state interactions have to be taken into account to describe the data.