Measurements of inclusive pion electroproduction

Measurements of the inclusive pion electroproduction reaction e^?+p → e^?+π^±+X made at the Wilson Synchrotron Laboratory are reported. Data were taken at points with nominal (Q², W) values of (0.6, 2.67), (1.2, 2.67), (2.0, 2.67) and (1.2, 2.15) in (GeV², GeV). A more complete angular distribution was taken at (1.2, 2.67). The virtual photoproduction cross section for π⁺ + missing mass is studied as a function of missing mass, Feynman scaling variables, Q² and W. The invariant cross section show a simple behavior as a function of Q² and W. Its dependenc on P_⊥², x′ and φ is determined.     

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.     

Contributions of exclusive pion electroproduction reactions to inclusive structure functions

The contributions of exclusive π⁺n, π⁰p, and π^?π⁺p channels to the inclusive structure function F ₂(x, Q ²) are determined from the CLAS collaboration data analysis. Reliability of the CLAS data on the inclusive structure function and single-pion electroproduction channels is verified. The total contribution of the uninvestigated π⁺π⁰n and π⁰p channels to this function and the integrated cross sections of these channels at photon virtualities Q ² = 0.4 and 0.5 GeV² are predicted.     

Generalized polarizabilities and electroexcitation of the nucleon

Generalized nucleon polarizabilities for virtual photons can be defined in terms of electroproduction cross sections as function of the 4-momentum transfer Q². In particular, the sum of the generalized electric and magnetic polarizabilities Σ=α+β and the spin polarizability γ can be expressed by virtual photon absorption cross sections integrated over the excitation energy. These quantities have been calculated within the framework of the recently developed unitary isobar model for pion photo- and electroproduction on the proton, which describes the available experimental data up to an excitation energy of about 1 GeV. Our results have been compared to the predictions of chiral perturbation theory.     

Precise pion electroproduction in thep(e,e′ π+)n reaction at W=1125 MeV

The reactione+p →> e+π ⁺+n at c.m. energyW=1125MeV and momentum transfer Q²=0.117GeV²/c₂ has been measured. The transverse and longitudinal structure functions have been separated by varying the polarization of the virtual photon (Rosenbluth plot) with a 3 to 4% error. In addition the longitudinal-transverse interference term has been determined measuring the right-left asymmetry with an accuracy of 3%. The experimental data are compared to model calculations, and the sensitivity of the results to the axial and pion formfactors is discussed.     

Optimal bounds for the pion form factor from analyticity and experimental data

Optimal bounds for the pion electromagnetic form factor F(t) below threshold and on the pion mean-square charge radius 〈r_π²〉 = 6F'(0) are derived. Use is made of analyticity arguments and of experimental data on F(t) from e⁺e^? → π⁺π^? as well as e^?p → e^?nπ⁺. The method accounts in an approximate way for the statistical errors of the experimental information. Numerical results for F(t) are calculated for the CEA as well as the DESY electroproduction data.     

Parity violation in pion electroproduction and photoproduction with a proton target

Parity violation in pion electroproduction and photoproduction on a proton target is investigated as a possible means of elucidating the structure of the electronic and non-leptonic neutral weak currents. We calculate both parity-violating effects caused directly by Z-boson exchange, which contributes only to electron scattering, and those due to parity-violating electromagnetic and nuclear interactions. The asymmetry in electroproduction is of order 20^?5, whereas that in photoproduction is ～10^?7. The sensitivity to the parameter sin²θ_w is investigated; it is a maximum at backward electron scattering angles. In addition to the Born terms, contributions from the Δ(1232) resonance and the light vector mesons [?(776) and ω(782)] are included in the model. Fits to the observed π⁰ and π⁺ electroproduction and photoproduction cross sections indicate that the model accounts for the production data in the medium energy region.     

Experimental investigation of ρ<Superscript>0</Superscript> photoproduction on the pion in the H1 experiment

Experimental results on quasielastic photoproduction of the ρ⁰ meson in association with a neutron, obtained at the HERA collider, are presented. The total and differential cross sections of the γp → ρ⁰ nπ⁺ reaction at the positron–proton center-of-mass energy of √s =319 GeV are measured. The data collected with the H1 detector in 2006 and 2007 correspond to an integrated luminosity of 1.16 pb^?1. The kinematic region of the photon–proton cms energy of 20 < W _γp <100 GeV, photon virtuality of Q ² < 2 GeV², and the ρ⁰ transverse momentum below 1 GeV/c is analyzed. Secondary neutrons with energies x _L > 0.35 (in proton-energy units) and emission angles below 0.75 mrad are selected. The model of double peripheral exchange, in which the ρ⁰ is elastically produced via the photon interaction with the virtual pion from the proton–neutron vertex, is employed for interpreting the results. The cross section for the ρ⁰ elastic photoproduction on the pion, γπ⁺→ ρ⁰π⁺, is extracted in the one-pion-exchange approximation. The magnitude of the cross section suggests that the γp → ρ⁰ nπ⁺ reaction is significantly affected by absorption.     

Final state interaction in pion electroproduction from nuclei near threshold

We have calculated cross sections for pion electroproduction from nuclei near threshold, including the distortion of the pion wave function by the pion-nucleus optical potential. Distortion effects near threshold are found to be significant, changing the ratio σ_π-/σ_π+ for production of 10 MeV pions from ¹⁶O by nearly fifty percent.     

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.     

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.     

Coherent π Electroproduction on the Deuteron

A general analysis of polarization phenomena for coherent pion electroproduction on deuterons is presented. The spin and isospin structures of the γ*+d→d+P⁰ amplitudes (where γ* is a virtual photon) are established and relationships between meson electroproduction on deuterons and on nucleons are given in the framework of the impulse approximation. The reaction e+d→e+d+π⁰ is investigated in detail, for a relatively large value of momentum transfer, 0.5 GeV²≤−k²≤2 GeV², both at threshold and in the region of Δ-isobar excitation. Special attention is devoted to the sensitivity of different contributions to the exclusive cross section for d(e, eπ⁰)d, as the γ*πω form factor or the NN-potential. The predicted k²-dependence of the cross section agrees well with the available experimental data.     

Virtual photons in pion electroproduction

We examine the applicability of the virtual photon spectrum to pion production experiments by using an exact calculation of pion electroproduction from the proton and from ³He. After deriving a new virtual spectrum formula which takes into account the recoil of light target nuclei and the proper electron kinematics near the endpoint, we find that the concept of a virtual photon spectrum in such experiments is very good.     

Observation of coherent <Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript> electroproduction on deuterons at large momentum transfer

The first experimental results for the coherent π⁰ electroproduction on a deuteron, e+d → e+d+π⁰, at large momentum transfer, are reported. The experiment was performed at Jefferson Laboratory at an incident electron energy of 4.05 GeV. A large pion production yield has been observed in the kinematical region 1.1<Q²<1.8 GeV², from the threshold to 200-MeV excitation energy in the dπ⁰ system. The Q² dependence is compared with theoretical predictions.     

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.     

Beyond leading order QCD perturbative corrections to the pion form factor

The order α_s²(Q²) corrections to the pion form factor, F_π(Q²), are calculated using perturbative quantum chromodynamics and dimensional regularization. In the $\text{MS}$ renormalization scheme these corrections are large. This means that reliable perturbative predictions cannot be made until momentum transfers, Q, of about 300–400 GeV are reached or unless one can sum the large perturbative terms to all orders. Attempts to reorganize the perturbation series so that the first term gives a better approximation of the complete sum indicate that at Q = 10 GeV the pion form factor may be about a factor of two larger than the leading order result.     

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.     

Particle ratios in inclusive electroproduction from hydrogen and deuterium

We present a high statistics study of particle ratios in electroproduction of forward hadrons. The π⁺/π^? ratios for a proton target rise monotonically to a value of 2.4 ± 0.2 at Q² of 3 (GeV/c)² and for a neutron target average 1.16 ± 0.04 from Q² of 0.35 to 3 (GeV/c)². We report the first data on electroproduction of $\text{p}$, and measure the cross sections of K^±, p, and $\text{p}$ relative to pions as a function of Q².     

Positive pion production from polarized protons by linearly polarized photons in the energy range 280–420 MeV

The method is described of measuring the polarization observables Σ, P and T for the reaction γp → nπ⁺ in a double polarization experiment (polarized target + polarized beam). The measured angular distribution of these observables are presented for the photon energy range 280–420 MeV at c.m. pion emission angles between 30° and 150°. The obtained experimental data are included in the energy-independent multipole analysis of the reactions γp → Nπ.