Threshold Pion Electroproduction Research Articles

Nucleon axial form factor at large momentum transfers

Using a Poincaré-covariant quark+diquark Faddeev equation and related symmetry-preserving weak interaction current, we deliver parameter-free predictions for the nucleon axialvector form factor, G_A(Q^2), on the domain 0le x=Q^2/m_N^2le 10, where m_N is the nucleon mass. We also provide a detailed analysis of the flavour separation of the proton G_A into contributions from valence u and d quarks; and with form factors available on such a large Q^2 domain, predictions for the flavour-separated axial-charge light-front transverse spatial density profiles. Our calculated axial charge ratio g_A^d/g_A^u=-0.32(2) is consistent with available experimental data and markedly larger in magnitude than the value typical of nonrelativistic quark models. The value of this ratio is sensitive to the strength of axialvector diquark correlations in the Poincaré-covariant nucleon wave function. Working with a realistic axialvector diquark content, the d and u quark transverse density profiles are similar. Some of these predictions could potentially be tested with new data on threshold pion electroproduction from the proton at large Q^2.

Axial form factor of the nucleon at large momentum transfers

Motivated by the emerging possibilities to study threshold pion electroproduction at large momentum transfers at Jefferson Laboratory following the 12 GeV upgrade, we provide a short theory summary and an estimate of the nucleon axial form factor for large virtualities in the $Q^2 = 1-10~\text{GeV}^2$ range using next-to-leading order light-cone sum rules.

Threshold pion electroproduction at large momentum transfers

We consider pion electroproduction close to threshold for ${Q}^{2}$ in the region $1--10\text{ }\text{ }{\mathrm{GeV}}^{2}$ on a nucleon target. The momentum transfer dependence of the S-wave multipoles at threshold, ${E}_{0+}$ and ${L}_{0+}$, is calculated in the chiral limit using light-cone sum rules. Predictions for the cross sections in the threshold region are given taking into account P-wave contributions that, as we argue, are model independent to a large extent. The results are compared with the SLAC E136 data on the structure function ${F}_{2}(W,{Q}^{2})$ in the threshold region.

Pion electroproduction, partially conserved axial-vector current, chiral Ward identities, and the axial form factor revisited

We re-investigate Adler's PCAC relation in the presence of an external electromagnetic field within the framework of QCD coupled to external fields. We discuss pion electroproduction within a tree-level approximation to chiral perturbation theory and explicitly verify a chiral Ward identity referred to as the Adler-Gilman relation. We critically examine soft-momentum techniques and point out how inadmissable approximations may lead to results incompatible with chiral symmetry. As a result we confirm that threshold pion electroproduction is indeed a tool to obtain information on the axial form factor of the nucleon.

Near-threshold photo- and electroproduction of neutral pions on protons

The state of the art of the problem on threshold neutral-pion production on protons by photons and electrons is examined. New experimental data on the threshold of pion production are analyzed within the phenomenological model based on the gauge invariance, the hypothesis of partial conservation of the axial-vector current, and allowance for obvious chiral-symmetry breaking. The amplitudes of the p-wave threshold multipoles and the photon asymmetry are derived for the pion photoproduction on protons with a photon energy of 159.5 MeV. The differential cross sections are calculated as functions of the pion emission angle and amplitudes of the s- and p-wave multipoles for the threshold pion electroproduction on protons at the squared momentum transfer k2 = 0.05 GeV2/c2. The total reaction cross sections are also obtained as functions of k2. The results obtained are compared with new experimental data and available theoretical predictions.

Pion charge radius from charged pion electroproduction

We analyze a low-energy theorem of threshold pion electroproduction which allows one to determine the charge radius of the pion. We show that at the same order where the radius appears, pion loops induce a correction to the momentum dependence of the longitudinal dipole amplitude $L_{0+}^{(-)}$. This model-independent correction amounts to an increase of the pion charge radius squared from the electroproduction data by about 0.26~fm$^2$. It sheds light on the apparent discrepancy between the recent determination of the pion radius from electroproduction data and the one based on pion-electron scattering.

Pion electroproduction at threshold.

By using the partially conserved axial-vector current hypothesis and the electromagnetic current conservation law, we calculate transverse and longitudinal multipoles for threshold pion electroproduction on the nucleon. We include off-shell form factors for the axial-vector current, the electromagnetic current, and the pion-nucleon vertex. We confirm that if the electromagnetic off-shell form factors are assumed to be finite in the chiral limit of the vanishing pion mass, the low-energy theorems are unaffected by them. However, we show that if one of these form factors has simple-pole singularity in the chiral limit, it shows up in the threshold amplitudes at next-to-leading order predicted by the low-energy theorems.

Determining the axial radius of the nucleon from data on pion electroproduction

We discuss a low-energy theorem of threshold pion electroproduction which allows one to determine the axial root-mean-square radius ${\mathit{r}}_{\mathit{A}}$ of the nucleon. We show that at the same order where the radius appears, pion loops induce a small correction to the momentum dependence of the electric dipole amplitude ${\mathit{E}}_{0+}^{(\mathrm{\ensuremath{-}})}$. This correction amounts to a decrease of the axial mean-square radius by 5% from the electroproduction data and allows one to explain the small discrepancy to the values determined from (anti)neutrino-proton scattering data.

On the low-energy theorems for threshold pion electroproduction

We consider pion electroproduction at threshold to one loop order in chiral perturbation theory. We derive novel contributions to the low-energy theorems for the S-wave multipoles E 0+ and L 0+ at threshold to order O( μ 2, v) with μ= M π / m the ratio of the pion and nucleon mass and v= k 2/ m 2 related to the four-momentum of the virtual photon. At next-to-leading order, the effect of infrared singularities generated by virtual pions becomes visible. We also discuss the inclusion of photon-nucleon vertex form factors.

Pion electroproduction at threshold and PCAC

Threshold pion electroproduction is calculated in a model-independent way based on electromagnetic current conservation, PCAC, and crossing symmetry. The threshold s-wave multipoles E 0+ and L 0+ are expanded in terms of two dimensionless parameters, the pion-nucleon mass ratio μ = m π M , and ν 2 = k 2 M 2 , where k is the four-momentum of the virtual photon. Model-dependent terms appear in order μν 2 and μ 2 for the charged production amplitudes and in order μν 2 and μ 3 in the neutral production amplitudes. We comment on recipes to restore gauge invariance for the pseudovector electroproduction Born terms and their relationship with low-energy theorems. Finally, we discuss the possibility of determining the nucleon axial radius using threshold pion electroproduction.

(e, e′π) reaction on light nuclei and spin-isospin strength distribution effects

We study threshold pion electroproduction on light $T=0$ nuclei. The probe is especially interesting because it mixes longitudinal (spin component parallel to momentum transfer, $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ coupling) and transverse ($\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ coupling) channels. Using the local density approximation for the treatment of possible nuclear spin-isospin mode enhancements, we calculate cross sections for both exclusive and inclusive measurements. For discrete nuclear levels we study differential cross sections of various pionlike levels, and these are compared with a nonpionlike excitation. The cross sections for exclusive excitations are extremely small except for forward angles. The inclusive cross sections, achieved by summing over all nuclear states, are considerably larger since these include the quasifree excitation. All cases are studied as a function of ${g}^{\ensuremath{'}}$, the Migdal spin-isospin parameter. We find a strong influence of kinematical conditions (especially the energy transfer) and of nuclear density on enhancement phenomena.NUCLEAR REACTIONS $^{16}\mathrm{O}(e, {e}^{\ensuremath{'}}{\ensuremath{\pi}}^{\ensuremath{-}})^{16}\mathrm{F}^{*}$, $^{16}\mathrm{O}(e, {e}^{\ensuremath{'}}{\ensuremath{\pi}}^{\ensuremath{-}})X$; threshold pion production cross sections for exclusive and inclusive measurements; spin-isospin strength distribution effects.

Threshold pion electroproduction and the nuclear response surface

Abstract Information gained from inelastic electron scattering is used as a guide to the treatment of the nuclear response surface probed in pion electroproduction near threshold. A comparison of theory with the Mainz data is made.

Study of neutrino interactions in hydrogen and deuterium: Description of the experiment and study of the reactionν+d→μ−+p+ps

This paper gives a detailed description of an experiment which studies the interactions of muon-type neutrinos in hydrogen and deuterium. The experiment was performed at the Zero Gradient Synchrotron using the wide-band neutrino beam incident on the Argonne 12-foot bubble chamber filled with hydrogen and deuterium. The neutrino energy spectrum peaks at 0.5 GeV and has a tail extending to 6 GeV. The shape and intensity of the flux is determined using measurements of pion yields from beryllium. The produced pions are focused by one or (for the latter part of the experiment) two magnetic horns. A total of 364000 pictures were taken with a hydrogen filling of the bubble chamber and 903 000 with a deuterium filling. The scanning and other analyses of the events are described. The most abundant reaction occurs off neutrons and is quasi-elastic scattering $\ensuremath{\nu}d\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}p{p}_{s}$. The separation of these events from background channels is discussed. The total and differential cross sections are analyzed to obtain the axial-vector form factor of the nucleon. Our result, expressed in terms of a dipole form factor, gives an axial-vector mass of 0.95\ifmmode\pm\else\textpm\fi{}0.09 GeV. A comparison is made to previous measurements using neutrino beams, and also to determinations based upon threshold pion electroproduction experiments. In addition, the data are used to measure the weak vector form factor and so check the conserved-vector-current hypothesis.

Axial-vector nucleon form factor from pion electroproduction on a proton

The results of the analysis for the cross section of threshold pion electroproduction on protons in the range of squared four-momentum transfer 2.4–4.9 fm −2 are presented. The validity of a current algebra method and PAe PCAC hypothesis for the description of pion electroproduction is shown. The values of an axial-vector form factor are obtained.