Pion Electroproduction Cross Section Research Articles

Deep Exclusive Electroproduction of π^{0} at High Q^{2} in the Quark Valence Regime.

We report measurements of the exclusive neutral pion electroproduction cross section off protons at large values of x_{B} (0.36, 0.48, and 0.60) and Q^{2} (3.1 to 8.4 GeV^{2}) obtained from Jefferson Lab Hall A experiment E12-06-014. The corresponding structure functions dσ_{T}/dt+εdσ_{L}/dt, dσ_{TT}/dt, dσ_{LT}/dt, and dσ_{LT^{'}}/dt are extracted as a function of the proton momentum transfer t-t_{min}. The results suggest the amplitude for transversely polarized virtual photons continues to dominate the cross section throughout this kinematic range. The data are well described by calculations based on transversity generalized parton distributions coupled to a helicity flip distribution amplitude of the pion, thus providing a unique way to probe the structure of the nucleon.

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.

Charged-pion electroproduction above the resonance region

[Background] Above the nucleon resonance region, the $N(e,e'\pi^\pm)N'$ data cannot be explained by conventional hadronic models. For example, the observed magnitude of the transverse cross section is significantly underestimated in a framework with Reggeized background amplitudes. [Purpose] Develop a phenomenological framework for the $N(e,e'\pi^\pm)N'$ reaction at high invariant mass $W$ and deep photon virtuality $Q^2$. [Method] Building on the work of Kaskulov and Mosel, a gauged pion-exchange current is introduced with a running cutoff energy for the proton electromagnetic transition form factor. A new transition form factor is proposed. It respects the correct on-shell limit, has a simple physical interpretation and reduces the number of free parameters by one. [Results] A study of the $W$ dependence of the $N(e,e'\pi^\pm)N'$ lends support for the newly proposed transition form factor. In addition, an improved description of the separated and unseparated cross sections at $-t \lesssim 0.5 \;\text{GeV}^2$ is obtained. The predictions overshoot the measured unseparated cross sections for $-t > 0.5 \;\text{GeV}^2$. Introducing a strong hadronic form factor in the Reggeized background amplitudes brings the calculations considerably closer to the high $-t$ data. [Conclusions] Hadronic models corrected for resonance/parton duality describe the separated pion electroproduction cross sections above the resonance region reasonably well at low $-t$. In order to validate the applicability of these models at high $-t$, separated cross sections are needed. These are expected to provide a more profound insight into the relevant reaction mechanisms.

Hadron Structure in Chiral Perturbation Theory

We present our predictions for meson form factors for the SU(3) octet and investigate their impact on the pion electroproduction cross sections. The electric and magnetic polarizabilities of the SU(3) octet of mesons and baryons are analyzed in detail. These extensive calculations are made possible by the recent implementation of semi-automatized calculations in fully-relativistic chiral perturbation theory, which allows evaluation of polarizabilities from Compton scattering up to next-to-the-leading order.

Two photon exchange for exclusive pion electroproduction

We perform detailed calculations of two-photon-exchange QED corrections to the cross section of pion electroproduction. The results are obtained with and without the soft-photon approximation; analytic expressions for the radiative corrections are derived. The relative importance of the two-photon correction is analyzed for the kinematics of several experiments at Jefferson Lab. A significant, over 20%, effect due to two-photon exchange is predicted for the backward angles of electron scattering at large transferred momenta.

Near-threshold neutral pion electroproduction at high momentum transfers and generalized form factors

We report the measurement of near threshold neutral pion electroproduction cross sections and the extraction of the associated structure functions on the proton in the kinematic range $Q^2$ from 2 to 4.5 GeV$^2$ and $W$ from 1.08 to 1.16 GeV. These measurements allow us to access the dominant pion-nucleon s-wave multipoles $E_{0+}$ and $S_{0+}$ in the near-threshold region. In the light-cone sum-rule framework (LCSR), these multipoles are related to the generalized form factors $G_1^{\pi^0 p}(Q^2)$ and $G_2^{\pi^0 p}(Q^2)$. The data are compared to these generalized form factors and the results for $G_1^{\pi^0 p}(Q^2)$ are found to be in good agreement with the LCSR predictions, but the level of agreement with $G_2^{\pi^0 p}(Q^2)$ is poor.

Scaling study of the pion electroproduction cross sections

The ${}^{1}\mathrm{H}(e, {e}^{'}{\ensuremath{\pi}}^{+})n$ cross section was measured for arange of four-momentum transfer up to ${Q}^{2}=3.91 {\mathrm{GeV}}^{2}$ at values of the invariant mass $W$ above the resonance region. The ${Q}^{2}$ dependence of the longitudinal component was found to be consistent with the ${Q}^{2}$-scaling prediction for hard exclusive processes. This suggests that the QCD factorization theorem is applicable at rather low values of ${Q}^{2}$. The transverse term falls off slower than the naive ${Q}^{\ensuremath{-}8}$ expectation and remains appreciable even at ${Q}^{2}=3.91 {\mathrm{GeV}}^{2}$.

Determination of the Pion Charge Form Factor atQ2=1.60and2.45 (GeV/c)2

The 1H(e,e'pi+)n cross section was measured at four-momentum transfers of Q2=1.60 and 2.45 GeV2 at an invariant mass of the photon nucleon system of W=2.22 GeV. The charged pion form factor (F(pi)) was extracted from the data by comparing the separated longitudinal pion electroproduction cross section to a Regge model prediction in which F(pi) is a free parameter. The results indicate that the pion form factor deviates from the charge-radius constrained monopole form at these values of Q2 by one sigma, but is still far from its perturbative quantum chromodynamics prediction.

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 E 0 = 855, 675, 600, and 555 MeV at fixed four-momentum transfer Q 2 = 0.045 GeV 2, 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.

Neutral and charged current inclusive neutrino reactions inC12and the pion-electroproduction cross section

Total muon-capture rates and inclusive pion-electroproduction cross sections in $^{12}\mathrm{C}$ are used to obtain inclusive neutral and charged current neutrino cross sections in $^{12}\mathrm{C}$. These results are obtained for $150 \mathrm{MeV} \ensuremath{\le}{E}_{\ensuremath{\nu}}\ensuremath{\le}250 \mathrm{MeV}$ for the charged current case and $50 \mathrm{MeV} \ensuremath{\le}{E}_{\ensuremath{\nu}}\ensuremath{\le}150 \mathrm{MeV}$ for the neutral current case. Comparison is made with other calculations.

Pion electroproduction from 6Li

The pion electroproduction cross section from 6Li is calculated assuming the 6He nucleus is detected. The wave-functions used in this calculation are those which gave the best agreement with the 6Li(γ,π +) 6He data. The electro-production experiment will provide a useful check of these wave functions.

The k2-dependence of the transverse pion electroproduction cross section in a generalized born term model

Data on π +-electroproduction off protons are analysed in a generalized Born term model, where the off-shell nucleon form factor F 1( k 2) is allowed to differ from its on-shell value. The longitudinal-transverse interference cross section is sensitive to the ratio of the nucleon form factor to the pion form factor, and the data require this ratio to be larger than one. The resulting transverse cross section, integrated over a small t-interval, follows the slow decrease of the total inelastic cross section as a function of the photon mass squared.

A measurement of pion electroproduction cross-section near threshold

A measurement of pion electroproduction cross-section near threshold

A measurement of longitudinal photon contribution in pion electroproduction from protons

A measurement of the pion electroproduction cross section from protons, at a transfer q 2 = −3.4 fm −2 and a πN mass of 1136 MeV, gave the values σ L = 27.0 ± 902 μb, σ T=81.8 ± 4.3μb, σ L σ T = 0.33 ± 0.13 . It is shown that this result is very sensitive to a correct application of radiative corrections but rather insensitive to the exact analytic expressions used.

Proposal for Determining the Electromagnetic Form Factor of the Pion

The possibility of measuring the electromagnetic form factor of the pion by extrapolation of the cross section for ${e}^{\ensuremath{-}}+p\ensuremath{\rightarrow}n+{\ensuremath{\pi}}^{+}+{e}^{\ensuremath{-}}$ has been investigated. The method is based on the existence of a pole in the pion-electroproduction scattering amplitude as a function of the invariant momentum-transfer of the nucleon. The residue of this pole is the pion form factor multiplied by a known coefficient. Since the pole lies slightly outside the physical region of the invariant momentum transfer, an extrapolation of the experimental data is required. An approximate calculation of the pion electroproduction cross section has been made in order to estimate the experimental accuracy necessary for a significant extrapolation. Accuracy is required which is an order of magnitude better than that achieved at present in similar experiments.