Proton Form Factors Research Articles

Proton Form Factor Obtained from Correspondence Arguments between Resonance and Parton Pictures

We study the proton magnetic form factor in the form of two solutions satisfying the correspondence requirement between the resonance and the parton pictures. Both solutions, suggested by QCD and the new scaling law, give excellent fits to the data. Discussions about the results are also given.

Weak and electromagnetic form factors of baryons at large momentum transfer

Perturbative quantum-chromodynamic predictions are given for the weak and electromagnetic elastic and transition form factors of baryons at large momentum transfer $Q$. The leading (helicity-conserving) octet and decuplet form factors can all be expressed as linear combinations of the proton and neutron magnetic form factors. The predictions for the spin structure and relative normalization of the baryon form factors reflect the assumed $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ structure of the electromagnetic and weak currents, quark and gluon hard-scattering dynamics, and the helicity-flavor symmetry of baryon wave functions at short distances. The results hold to all orders in ${\ensuremath{\alpha}}_{s}({Q}^{2})$ and to leading order in $\frac{m}{Q}$. We also discuss the special features of the contribution of the end-point $x\ensuremath{\sim}1$ region to baryon form factors.

On a possible structure in the proton elastic form factor

We investigate in the proton form factor the possibility to have a zero in the space-like region. As a consequence thee-p differential cross-section would have a dip and a second maximum which are accessible to experiment. If the existence of such structure would be revealed it would be very important for understanding the composite nature of the proton.

Study of the reaction e +e −→p [formula omitted] in the total energy range 1925–2180 MeV

The e +e − → p p cross section has been measured between 1925 and 2180 MeV. About 50 p p events were detected. The total cross section decreases from 1.31 ± 0.4 nb near 1937 MeV to 0.55 ± 0.2 nb near 2135 MeV. The proton form factors | G E | 2 and | G M | 2, assumed identical, decrease from 0.15 ± 0.05 to 0.043 ± 0.015. They are an order of magnitude higher than predicted by the well-known dipole fit. The energy range has been scanned in steps of about 2 MeV. No significant structure was found in this p p sample.

Bag-model electromagnetic form factors

The electromagnetic form factors of the proton and neutron are calculated using the MIT-bag-model wave functions and parameters. The calculated form factors are in good agreement with experiment. In particular, the first zero of the calculated form factor is at a surprisingly large value of q/sup 2/. The calculation shows how to restore momentum conservation to bag-model matrix elements.

Appearance of the second dip in elasticppscattering

One form of a Chou-Yang model is used successfully to fit all $\mathrm{pp}$ data for ${P}_{\mathrm{Lab}}=50 \mathrm{to} 1500$ GeV/c, and $\ensuremath{-}t=0.0 \mathrm{to} 12$ Ge${\mathrm{V}}^{2}$ with a differential cross section that runs twelve orders of magnitude from ${10}^{2}$ mb/Ge${\mathrm{V}}^{2}$ to ${10}^{\ensuremath{-}10}$ mb/Ge${\mathrm{V}}^{2}$. The $t$ dependence is fixed by the proton form factors alone, and there is only one free energy-dependent parameter ${\ensuremath{\mu}}_{1}(s)$ in the model. Specific predictions concerning the appearance of a second minimum in the $\mathrm{pp}$ differential cross section are made.

The ratio of the magnetic to the electric proton form factors in Quantum Chromodynamics

We propose a two parameter expression for the high momentum transfer behaviour of the ratio of proton form factors G M( Q 2)/ Q E( Q 2) based on perturbation theory calculations in Quantum Chromodynamics. A fit to the present experimental data and its consistency with a previous fit to the high Q 2 behaviour of the Dirac form factor [1] is also discussed.

Improved coupled-channel treatment of the (d, n̄) threshold effect

Calculations for the 90Zr(d, p) excitation function in a charge-exchange coupling model suggest that the ( d, n ) threshold effect can be explained with the resonant solution of the Lane equations taken as the proton form factor.

Electromagnetic form factors of the peoton at low four-momentum transfer (II)

The 300 MeV electron linear accelerator of Mainz has been used to measure the angular dependence of the electron-proton elastic scattering cross sections at seven different energies for squared four-momentum transfers between 0.13 and 4.7 fm −2. The proton form factors have been extracted from the cross sections by means of Rosenbluth plots and by fitting parametrized analytical functions directly to the cross sections. The best fit is compared to the data of other laboratories. The previously reported deviations from the dipole fit have been confirmed. From the form factors at q 2<0.9 fm 2 the proton r.m.s. radius has been determined. A determination of the spectral function of the nucleon isovector form factor G E V in the time-like is obtained using a realistic ϱ resonance.

Scaling laws for large-momentum-transfer processes

Dimensional scaling laws are developed as an approach to understanding the energy dependence of high-energy scattering processes at fixed center-of-mass angle. Given a reasonable assumption on the short-distance behavior of bound states, and the absence of an internal mass scale, we show that at large $s$ and $t$, $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}(AB\ensuremath{\rightarrow}CD)\ensuremath{\sim}{s}^{\ensuremath{-}n+2}f(\frac{t}{s})$; $n$ is the total number of fields in $A$, $B$, $C$, and $D$ which carry a finite fraction of the momentum. A similar scaling law is obtained for large-${p}_{\ensuremath{\perp}}$ inclusive scattering. When the quark model is used to specify $n$, we find good agreement with experiments. For instance, this accounts naturally for the ${({q}^{2})}^{\ensuremath{-}2}$ asymptotic behavior of the proton form factor. We examine in detail the field-theoretic foundations of the scaling laws and the assumption which needs to be made about the short-distance and infrared behavior of a bound state.

A modified born term model for π± Δ electroproduction

An electric Born type model is used to describeπ±Δ electroproduction at high energies. The electric pion form factor is taken from VDM; the contact term form factor and theΔ form factor are set equal to the proton form factor (or equal to zero) which is left as an arbitrary parameter, and is determined by a fit of the model to the recentπ+δ0 andπ−Δ++ electroproduction data.

Stripping to analog resonances

Abstract Stripping to analog resonances is studied by expressing the DWBA cross section in terms of the resolvent operator appropriate to the system composed of the proton and the target. The resolvent operator is decomposed, by means of the Feshbach projection operator technique, into parts corresponding to the entrance channel, the analog state and the compound states. The approximation scheme is similar to that used in our previous treatment of proton scattering at an analog resonance. The complex proton form factor depends on the Green function satisfying the inhomogeneous Schrodinger equation corresponding to elastic scattering and on the Coulomb potential generated by the target. The method is applied to ( 3 He, d) stripping to analogs in 93, 95, 97 Tc.

SU 6 Quark model, nucleon resonance electroproduction and spin-dependent electroproduction structure functions

The electromagnetic resonance excitation form factors for proton and neutron initial states are calculated in the nonrelativistic symmetric quark model for resonances in the 56 (L = 0), 70 (L = 1) and 56 (L = 2). Initially the radial wave function for each supermultiplet is assumed arbitrary and the results are used to calculate the resonance part of both spin independent and dependent electroproduction structure functions. Following Close, Gilman and Karliner the scaling behaviour of the structure functions is then discussed and relations with the naive quark-parton model made. Further a common radial wave function for all of the supermultiplets is assumed so there is then just a single undetermined form factor. Sum rules such as the Cabibbo-Radicati are considered and by demanding their saturation by the 56 and 70 additional dynamical constraints are derived. The observed helicity structure for excitation of theD13 andF15 is shown to arise naturally and change less dramatically withq2 than for a harmonicoscillator model.

On the electromagnetic form factor of nucleons

The proton form factor obtained from the oscillator model for quark structure is corrected by assuming that the latter has similar electromagnetic structure as pions. The structure of the proton form factor thus obtained is expected to be valid up to sufficiently large values of the momentum-transferred squared. However, in the small-q2 limit it agrees well with models used earlier to fit the experimental data.

A measurement of the ratio GE/GE of the proton form factors at very low momentum transfer

The ratioμGEGM of the proton form factors was determined by measuring the electron scattering cross section of the proton relative to that of12C. Data were taken atq2=0.09, 0.16, 0.25, and 0.36 fm−2, yielding a weighted mean ofμGE/GM=1.01±0.03.

Elastic electron-proton scattering between 0.05 and 0.30 (GeV/c) 2

Elastic electron proton scattering has been used to check the validity of the dipole fit of the proton form factors at momentum transfer between 0.05 and 0.30 (GeV/ c) 2. The general behaviour of the cross sections is in agreement with previous measurements and is close to the dipole predictions but there is the suggestion of some small amplitude deviations. It is speculated that these deviations may be related to similar effects in the proton formfactor derived from the ISR pp elastic scattering data via a Chou-Yang model.

Measurement of proton and neutron electromagnetic form factors at squared four-momentum transfers up to 3 (GeV/c) 2

Electron-proton elastic scattering cross sections have been measured at squared four-momentum transfers q 2 of 0.67, 1.00, 1.17, 1.50, 1.75, 2.33 and 3.00 (GeV/ c) 2 and Electron scattering angles θ e between 10° and 20° and at about 86° in the laboratory. The proton electromagnetic form factors G E p and G M p were determined. The results indicate that G E p ( q 2) decreases faster with increasing q 2 than G M p ( q 2). Quasi-elastic electron-deuteron cross sections have been determined at values of q 2 = 0.39, 0.565, 0.78, 1.0 and 1.5 (GeV/ c) 2 and scattering angles between 10° and 12°. At q 2 = 0.565 (GeV/ c 2 data have also been taken with θ e = 35° and at q 2 = 1.0 and 1.5 (GeV/ c) 2 with θ e = 86°. Electron-proton as well as electron-neutron scattering cross sections have been deduced by the ratio method. The theoretical uncertainties of this procedure are shown to be small by comparison of the bound with the free proton cross sections. The magnetic form factor of the neutron G M n derived from the data is consistent with the scaling law. The charge form factor of the neutron is found to be small.

Neutron and Proton Form Factors

The conclusions of a paper of the above title by Hammer and Weber, recently published in this journal, are criticized.Received 11 July 1972DOI:https://doi.org/10.1103/PhysRevLett.29.1042©1972 American Physical Society

Neutron and Proton Form Factors

Neutron and Proton Form Factors

Strong-interaction form factor of proton in high-energy proton-proton elastic scattering

An analysis of high-energy proton-proton elastic-scattering data is made in terms of one-particle exchange type amplitude. The results show that the proton form factor is constant at large momentum transfer. This may be interpreted as evidence for the existence of a pointlike core in the proton.