Proton Form Factors Research Articles

General analysis and numerical estimations of polarization observables in thep¯+p→π0+e++e−reaction in an exclusive experimental setup

The dependence of the differential cross section and polarization observables in the $\overline{p}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+{e}^{+}+{e}^{\ensuremath{-}}$ reaction on the polarizations of the proton target and antiproton beam (the produced electron may be unpolarized or longitudinally polarized) have been derived in a general form using hadron electromagnetic current conservation and $P$-parity invariance of the hadron electromagnetic interaction. The analysis was done for the case of an exclusive experimental setup where the produced electron and pion are detected in coincidence. The explicit dependence of all polarization observables on two, from five, kinematic variables (the azimuthal angle $\ensuremath{\phi}$ and the virtual-photon parameter $\ensuremath{\epsilon}$) have been obtained assuming one-photon exchange. The application to the particular case of a mechanism which contains information on time-like proton form factors in the unphysical region is considered in the Born approximation.

Final analysis of proton form factor ratio data atQ2=4.0, 4.8, and 5.6 GeV2

Precise measurements of the proton electromagnetic form factor ratio $R = \mu_p G_E^p/G_M^p$ using the polarization transfer method at Jefferson Lab have revolutionized the understanding of nucleon structure by revealing the strong decrease of $R$ with momentum transfer $Q^2$ for $Q^2 \gtrsim 1$ GeV$^2$, in strong disagreement with previous extractions of $R$ from cross section measurements. In particular, the polarization transfer results have exposed the limits of applicability of the one-photon-exchange approximation and highlighted the role of quark orbital angular momentum in the nucleon structure. The GEp-II experiment in Jefferson Lab's Hall A measured $R$ at four $Q^2$ values in the range 3.5 GeV$^2 \le Q^2 \le 5.6$ GeV$^2$. A possible discrepancy between the originally published GEp-II results and more recent measurements at higher $Q^2$ motivated a new analysis of the GEp-II data. This article presents the final results of the GEp-II experiment, including details of the new analysis, an expanded description of the apparatus and an overview of theoretical progress since the original publication. The key result of the final analysis is a systematic increase in the results for $R$, improving the consistency of the polarization transfer data in the high-$Q^2$ region. This increase is the result of an improved selection of elastic events which largely removes the systematic effect of the inelastic contamination, underestimated by the original analysis.

Baryon Form Factors at Threshold

An extensive study of the e + e − → p p ¯ BaBar cross section data is presented. Two unexpected outcomes have been found: the modulus of the proton form factor is normalized to one at threshold, i.e.: | G p ( 4 M p 2 ) | = 1 , as a pointlike fermion, and the resummation factor in the Sommerfeld formula is not needed. Other e+e− → baryon-antibaryon cross sections show a similar behavior near threshold.

Description of the spacelike and timelike proton form factors at large momentum transfer in the QCD factorization approach

We propose QCD factorization approach for description of the soft spectator scattering contribution. It is expected that such contribution is very important for description of the many exclusive processes at moderate values of Q2. Assuming the dominance of this mechanism we provide qualitative consideration of the proton form factors in the spacelike and timelike regions. Using the same approach we also provide estimates of the cross sections for the processes γγ→pp̄ and pp̄→γγ at large energy and momentum transfer.

Hadron Medium Modifications

Proton recoil polarization in quasielastic electron scattering is a powerful tool to study properties of nucleons bound in the nuclear medium. The most precise results have been obtained at Jefferson Lab in the 4 He(e, e ′ p ) 3 H reaction at four momentum transfers of Q 2 = 0.8 (GeV/ c ) 2 and at 1.3 (GeV/ c ) 2 . The ratio of polarization-transfer components, P ′ x / P ′ z , is significantly reduced compared to the ratio obtained in elastic 1 H(e, e ′ p ) scattering. This depletion is well described with models which include in-medium modifications of the proton form factor or, alternatively, by strong charge-exchange final-state interactions. A future experiment will measure the dependence of this effect on the momentum of the struck nucleon in both, the 4 He(e, e ′ p ) 3 H and 2 H(e, e ′ p ) n reactions.

Reexamination of phenomenological two-photon exchange corrections to the proton form factors ande±pscattering

We extract the two-photon exchange (TPE) contributions to electron--proton elastic scattering using two parametrizations and compare the results to different phenomenological extractions and direct calculations of the TPE effects. We find that many of the extractions give similar results, and highlight the common assumptions and the impact of not including such assumptions. We provide a simple parametrization of the TPE contribution to the unpolarized cross section, along with an estimate of the fit uncertainties and the uncertainties associated with the assumptions made in the extraction. We look at the contributions as extracted from various e--p elastic scattering observables, and make predictions for ratio $R^{e^{+} e^{-}}$ of positron-proton to electron-proton elastic scattering cross sections.

THE PROTON FORM FACTOR RATIO AT LOW Q2: NEW RESULTS FROM JEFFERSON LAB

Recently an experiment at Jefferson Lab has measured the proton form factor ratio, [Formula: see text], down to Q2 ~ 0.3 GeV 2 with unprecedented precision. Based on the results from this experiment, a re-analysis was carried out for the world data on proton form factors, and a new result was extracted for the proton charge radius. The new result is consistent with published CODATA results and is at odds with the new muonic hydrogen measurement at PSI. We present the results of the new measurement, as well as discuss an upcoming experiment to measure the form factor ratio down to even lower Q2.

Testing electromagnetic proton form factors in the annihilation process [formula omitted

We study the annihilation channel in proton antiproton collisions with production of a single neutral pion and an electron-positron pair. It is shown that this reaction allows access to the proton electromagnetic form factors in the ‘unphysical’ region and to the difference between complex phases of the Dirac and Pauli proton form factors. The differential cross section is given in the laboratory frame in an experimental setup where all outgoing particles are fully detected.

Soft spectator scattering in the nucleon form factors at largeQ2within the soft collinear effective theory approach

The proton form factors at large momentum transfer are dominated by two contributions which are associated with the hard and soft rescattering respectively. Motivated by a very active experimental form factor program at intermediate values of momentum transfers, $Q^{2}\sim 5-15 \text{GeV}^{2}$, where an understanding in terms of only a hard rescattering mechanism cannot yet be expected, we investigate in this work the soft rescattering contribution using soft collinear effective theory (SCET). Within such description, the form factor is characterized, besides the hard scale $Q^2$, by a semi-hard scale $Q \Lambda$, which arises due to presence of soft spectators, with virtuality $\Lambda^2$ ($\Lambda \sim 0.5$ GeV), such that $Q^{2}\gg Q\Lambda\gg \Lambda^{2}$. We show that in this case a two-step factorization can be successfully carried out using the SCET approach. In a first step (SCET$_I$), we perform the leading order matching of the QCD electromagnetic current onto the relevant SCET$_I$ operators and perform a resummation of large logarithms using renormalization group equations. We then discuss the further matching onto a SCET$_{II}$ framework, and propose the complete factorization formula for the Dirac form factor, accounting for both hard and soft contributions. We also present a qualitative discussion of the phenomenological consequences of this new framework.

Proton Form Factors: phenomenology

A general description of proton form factors is presented, in the whole kinematical region. The existing data and selected phenomenological models are briefly discussed.

FUTURE MEASUREMENTS OF THE PROTON TIME LIKE FORM FACTORS WITH $\rm {{\bar PANDA}}$

We present feasibility studies of a precise measurement of the |GE| and |GM| proton form factors that will be possible in the future with the [Formula: see text] detector.

Exact results in QED

This review is devoted to exact calculations of cross sections of QED processes in relativistic approach. We consider the case when the velocity of final heavy particles are not particularly close to the speed of light. Especially the cases of muon radiative pair creation is considered. In frames of QED with pion form-factor we estimate the pion radiative pair creation. All leading terms are included in the frames of structure function approach. The annihilation of electron-positron to the hadronic final state with one additional tagged photon is considered. The radiative corrections are calculated and the numerical estimation is made. Target spin asymmetry and charge asymmetry are investigated for eμ scattering processes. Initial state radiation (returning to resonance) mechanism is investigated including radiative corrections to initial and final states. Possible method of experimental extraction of the ratio of electric and magnetic form-factors of proton is suggested for different processes in lepton proton scattering. Some useful algebraic relations and integrals are presented.

HighQ2behavior of the electromagnetic form factors in the relativistic hypercentral constituent quark model

The ratio $R_p$ between the electric and magnetic proton form factors has been recently measured at JLab up to $Q^2=8.5 ~GeV^2$. We have extended the calculation of the nucleon form factors with the hypercentral Constituent Quark Model and compared them with the data on $R_p$ and on the $Q^2$ behavior of the ratio $Q^2 F_2/F_1$. In both cases the theoretical curves agree with the experimental points.

Polarization Transfer in theHe4(e→,e′p→)H3Reaction atQ2=0.8and1.3 (GeV/c)2

Proton recoil polarization was measured in the quasielastic 4He(e,e'p)3H reaction at Q^2 = 0.8 (GeV/c)^2 and 1.3 (GeV/c)^2 with unprecedented precision. The polarization-transfer coefficients are found to differ from those of the 1H(e,e' p) reaction, contradicting a relativistic distorted-wave approximation, and favoring either the inclusion of medium-modified proton form factors predicted by the quark-meson coupling model or a spin-dependent charge-exchange final-state interaction. For the first time, the polarization-transfer ratio is studied as a function of the virtuality of the proton.

BABAR measurement of baryon time-like form factors via initial state radiation

BABAR has measured with unprecedented accuracy the e+e− →pp̄ and e+e− → Λ cross sections by means of the initial state radiation technique, which has the advantages of good efficiency, good energy resolution and full angular acceptance, even exactly at threshold. A peculiar feature of these cross sections is their non-vanishing values at threshold. In the case of charged baryons, this phenomenon is expected according to the Coulomb interaction between the outgoing baryon and antibaryon. Once this Coulomb enhancement factor is taken into account, the striking result is achieved that the proton form factor at threshold is |Gp(4Mp2)| = 1, that is what is expected for pointlike fermion pairs, in spite of the proton structure. However a Coulomb enhancement factor is not expected for neutral fermions, likely in contradiction with the BABAR data. Qualitatively this behaviour is consistent with Coulomb interactions at the valence quark level.

Effects of C-, P-, T-symmetries violation in the polarized elastic electron-proton electroweak scattering

Analytical expressions are obtained for the angular distributions and spin asymmetries of the processes of elastic electromagnetic and electroweak scattering of high energy electrons on polarized/unpolarized proton target with account of C-, P- and T/CP-invariance violating anapole and electric dipole moments, as well as neutral weak electric, magnetic and axial form factors of the proton. Behavior of the P- and T- odd spin asymmetries is studied in dependence of the electron’s energy and scattering angle and proton form factors parameters.

Two-photon-exchange contribution to proton form factors in both space-like and time-like regions

The two two-photon exchange corrections to the unpolarized cross section and polarized observable PT, PL in elastic ep scattering are discussed in a simple hadronic model. Comparing with previous results, the Δ contribution are re-analysed. And the similar corrections in e+e− → pp̄ are also discussed.

At threshold and proton form factor

The reactions at energy threshold are studied in a non-perturbative quark model. The vector meson dominance ansatz, in which the primary pair forms first a vector meson which in turn decays into a hadron pair, is applied in the work. The vector mesons ρ(770), ρ(1450), ρ(1700), ρ(2005), ρ(2150), ω(782), ω(1420) ω(1650), ω(1925), ω(2145) and ω(2305) are employed as the intermediate states of the processes . The work reproduces well the experimental data for the cross section of the reaction and data of the proton form factor. The ratio of the cross section to the one is found to be smaller than 1 at energies around 2.0 GeV.

Feasibility studies of the time-like proton electromagnetic form factor measurements with $ \overline{{P}}$ANDA at FAIR

The possibility of measuring the proton electromagnetic form factors in the time-like region at FAIR with the \( \overline{{P}}\)ANDA detector is discussed. Detailed simulations on signal efficiency for the annihilation of \( \bar{{p}}\) + p into a lepton pair as well as for the most important background channels have been performed. It is shown that precise measurements of the differential cross-section of the reaction \( \bar{{p}}\) + p \( \rightarrow\) e - + e + can be obtained in a wide kinematical range. The determination of the ratio R of the moduli of the electric and magnetic proton form factors will be possible up to a value of momentum transfer squared of q 2 ≃ 14 (GeV/c)^2 with absolute precision from 0.01 to 0.5 (for R ∼ 1 . The total \( \bar{{p}}\) + p \( \rightarrow\) e - + e + cross-section will be measured up to q 2 ≃ 28 (GeV/c)^2. The results obtained from simulated events are compared to the existing data. Sensitivity to the two-photon exchange mechanism is also investigated.

Time-like proton form factor measurement with P̄ANDA

The electromagnetic probe is an excellent tool to investigate the structure of the nucleon. The nearly 4π detector PANDA, will allow to make a precise determination of the electromagnetic form factors of the proton in the time-like region with unprecedented precision. In the one-photon exchange approximation, the center of mass unpolarized differential cross section of the reaction p̄p → e+e− is a linear combination of the squared moduli of the electric GE and magnetic GM proton form factors. The precise measurement of the angular distribution over almost full angular range then directly gives these quantities. At present only two experiments have provided the ratio R = |GE|/|GM| but with large statistical uncertainties. It is shown that with strict PID cuts and a kinematic fit, the dominant background, p̄p → π+π−, can be supressed to much less than 1% of the signal, without affecting the extraction of the ratio R. P̄ANDA will therefore offer a unique opportunity to measure the ratio with a precision ranging from <1% at low q2 up to 30% for q2 = 14 (GeV/c)2.