Electric Form Factor Research Articles

Time-like Proton Form Factors with Initial State Radiation Technique

Electromagnetic form factors are fundamental quantities describing the internal structure of hadrons. They can be measured with scattering processes in the space-like region and annihilation processes in the time-like region. The two regions are connected by crossing symmetry. The measurements of the proton electromagnetic form factors in the time-like region using the initial state radiation technique are reviewed. Recent experimental studies have shown that initial state radiation processes at high luminosity electron-positron colliders can be effectively used to probe the electromagnetic structure of hadrons. The BABAR experiment at the B-factory PEP-II in Stanford and the BESIII experiment at BEPCII (an electron positron collider in the τ-charm mass region) in Beijing have measured the time-like form factors of the proton using the initial state radiation process e+e−→pp¯γ. The two kinematical regions where the photon is emitted from the initial state at small and large polar angles have been investigated. In the first case, the photon is in the region not covered by the detector acceptance and is not detected. The Born cross section and the proton effective form factor have been measured over a wide and continuous range of the the momentum transfer squared q2 from the threshold up to 42 (GeV/c)2. The ratio of electric and magnetic form factors of the proton has been also determined. In this report, the theoretical aspect and the experimental studies of the initial state radiation process e+e−→pp¯γ are described. The measurements of the Born cross section and the proton form factors obtained in these analyses near the threshold region and in the relatively large q2 region are examined. The experimental results are compared to the predictions from theory and models. Their impact on our understanding of the nucleon structure is discussed.

Electromagnetic form factors in noncommutative space time

Electric and magnetic moment distributions are presenting by form factors (FF)s. Noncommutative space-time (NCST) includes an additional Lorentz index which are effecting on FFs. In this content we investigate electron-proton elastic scattering to impose the noncommutative effect on FFs and to obtain their physical meaning. Two Rosenbluth and polarization methods are utilized in NCST. The second method is not affected by NCST. When we resort to polarization method, the ratio of electric form factor to magnetic form factor in NCST is identical to the one in normal space time. This indicates the priority of polarization method to measure experimentally the concerned ratio as is expecting. On the other hand, the pure NC effect makes to appear an extra ratio, denoted by R_{NC}. If we let the variation of this quantity to cover the difference between the experimental results for Resonbluth and polarization ratio then the accepted lower limit of Lambda _{NC} as NC scale is achieved which is corresponding to 180^circ for the scattering angle.

Electromagnetic effects in elastic neutrino scattering on nucleons

We study the electromagnetic contribution to elastic neutrino-proton and neutrino-neutron scattering processes. The neutrino electromagnetic charge, magnetic, electric, and anapole form factors of both diagonal and transition types in the mass basis are taken into account in the present formalism. When treating the nucleon electromagnetic vertex, we take into account not only the charge and magnetic form factors of a nucleon, but also its electric and anapole form factors. We examine how the effects of the neutrino millicharge can be disentangled from those of the strange quark contributions to the nucleon’s weak neutral current form factors.

A measurement of two-photon exchange in Super-Rosenbluth separations with positron beams

The proton electric and magnetic form factors, $G_E$ and $G_M$, are intrinsically connected to the spatial distribution of charge and magnetization in the proton. For decades, Rosenbluth separation measurements of the angular dependence of elastic e$^-$-p scattering were used to extract $G_E$ and $G_M$. More recently, polarized electron scattering measurements, aiming to improve the precision of $G_E$ extractions, showed significant disagreement with Rosenbluth measurements at large momentum transfers ($Q^2$). This discrepancy is generally attributed to neglected two-photon exchange (TPE) corrections. At larger $Q^2$ values, a new `Super-Rosenbluth' technique was used to improve the precision of the Rosenbluth extraction, allowing for a better quantification of the discrepancy, while comparisons of e$^+$-p and e$^-$-p scattering indicated the presence of TPE corrections, but at $Q^2$ values below where a clear discrepancy is observed. In this work, we demonstrate the significant benefits to combining the Super-Rosenbluth technique with positron beam measurements. This approach provides a greater kinematic reach and is insensitive to some of the key systematic uncertainties in previous positron measurements.

Calculation of the derivative of nucleon form factors in Nf=2+1 lattice QCD at Mπ=138 MeV on a (5.5 fm)3 volume

We present a direct calculation for the first derivative of the isovector nucleon form factors with respect to the momentum transfer ${q}^{2}$ using the lower moments of the nucleon 3-point function in the coordinate space. Our numerical simulations are performed using the ${N}_{f}=2+1$ nonperturbatively $O(a)$-improved Wilson quark action and Iwasaki gauge action near the physical point, corresponding to the pion mass ${M}_{\ensuremath{\pi}}=138\text{ }\text{ }\mathrm{MeV}$, on a $(5.5\text{ }\text{ }\mathrm{fm}{)}^{4}$ lattice at a single lattice spacing of $a=0.085\text{ }\text{ }\mathrm{fm}$. In the momentum derivative approach, we can directly evaluate the mean square radii for the electric, magnetic, and axial-vector form factors, and also the magnetic moment without the ${q}^{2}$ extrapolation to the zero momentum point. These results are compared with the ones determined by the standard method, where the ${q}^{2}$ extrapolations of the corresponding form factors are carried out by fitting models. We find that the new results from the momentum derivative method are obtained with a larger statistical error than the standard method, but with a smaller systematic error associated with the data analysis. Within the total error range of the statistical and systematic errors combined, the two results are in good agreement. On the other hand, two variations of the momentum derivative of the induced pseudoscalar form factor at the zero momentum point show some discrepancy. It seems to be caused by a finite volume effect, since a similar trend is not observed on a large volume, but seen on a small volume in our pilot calculations at a heavier pion mass of ${M}_{\ensuremath{\pi}}=510\text{ }\text{ }\mathrm{MeV}$. Furthermore, we discuss an equivalence between the momentum derivative method and the similar approach with the point splitting vector current.

Proton and neutron form factors from deformed gravity/gauge duality

In this work we study the electric and magnetic Sachs form factors for proton and neutron by using a deformed gravity/gauge model. We describe holographically baryons as well as gauge bosons which are ruled by the parameters kB and kγ, associated with confinement and kinematical energy scales, respectively. Then, we construct the interaction action and calculate the electric and magnetic form factors for the proton and the neutron, and their electromagnetic sizes. The obtained results are compatible with those found in the literature from experimental and theoretical data.

Electric dipole moments of three-nucleon systems in the pionless effective field theory

We calculate the electric dipole moments (EDMs) of three-nucleon systems at leading order in pionless effective field theory. The one-body contributions that arise from permanent proton and neutron EDMs and the two-body contributions that arise from charge-parity-odd nucleon-nucleon interactions are taken into account. Neglecting the Coulomb interaction, we consider the triton and $^{3}\mathrm{He}$, and also investigate them in the Wigner-SU(4) symmetric limit. We also calculate the electric dipole form factor and find numerically that the momentum dependence of the electric dipole form factor in the Wigner limit is, up to an overall constant (and numerical accuracy), the same as the momentum dependence of the charge form factor. Finally, we study the cutoff dependence of these observables and find that they are properly renormalized.

Proton and neutron form factors with quark orbital excitations

Nucleon form factors play an especially important role in studying the dynamics of nucleons and explicit structure of the wave functions at arbitrary nucleon velocity. The purpose of the paper is to explain theoretically all four nucleon form factors measured experimentally in the cross section measurements (by the Rosenbluth method), yielding almost equal normalized form factors $G^p_E,G^p_M,G^n_M$, as well as in the polarization transfer experiments, where a strongly decreasing proton electric form factor has been discovered. It is shown, using relativistic hyperspherical formalism, that the nucleon wave functions in the lowest approximation provide almost equal normalized form factors as seen in the Rosenbluth cross sections, but in the higher components they contain a large admixture of the quark orbital momenta, which strongly decreases $G^p_E$ and this effect is possibly detected in the polarization transfer method (not seen in the classical cross section experiments). Moreover, the same admixture of the higher components explains the small positive form factor $G^n_E$. The resulting form factors, $G^p_M(Q),G^p_E(Q),G^n_M(Q)$ are calculated up to $Q^2\approx 10$ GeV$^2$, using the standard and the Lorentz contracted wave functions and shown to be in reasonable agreement with experimental data.

Model-independent extraction of the proton charge radius from PRad data

The proton radius puzzle has motivated several new experiments that aim to extract the proton charge radius and resolve the puzzle. Recently, PRad, a new electron–proton scattering experiment at Jefferson Lab, reported a proton charge radius of [Formula: see text]. The value was obtained by using a rational function model for the proton electric form factor. We perform a model-independent extraction using [Formula: see text]-expansion of the proton charge radius from PRad data. We find that the model-independent statistical error is more than 50% larger compared to the statistical error reported by PRad.

Nπ -state contamination in lattice calculations of the nucleon electromagnetic form factors

The nucleon-pion-state contribution to QCD two-point and three-point functions relevant for lattice calculations of the nucleon electromagnetic form factors are studied in chiral perturbation theory. To leading order the results depend on a few experimentally known low-energy constants only, and the nucleon-pion-state contribution to the form factors can be estimated. The nucleon-pion-state contribution to the electric form factor $G_{\rm E}(Q^2)$ is at the +5 percent level for a source-sink separation of 2 fm, and it increases with increasing momentum transfer $Q^2$. For the magnetic form factor the nucleon-pion-state contribution leads to an underestimation of $G_{\rm M}(Q^2)$ by about 5 percent that decreases with increasing $Q^2$. For smaller source-sink separations that are accessible in present-day lattice simulations the impact is larger, although the ChPT results may not be applicable for such small time separations. Still, a comparison with lattice data at $t\approx 1.6$ fm works reasonably well.

Standardization of electric vehicle battery pack geometry form factors for passenger car segments in India

The Electric Vehicles (EV) adaptability is at the early stage in India due to many performances and commercial constraints among the potential customers. Battery Electric Vehicles (BEV) are slowly picking up in the Indian market and likely to grow due to stringent Government regulations and Green Mobility initiatives. The primary constraint in EV purchase is the driving range offered by Original Equipment Manufacturers (OEM) and EV range anxiety. This paper discusses the current battery pack integration among Indian Original Equipment Manufacturers (OEMs), design challenges, and the need for Standardised Battery Pack envelope (SBP). This study analyses the India OEMs vehicle data and, using a statistical and engineering assessment model, recommends the critical standard dimensions, type, size for the Standardised Battery Pack (SBP). This is possible by means of Electric Vehicle (EV) skateboard platform architecture, and platform sharing proliferate among EV manufacturers and start-ups. The model verifies the results by analytical and Simulation techniques. The results show the proposed model with SBP gives higher flexibility, improved driving range ,convenient battery swapping operation, improved operation time, and helps in second-life applications. This study's limitation is that due to the rapid advancement in battery technology, a specific battery chemistry is under consideration throughout the study.

New extraction of the Re+e− elastic scattering cross-section ratio based on a simplified phenomenological hard two-photon-exchange correction approach

In this work, we present a prediction of the positron-proton and electron-proton elastic scattering cross-section ratio ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ based on a new phenomenological parametrization of the hard two-photon-exchange (TPE) corrections to electron-proton elastic scattering cross section ${\ensuremath{\sigma}}_{R}$. The TPE parametrization proposed in this work is rather simple, as it only requires the use of suitable global fits of both the Rosenbluth magnetic ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{M}$, and the true magnetic ${G}_{M}$ form factors, or alternatively, the electric form factors ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{E}$ and ${G}_{E}$. We compare our results to recent extractions, and world's data on ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ with emphasis mainly on the kinematics range of the recent direct measurements from the CLAS, VEPP-3, and OLYMPUS experiments. With the proper choice of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{M}$ and ${G}_{M}$ parametrizations, and while our results are in generally good agreement with ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ measurements taken at high $\ensuremath{\varepsilon}$ points and for all ${Q}^{2}$ range, they agree remarkably well, within the error bands of the predictions, with ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ measurements taken at low-$\ensuremath{\varepsilon}$ points for ${Q}^{2}=1.0$ and $1.5\phantom{\rule{0.16em}{0ex}}{(\mathrm{GeV}/\mathrm{c})}^{2}$, where emphasis should be placed for evidence of hard TPE correction. Finally, we believe that the assumption that hard TPE corrections could account for the discrepancy on the proton's form factors ratio ${\ensuremath{\mu}}_{p}{G}_{E}/{G}_{M}$ is still an open question as more measurements of ${R}_{{e}^{+}{e}^{\ensuremath{-}}}$ are clearly needed for ${Q}^{2}>\phantom{\rule{4pt}{0ex}}2.1\phantom{\rule{0.16em}{0ex}}{(\mathrm{GeV}/\mathrm{c})}^{2}$, in the region where the discrepancy is significant.

Measurement of proton electromagnetic form factors in the time-like region using initial state radiation at BESIII

The electromagnetic process e+e−→pp¯ is studied with the initial-state-radiation technique using 7.5 fb−1 of data collected by the BESIII experiment at seven energy points from 3.773 to 4.600 GeV. The Born cross section and the effective form factor of the proton are measured from the production threshold to 3.0 GeV/c2 using the pp¯ invariant-mass spectrum. The ratio of electric and magnetic form factors of the proton is determined from the analysis of the proton-helicity angular distribution.

Measurement of the neutron charge radius and the role of its constituents

The neutron is a cornerstone in our depiction of the visible universe. Despite the neutron zero-net electric charge, the asymmetric distribution of the positively- (up) and negatively-charged (down) quarks, a result of the complex quark-gluon dynamics, lead to a negative value for its squared charge radius, langle {r}_{{rm{n}}}^{2}rangle. The precise measurement of the neutron’s charge radius thus emerges as an essential part of unraveling its structure. Here we report on a langle {r}_{{rm{n}}}^{2}rangle measurement, based on the extraction of the neutron electric form factor, {G}_{{rm{E}}}^{{rm{n}}}, at low four-momentum transfer squared (Q2) by exploiting the long known connection between the N → Δ quadrupole transitions and the neutron electric form factor. Our result, langle {r}_{{rm{n}}}^{2}rangle =-0.110pm 0.008,({{rm{fm}}}^{2}), addresses long standing unresolved discrepancies in the langle {r}_{{rm{n}}}^{2}rangle determination. The dynamics of the strong nuclear force can be viewed through the precise picture of the neutron’s constituent distributions that result into the non-zero langle {r}_{{rm{n}}}^{2}rangle value.

New fit of timelike proton electromagnetic formfactors from e+e− colliders

The data on the proton form factors in the time-like region from the BaBar, BESIII and CMD-3 Collaborations are examined to have coherent pieces of information on the proton structure. Oscillations in the annihilation cross section, previously observed, are determined with better precision. The moduli of the individual form factors, determined for the first time, their ratio and the angular asymmetry of the annihilation reaction $e^+e^-\to\bar p p$ are discussed. Fiits of the available data on the cross section, the effective form factor, and the form factor ratio, allow to propose a description of the electric and magnetic time-like form factors from the threshold up to the highest momenta.

Measurements of Σ+ and Σ− time-like electromagnetic form factors for center-of-mass energies from 2.3864 to 3.0200 GeV

The Born cross sections of the e+e−→Σ+Σ¯− and e+e−→Σ−Σ¯+ processes are determined for center-of-mass energy from 2.3864 to 3.0200 GeV with the BESIII detector. The cross section lineshapes can be described properly by a pQCD function and the resulting ratio of effective form factors for the Σ+ and Σ− is consistent with 3. In addition, ratios of the Σ+ electric and magnetic form factors, |GE/GM|, are obtained at three center-of-mass energies through an analysis of the angular distributions. These measurements, which are studied for the first time in the off-resonance region, provide precision experimental input for understanding baryonic structure. The observed new features of the Σ± form factors require more theoretical discussions for the hyperons.

Electric quadrupole form factors of singly heavy baryons with spin 3/2

Abstract We study the electromagnetic form factors of the lowest-lying singly heavy baryons in a pion mean-field approach, which is also known as the SU(3) chiral quark-soliton model. In the limit of the heavy-quark mass, the dynamics inside a singly heavy baryon is governed by the $N_c-1$ valence quarks, while the heavy quark remains as a static one. In this framework, a singly heavy baryon is described by combining the $N_c-1$ soliton with the singly heavy quark. In the infinitely heavy-quark mass limit, we can compute the electric quadrupole form factors of the baryon sextet with spin 3/2, with the rotational $1/N_c$ and linear corrections of the explicit flavor SU(3) symmetry breaking taken into account. We find that the sea-quark contributions or the Dirac-sea level contributions dominate over the valence-quark contributions in the lower $Q^2$ region. We examined the effects of explicit flavor SU(3) symmetry breaking in detail. The numerical results are also compared with the recent data from the lattice calculation with the unphysical value of the pion mass considered, which was used in the lattice calculation.

Electric form factors of nucleons and charge deuteron form factor

Electric form factors of nucleons and charge deuteron form factor

New prediction of elastic scattering cross sections ratio Re+ e− based on phenomenological two-photon exchange corrections

The proton’s electric and magnetic form factors (FFs) and their ratio Rp = are fundamental and essential ingredients needed to parametrize the internal structure of the proton as well as many composite particles. However, the inconsistency in the results reported on these FFs and their ratio as measured by the Rosenbluth method and the polarization transfer method has led the community to believe that such a discrepancy is due to a systematic difference between the two methods. It was proposed that missing higher order radiative correction to the electron-proton elastic scattering cross section σR (ϵ, Q 2) and in particular two-photon exchange correction (TPE) should be applied in order to reconcile these measurements. The effect of TPE on electron-proton scattering observables was studied extensively in the last few years. However, the most direct method for measuring TPE contributions is the comparison of positron-proton and electron-proton elastic scattering cross sections ratio Re+ e− (ϵ, Q 2). In this proceedings, I present a new prediction of the ratio Re+ e− as determined using a new parametrization of TPE corrections to σR . I then compare my results to several previous phenomenological extractions, TPE hadronic calculations, and previous and recent direct measurements of Re+ e− .

Calculation magnetic dipole moments, electric quadrupole moments and form factors for some Ti isotopes

This paper presents calculations of the magnetic moments, the quadrupole moments, and the form factors of a number of titanium isotopes as determined using the shell model space. The calculations of the shell model have adopted the model space (MS) with core-polarization effects, which were included for two types of effective g factors and different effective charges. The wave functions are generated using the harmonic oscillator potential (HO) with size parameters b, which for these isotopes are calculated. The one body density matrices (OBDM) for these isotopes were obtained using the NuShellX@MSU code, which used an adopted fpd6 interaction and fp model space. Reasonable results are obtained that show the collapse of the magicity property at neutron number N = 28.