Magnetic Form Factor Research Articles

Magnetic phase transitions and spin density distribution in the molecular multiferroic system GaV4S8

We have carried out neutron diffraction and small angle neutron scattering measurements on a high quality single crystal of the cubic lacunar spinel multiferroic, GaV$_4$S$_8$, as a function of magnetic field and temperature to determine the magnetic properties for the single electron that is located on the tetrahedrally coordinated V$_4$ molecular unit. Our results are in good agreement with the structural transition at 44 K from cubic to rhombohedral symmetry where the system becomes a robust ferroelectric, while long range magnetic order develops below 13 K in the form of an incommensurate cycloidal magnetic structure, which can transform into a N\'eel-type skyrmion phase in a modest applied magnetic field. Below 5.9(3) K, the crystal enters a ferromagnetic phase, and we find the magnetic order parameter indicates a long range ordered ground state with an ordered moment of 0.23(1) ${\mu}_\mathrm{B}$ per V ion. Both polarized and unpolarized neutron data in the ferroelectric-paramagnetic phase have been measured to determine the magnetic form factor. The data are consistent with a model of the single spin being uniformly distributed across the V$_4$ molecular unit, rather than residing on the single apical V ion, in substantial agreement with the results of first-principles theory. In the magnetically ordered state, polarized neutron measurements are important since both the cycloidal and ferromagnetic order parameters are clearly coupled to the ferroelectricity, causing the structural peaks to be temperature and field dependent. For the ferromagnetic ground state, the spins are locked along the $[1,1,1]$ direction by a surprisingly large anisotropy.

Neutral-current neutrino scattering from the deuteron

Neutral-current neutrino scattering from the deuteron leading to proton-neutron final states is considered using an approach that incorporates relativistic dynamics and consequently provides robust modeling at relatively high energies and momenta. In this work the focus is placed on the fully exclusive reaction where both the proton and neutron in the final state are assumed to be detected. Accordingly, the incident neutrino energy, the neutrino scattering angle and the scattered neutrino's energy can all be reconstructed. It is shown that for specific choices of kinematics the reaction proceeds mainly via scattering from the proton, while for other choices of kinematics it proceeds mainly from the neutron. Specific asymmetries are introduced to focus on these attributes. Measurements in both regions have the potential to yield valuable information on the nucleon's electroweak form factors at momentum transfers up to a (GeV/c)$^2$. In particular, the cross sections are shown to be very sensitive to the isoscalar axial-vector form factor, and sensitive but less so to the magnetic strangeness form factor. Comparisons with other reactions, specifically charge-changing neutrino reactions and both parity-conserving and -violating electron scattering, have the potential to provide new ways to test the Standard Model.

Two-photon-exchange effects in ep→enπ+ and their corrections to separated cross sections σL,T,LT,TT at small −t

In this work, the two-photon-exchange (TPE) effects in $ep\rightarrow en\pi^+$ at small $-t$ are discussed within a hadronic model. Under the pion dominance approximation the TPE contribution to the amplitude can be described by a scalar function in the limit $m_e\rightarrow 0$. The TPE contributions to the amplitude and the unpolarized differential cross section are both estimated when only the elastic intermediate state is considered. We find that the TPE corrections to the unpolarized differential cross section are about from $-4\%$ to $-20\%$ at $Q^2=1$--$ 1.6$ GeV$^2$. After considering the TPE corrections to the experimental data sets of unpolarized differential cross section, we analyze the TPE corrections to the separated cross sections $\sigma_{\textrm{L,T,LT,TT}}$. We find that the TPE corrections (at $Q^2=1$--$1.6$ GeV$^2$) to $\sigma_{\textrm{L}}$ are about from $-10\%$ to $-30\%$, to $\sigma_{\textrm{T}}$ are about $20\%$, and to $\sigma_{\textrm{LT,TT}}$ are much larger. By these analysis, we conclude that the TPE contributions in $ep\rightarrow en\pi^+$ at small $-t$ are important to extract the separated cross sections $\sigma_{\textrm{L,T,LT,TT}}$ and the electromagnetic magnetic form factor of $\pi^+$ in the experimental analysis.

Elastic Magnetic Electron Scattering from odd-A Nuclei

Magnetic form factors from odd-A spherical and deformed nuclei corresponding to elastic electron scattering are calculated in the plane-wave Born approximation. The nuclear structure of the target is described within a deformed self-consistent mean-field calculation with effective interactions of Skyrme type and pairing correlations in the BCS approximation. We focus our attention to stable nuclei where experimental information is available. It is shown that the deformed formalism improves the agreement with experiment in deformed nuclei, while reproducing equally well spherical nuclei by taking properly the spherical limit of the deformed model. Effects of the collective rotation and nucleon-nucleon correlations are also studied. These results demonstrate the ability of the method to address electron scattering from unstable nuclei to be measured in future experiments on electron-ion beam colliders.

Sea quark contributions to nucleon electromagnetic form factors with the nonlocal chiral effective Lagrangian * * Supported by the National Natural Sciences Foundations of China (11475186), the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD” project by NSFC (11621131001)

The sea quark contributions to the nucleon electromagnetic form factors of the up, down and strange quarks are studied with the nonlocal chiral effective Lagrangian. Both octet and decuplet intermediate states are included in the one loop calculations. Compared with the strange quark form factors, although their signs are the same, the absolute value of the light quark form factors are much larger. For both the electric and magnetic form factors, the contribution of the d quark is larger than of the u quark. The current lattice simulations of the light sea quark form factors are in between our results for the u and dquarks.

Proton form factor ratio μpGEp/GMp from double spin asymmetry

The ratio of the electric and magnetic form factor of the proton, $\mu_p G_E^p/G_M^p$, has been measured for elastic electron-proton scattering with polarized beam and target up to four-momentum transfer squared, $Q^2=5.66$ (GeV/c)$^2$ using the double spin asymmetry for target spin orientation aligned nearly perpendicular to the beam momentum direction. This measurement of $\mu_p G_E^p/G_M^p$ agrees with the $Q^2$ dependence of previous recoil polarization data and reconfirms the discrepancy at high $Q^2$ between the Rosenbluth and the polarization-transfer method with a different measurement technique and systematic uncertainties uncorrelated to those of the recoil-polarization measurements. The form factor ratio at $Q^2$=2.06 (GeV/c)$^2$ has been measured as $\mu_p G_E^p/G_M^p = 0.720 \pm 0.176_{stat} \pm 0.039_{sys}$, which is in agreement with an earlier measurement with the polarized target technique at similar kinematics. The form factor ratio at $Q^2$=5.66 (GeV/c)$^2$ has been determined as $\mu_p G_E^p/G_M^p=0.244\pm0.353_{stat}\pm0.013_{sys}$, which represents the highest $Q^2$ reach with the double spin asymmetry with polarized target to date.

Nucleon strange electromagnetic form factors

The role of the strange quarks on the low-energy interactions of the proton can be probed through the strange electromagnetic form factors. Knowledge of these form factors provides essential input for parity-violating processes and contributes to the understanding of the sea quark dynamics. We determine the strange electromagnetic form factors of the nucleon within the lattice formulation of Quantum Chromodynamics using simulations that include light, strange and charm quarks in the sea all tuned to their physical mass values. We employ state-of-the-art techniques to accurately extract the form factors for values of the momentum transfer square up to 0.8~GeV$^2$. We find that both the electric and magnetic form factors are statistically non-zero. We obtain for the strange magnetic moment $\mu^s=-0.017(4)$, the strange magnetic radius $\langle r^2_M \rangle^s=-0.015(9)$~fm$^2$, and the strange charge radius $\langle r^2_E \rangle^s=-0.0048(6)$~fm$^2$.

Hyperon Structure and CP tests at BESIII

Hyperons are a powerful diagnostic tool that can shed light on some of the most intriguing questions in contemporary physics. Electromagnetic form factors (EMFFs) are currently the best way to study hyperon structure. In the time-like region the EMFFs can be complex with a relative phase. A non-zero phase polarizes the final state even when the initial state is unpolarized. A dedicated data sample collected by the BESIII experiment allowed for a first complete reconstruction of Λ in the time-like region. The ratio, R and relative phase between the electric and magnetic form factor, ΔΦ are measured to be 0.96±0.14(stat)±0.002(syst) and 37°±12°(stat)±6°(syst), respectively. In addition, the BESIII experiment has collected the world’s largest J/ψ data sample. Due to symmetric excellent detector conditions and low hadronic background, the experiment offers a clean environment for CP-violation tests using . That hyperons can be polarized allows for a simultaneous measurement of angular distributions of hyperons and antihyperons and to test CP symmetry directly. This has been done for the process recently measured by the BESIII experiment. The experimental results showed that the asymmetry decay parameter α(Λ → ππ−) = +0.750±0.009±0.004, is nearly twenty percent larger compared to the old PDG tabulated value. The test on CP symmetry, is the most sensitive test for Λ CP-violation. Preliminary results are presented for the process . The asymmetry decay parameter and −0.015 ± 0.037 ± 0.008 are both measured for the first time.

Measurement of neutron and proton analyzing powers on C, CH, $$CH_2$$ and Cu targets in the momentum region 3–4.2 GeV/c

The analyzing powers for proton elastic scattering ($\vec p A\to pX$) and neutron charge exchange ($\vec n A\to p X$) reactions on nuclei have been measured on $ C$, $CH$, $CH_2$ and $Cu$ targets at incident neutron momenta 3.0 - 4.2 GeV/c by detecting one charged particle in forward direction. The polarized neutron measurements are the first of their kind. The experiment was performed using the Nuclotron accelerator in JINR Dubna, where polarized neutrons and protons were obtained from breakup of a polarized deuteron beam which has a maximum momentum of 13 GeV/c. The polarimeter ALPOM2 was used to obtain the analyzing power dependence on the transverse momentum of the final-state nucleon. These data have been used to estimate the figure of merit of a proposed experiment at Jefferson Laboratory to measure the recoiling neutron polarization in the quasi-elastic $^2H(\vec e,e'\vec n)$ reaction, which yields information on the charge and magnetic elastic form factors of the neutron.

Results of Measurements of the Analyzing Powers for Polarized Neutrons on C, CH2 and Cu Targets for Momenta Between 3 and 4.2 GeV/c

The analyzing powers for neutron charge exchange nA → pX reactions on nuclei have been measured on C, CH2 and Cu targets at incident neutron momenta 3.0 - 4.2 GeV/c by detecting one charged particle in forward direction. The polarized neutron measurements are the first of their kind. The experiment was performed using the Nuclotron accelerator in JINR Dubna, where polarized neutrons and protons were obtained from breakup of a polarized deuteron beam which has a maximum momentum of 13 GeV/c. The polarimeter ALPOM2 was used to obtain the analyzing power dependence on the transverse momentum of the final-state nucleon. These data have been used to estimate the figure of merit of a proposed experiment at Jefferson Laboratory to measure the recoiling neutron polarization in the quasi-elastic 2H(e, e′n) reaction, which yields information on the charge and magnetic elastic form factors of the neutron.

Nucléon Electromagnetic Form Factors in a constituent-quark model

The electromagnetic form factors of the nucléon are calculated in an extended chiral constituent-quark model where the effective interaction is described by the exchange of pseudoscalar and vector mesons belonging to the pseudoscalar and pseudovector octet, respectively, and a scalar meson . Two-body current-density operators, constructed consistently with the extended model Hamiltonian in order to preserve gauge invariance and current conservation, are found to give a significant contribution to the nucléon magnetic form factors and improve the estimates of the nucleon magnetic moments.

Improved extraction of the up- and down-quark contributions to the nucleon electromagnetic form factors

The nucleon (proton and neutron) electromagnetic form factors (FFs) are fundamental quantities in nuclear and elementary particle physics as they are essential ingredients needed to parametrize the internal structure of composite particles. The spatial distribution of charge and magnetization within the nucleon is encoded in the electric and magnetic FFs. These FFs have been extensively and precisely measured using elastic electron scattering. In addition, the combination of the proton and neutron FFs allows for the separation of the up- and down-quark contributions to the nucleon FFs. In this work, we improve on and extend to low- and high-Q2 values our original analysis and extract the up- and down-quark contributions to the nucleon electromagnetic FFs using worldwide data. In particular, we emphasize new precise data which cover the low-Q2 region which is sensitive to the large-scale structure of the nucleon. We compare our results to previous extractions and several recent theoretical calculations and models.

The next-to-leading order corrections to ρ meson electromagnetic form factors in the kT factorization approach

In this paper we calculate the next-to-leading-order (NLO) corrections to ρ-meson electromagnetic form factors by employing the kT factorization approach. We find that the NLO correction to Fi(Q2)(i=LT,TL) is around 30% of the leading-order (LO) contribution in the region Q2>2GeV2. The NLO correction to FLL(Q2) is close to 20% of the LO one in the region Q2>3GeV2. The NLO radiative corrections to the electric, magnetic, and quadruple form factors Fj(Q2)(j=1,2,3) are sizeable in magnitude and agree with those from other approaches.

Complete Measurement of the Λ Electromagnetic Form Factors

The exclusive process e^{+}e^{-}→ΛΛ[over ¯], with Λ→pπ^{-} and Λ[over ¯]→p[over ¯]π^{+}, has been studied at sqrt[s]=2.396 GeV for measurement of the timelike Λ electric and magnetic form factors, G_{E} and G_{M}. A data sample, corresponding to an integrated luminosity of 66.9 pb^{-1}, was collected with the BESIII detector for this purpose. A multidimensional analysis with a complete decomposition of the spin structure of the reaction enables a determination of the modulus of the ratio R=|G_{E}/G_{M}| and, for the first time for any baryon, the relative phase ΔΦ=Φ_{E}-Φ_{M}. The resulting values are R=0.96±0.14(stat)±0.02(syst) and ΔΦ=37°±12°(stat)±6°(syst), respectively. These are obtained using the recently established and most precise value of the asymmetry parameter α_{Λ}=0.750±0.010 measured by BESIII. In addition, the cross section is measured with unprecedented precision to be σ=118.7±5.3(stat)±5.1(syst) pb, which corresponds to an effective form factor of |G|=0.123±0.003(stat)±0.003(syst). The contribution from two-photon exchange is found to be negligible. Our result enables the first complete determination of baryon timelike electromagnetic form factors.

Elastic magnetic electron scattering from deformed nuclei

Magnetic form factors corresponding to elastic electron scattering from odd-A nuclei are presented. The calculations are carried out in plane-wave Born approximation. The one-body properties are obtained in a deformed self-consistent mean-field calculation based on a Skyrme HF+BCS method. Collective effects are also included in the cranking approximation. Results on several stable nuclei are compared with the available experimental information. It is shown that a deformed formalism improves the agreement with experiment in deformed nuclei, while reproducing equally well spherical nuclei by taking properly the spherical limit of the deformed model and the effect of nucleon-nucleon correlations. Thus, the capability of the model to describe magnetic form factors is demonstrated. This opens the door to explore also unstable nuclei of particular interest that could be measured in future experiments on electron-radioactive beam colliders.

Local chiral interactions and magnetic structure of few-nucleon systems

The magnetic form factors of $^2$H, $^3$H, and $^3$He, deuteron photodisintegration cross sections at low energies, and deuteron threshold electrodisintegration cross sections at backward angles in a wide range of momentum transfers, are calculated with the chiral two-nucleon (and three-nucleon) interactions including $\Delta$ intermediate states that have recently been constructed in configuration space. The $A\,$=$\,$3 wave functions are obtained from hyperspherical-harmonics solutions of the Schr\"odinger equation. The electromagnetic current includes one- and two-body terms, the latter induced by one- and two-pion exchange (OPE and TPE, respectively) mechanisms and contact interactions. The contributions associated with $\Delta$ intermediate states are only retained at the OPE level, and are neglected in TPE loop (tree-level) corrections to two-body (three-body) current operators. Expressions for these currents are derived and regularized in configuration space for consistency with the interactions. The low-energy constants that enter the contact few-nucleon systems. The predicted form factors and deuteron electrodisintegration cross section are in excellent agreement with experiment for momentum transfers up to 2--3 fm$^{-1}$. However, the experimental values for the deuteron photodisintegration cross section are consistently underestimated by theory, unless use is made of the Siegert form of the electric dipole transition operator. A complete analysis of the results is provided, including the clarification of the origin of the aforementioned discrepancy.

Mag2Pol: a program for the analysis of spherical neutron polarimetry, flipping ratio and integrated intensity data

Mag2Pol is a graphical user interface program which is devoted to the treatment of data from polarized neutron diffractometers with spherical polarization analysis. Nuclear and magnetic structure models can be introduced using space-group symbols and individual symmetry operators, respectively, and viewed in an OpenGL widget. The program calculates nuclear/magnetic structure factors, flipping ratios and polarization matrices for magnetic Bragg reflections, taking into account structural twins and magnetic domains. Spherical neutron polarimetry data can be analyzed by refining a magnetic structure model including magnetic domain populations in a least-squares fit and can also be correlated with an integrated intensity data set in a joint refinement. Further features are the simultaneous refinement of nuclear and magnetic structures with integrated intensity data and the analysis of flipping ratios either with tabulated magnetic form factors or using a multipole expansion of the magnetization density.

Nucleon form factors and root-mean-square radii on a (10.8 fm)4 lattice at the physical point

We present the nucleon form factors and root-mean-square (RMS) radii measured on a ${(10.8\text{ }\text{ }\mathrm{fm})}^{4}$ lattice at the physical point. We compute the form factors at small momentum transfer region in ${q}^{2}\ensuremath{\le}0.102\text{ }\text{ }{\mathrm{GeV}}^{2}$ with the standard plateau method choosing four source-sink separation times ${t}_{\mathrm{sep}}$ from 0.84 to 1.35 fm to examine the possible excited state contamination. We obtain the electric and magnetic form factors and their RMS radii for not only the isovector channel but also the proton and neutron ones without the disconnected diagram. We also obtain the axial-vector coupling and the axial radius from the axial-vector form factor. We find that these three form factors do not show large ${t}_{\mathrm{sep}}$ dependence in our lattice setup, and those RMS radii are consistent with the experimental values. On the other hand, the induced pseudoscalar and pseudoscalar form factors show the clear effects of the excited state contamination, which affect the generalized Goldberger-Treiman relation.

Λ hyperon spin polarization and CP tests at BESIII

In these proceedings two preliminary results from the BESIII collaboration on polarized Λ and $\bar \Lambda$ are reported. Both results are first observations and concern the resonant and non-resonant processes ${e^ - }{e^ + } \to J/\psi \to \Lambda \bar \Lambda$ and ${e^ - }{e^ + } \to {\gamma ^\ast} \to \Lambda \bar \Lambda$ at $\sqrt s = 2.396\,{\rm{GeV}}$, respectively. For $J/\psi \to \Lambda \bar \Lambda$ the relative phase between the electric and magnetic form factors, ΔΦ, has for the first time been determined, $\Delta \Phi = 42.4{(6)_{{\rm{stat}}}}(5)_{_{{\rm{syst}}}}^^\circ$. That $\Delta \Phi \ne 0$ allows for a simultaneous measurement also of the asymmetry decay parameters $\Lambda \to p{\pi ^ - }\,({\alpha _ - })$, $\bar \Lambda \to \bar p{\pi ^ + }\,({\alpha _ + })$ and $\bar \Lambda \to \bar n{\pi ^0}\,({\bar \alpha _0})$. The measured value of ${\alpha _ - } = 0.750 \pm 0.009 \pm 0.004$ differs by 17(3)% from the PDG value. The simultaneous measurement for the asymmetry parameters allows for the most precise test of CP violation conducted for Λ decays, ACP = −0.006(12)stat(7)syst. The reaction ${e^ - }{e^ + } \to \Lambda \bar \Lambda$ at $\sqrt s = 2.396\,{\rm{GeV}}$ is the first complete measurement of the time-like electric (GE) and magnetic (GM) form factor of any baryon as also the ratio R = |(GE/(GM)| and ΔΦ have been determined: R = 0.96(14)(12) and $\Delta \Phi = 37{(12)_{{\rm{stat}}}}(6)_{{\rm{stat}}}^\circ$. The obtained cross-section and effective form factor are σ = 119.0(53)stat(51)syst pb and |G| = 0.123(3)stat(3)syst, respectively.

Calculations of the deuteron form factors

On the received coefficients of the analytical forms for deuteron wave function in coordinate representation in form r^(l+1)*exp(-A*r) for the modern realistic nucleon-nucleon potentials NijmI, NijmII, Nijm93, Reid93 and Argonne v18 are calculated charge GC(p), quadrupole GQ(p) and magnetic GM(p) deuteron form factors. An original dipole fit for proton and neutron isoscalar electric and magnetic form factors is used for calculations. Theoretical calculations of values of the deuteron form factor are compared with their experimental data of world collaborations (Bates, BLAST, Bonn, JLab, Mainz, Naval Research Lab, NIKHEF, Orsay, Saclay, SLAC, Stanford, VEPP3 and VEPP4) and reviews (Abbott, Boden, Garcon and Karpius). The change of the sign of form factors is in the pulse regions at 4.7-4.9 fm-1 for GC; at 12.8-14.7 fm-1 for GQ; at 6.3-8.1 and 11.4-12.2 fm-1 for GM. The theoretical values for the form factors GQ(0) and GM(0) were calculated at the boundary condition for the momentum at p2=0. Calculated positions of the zero for deuteron form factors are compared with values for other potential models. The peculiarities of parametrizations of deuteron form factors for theoretical approaches and fits of theoretical calculations to experimental values, which are described in the cited literature, are analyzed. Formulas for spherical and quadrupole form factors are writed, which are expressed in terms of the coefficients for the indicated deuteron wave function. At large values of momentum the asymptotics of the deuteron form factors are determined by the coefficients of the analytical forms for deuteron wave function, nucleon isoscalar form factors and the order of momentum in the denominator. The further use of deuteron form factors for obtaining polarization observables in processes involving deuteron as a projectile is discussed.