Charge Form Factor Research Articles

Maximum entropy method for valence quark distributions in exotic hadrons: a study of the Zc(3900) case

In this study we demonstrate the application of the maximum entropy method (MEM) to determine the valence quark distribution of exotic hadrons. Our investigation yields three key findings. Firstly, we observe a significant shift towards smaller Bjorken scale x in the peak position of the valence quark distribution for hadrons with an increasing number of valence quarks, consistent with previous results by Kawamura and Kumano. Secondly, assuming that the Zc(3900) initially consists of four valence quarks, we employ MEM to determine its initial valence quark distribution, estimating a radius of rc=1.276 fm at an extremely low resolution scale Q2. Furthermore, we identify a notable discrepancy between our computed charge form factor Gc(q) at leading order and the outcomes of hadron molecular state calculations. We propose that this form factor can be extracted from the QCD counting rule cross-section, which is grounded in generalized distribution amplitudes (GDA) linked to the multi-quark states.

Quark counting, Drell-Yan West, and the pion wave function

The relation between the pion's quark distribution function, q(x), its light-front wave function, and the elastic charge form factor, F(Δ2), is explored. The square of the leading-twist pion wave function at a special probe scale, ζH, is determined using models and Poincaré covariance from realistic results for q(x). This wave function is then used to compute form factors with the result that the Drell-Yan-West and quark counting relationships are not satisfied. A new relationship between q(x) and F(Δ2) is proposed. Published by the American Physical Society 2024

Limits on an improved action for contact effective field theory in two-body systems

We consider a possible resummation of subleading effects in two-body systems with a large scattering length as described by a short-range effective field theory (EFT). In particular, we investigate the consequences of a resummation of part of the range corrections. Explicit calculations of the two-body phase shifts and charge form factor indicate that, except for extreme choices, resummations do not alter the convergence of the EFT expansion and are often beneficial at the lowest orders. We have considered the expansion when the regulator cutoff is removed as well as when it is finite, and find that the cutoff is not an important factor for resummations. Our results connect with other works where the partial resummation is induced by potentials with finite cutoffs or interaction ranges.

Realistic Shell Model Interpretation for the Nuclear Structure of Some 1f-2p Shell Nuclei

The charge density distributions (CDD), charge form factors, occupation numbers of states, and root mean square charge (rmsch) radii, have been calculated for several 1f-2p shell-model nuclei, such as 48Ti, 50Ti, 50Cr, 52Cr, 58Ni, and 60Ni nuclei using the wave functions for a single particle in a harmonic oscillator (HO) potential. The size parameter b of the HO potential is considered as a free parameter chosen to reproduce the rmsch radii. The nuclear real states occupation numbers have been assumed to differ from the simple shell model predictions. Introducing extra parameters such as and to characterize the disparity between the occupation numbers of real states and those anticipated by the simple shell model, leads to achieving a high level of agreement between the calculations and experimental data. Obtained results lead to the conclusion that the proposed parameters and , bring the calculated CDD and form factors closer to the experimental data along with all values of radius r and momentum transfer q, respectively.

Electron Scattering from Stable and Exotic Li Isotopes

The nuclear shell model was used to investigate the bulk properties of lithium isotopes (6,7,8,9,11Li), i.e., the ground state density distributions and C0 and C2 components of charge form factors. The theoretical treatment was based on supposing that the Harmonic-oscillator (HO) potential governs the core nucleons while the valence nucleon(s) move through Hulthen potential. Such assumptions were applied for both stable and exotic lithium isotopes. The HO size parameters ( and ), the core radii ( ) and the attenuation parameters ( and ) were fixed to recreate the available empirical size radii for lithium isotopes under study.

Elastic neutrino scattering on nucleons and neutrino electromagnetic properties

We study the electromagnetic contribution to elastic neutrino-nucleon 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 the effects of the neutrino magnetic moment on elastic neutrino-nucleon scattering and how they can be disentangled from those of the strange form factors contributions to the nucleon’s weak neutral current.

Ground State Structure of Helium and Phosphorus Isotopes using the Radial Wave Functions of Harmonic-Oscillator and Hulthen Potentials

The ground state density distributions and electron scattering Coulomb form factors of Helium (4,6,8He) and Phosphorate (27,31P) isotopes are investigated in the framework of nuclear shell model. For stable (4He) and (31P) nuclei, the core and valence parts are studied through Harmonic-oscillator (HO) and Hulthen potentials. Correspondingly, for exotic (6,8He) and (27P) nuclei, the HO potential is applied to the core parts only, while the Hulthen potential is applied to valence parts. The parameters for HO and Hulthen are chosen to reproduce the available experimental size radii for all nuclei under study. Finally, the CO component of electron scattering charge form factors are also investigated. Unfortunately, there is no analytic solution to the Hulthen potential except for the states which are harnessed to the current calculation.

Hadronic structure on the light front. VI. Generalized parton distributions of unpolarized hadrons

We discuss the generalized parton distributions (GPDs) for unpolarized hadrons, as a continuation of our recent work on hadronic structure on the light front. We analyze the unpolarized GPDs for the light nucleon and delta, as well as generic mesons, using the lowest Fock states. We use these GPDs to reconstruct the charge and gravitational form factors, and discuss their relative sizes. The results are also compared to reported QCD lattice results.

Cross Sections for Coherent Elastic and Inelastic Neutrino-Nucleus Scattering

The prospects of extracting new physics signals in coherent elastic neutrino–nucleus scattering (CEνNS) processes are limited by the precision with which the underlying nuclear structure physics, embedded in the weak nuclear form factor, is known. We present calculations of charge and weak nuclear form factors and CEνNS cross sections on 12C, 16O, 40Ar, 56Fe and 208Pb nuclei. We obtain the proton and neutron densities, and charge and weak form factors by solving Hartree–Fock (HF) equations with a Skyrme (SkE2) nuclear potential. We validate our approach by comparing 208Pb and 40Ar charge form factor predictions with available elastic electron scattering data. Since CEνNS experiments at stopped-pion sources are also well suited to measure inelastic charged–current and neutral–current neutrino–nucleus cross sections, we also present calculations for these processes, incorporating a continuum Random Phase Approximation (CRPA) description on top of the HF–SkE2 picture of the nucleus. Providing both coherent as well as inelastic cross sections in a consistent framework, we aim at obtaining a reliable and detailed comparison of the strength of these processes in the energy region below 100 MeV. Furthermore, we attempt to gauge the level of theoretical uncertainty pertaining to the description of the 40Ar form factor and CEνNS cross sections by comparing relative differences between recent microscopic nuclear theory and widely-used phenomenological form factor predictions. Future precision measurements of CEνNS will potentially help in constraining these nuclear structure details that will in turn improve prospects of extracting new physics.

Properties of Pb208 predicted from the relativistic equation of state in the full Dirac space

Relativistic Brueckner-Hartree-Fock (RBHF) theory in the full Dirac space allows one to determine uniquely the momentum dependence of scalar and vector components of the single-particle potentials. In order to extend this new method from nuclear matter to finite nuclei, as a first step, properties of $^{208}\mathrm{Pb}$ are explored by using the microscopic equation of state for asymmetric nuclear matter and a liquid droplet model. The neutron and proton density distributions, the binding energies, the neutron and proton radii, and the neutron skin thickness in $^{208}\mathrm{Pb}$ are calculated. In order to further compare the charge densities predicted from the RBHF theory in the full Dirac space with the experimental charge densities, the differential cross sections and the electric charge form factors in the elastic electron-nucleus scattering are obtained by using the phase-shift analysis method. The results from the RBHF theory are in good agreement with the experimental data. In addition, the uncertainty arising from variations of the surface term parameter ${f}_{0}$ in the liquid droplet model is also discussed.

Search for Damped Oscillating Structures from Charged Pion Electromagnetic Form Factor Data

The damped oscillating structures recently revealed by a three parametric formula from the proton “effective” form factor data extracted of the measured total cross section σtotbare(e+e−→pp¯) still seem to have an unknown origin. The conjectures of their direct manifestation of the quark-gluon structure of the proton indicate that they are not specific only of the proton and neutron, but they have to be one’s own, similar to other hadrons. Therefore, the oscillatory structures from the charged pion electromagnetic form factor timelike data, extracted of the process e+e−→π+π− are investigated by using the same procedure as in the case of the proton. The analysis shows the appearance of the oscillating structures in the description of the charged pion electromagnetic form factor timelike data by three parametric formula with a rather large value of χ2/ndf, while the description of the data by the physically well-founded Unitary and Analytic model has not revealed any damped oscillating structures. From the obtained result on the most simple object of strong interactions, one can conclude that damped oscillating structures received from the “effective” proton form factor data are probably generated by a utilization of the improper three parametric formula which does not describe these data with sufficient precision.

Features of determining the charge deuteron form factor G C (p)

Abstract The main features of obtaining the asymptotic behavior of the charge deuteron form factor G C (p) at large values of the momentum have been analyzed. The asymptotic behavior of the charge form factor G C (p) was determined by taking into account the analytic form of deuteron wave function in the coordinate representation and the original dipole fit for the nucleon form factors. Asymptotic values of charge form factor G C (p) has been obtained for the nucleon-nucleon phenomenological potential Reid93 and compared with the calculations for eight different nucleon form factors models and their approximations. In the wide range up to 10.5 fm−1 of transmitted momentum, the basic forms of the asymptotic behavior of the charge deuteron form factor have been demonstrated and compared with the experimental data of the leading modern collaborations and reviews. The secondary maximum for G C (p) for the potential Reid93 will be located at the momentum range at 5.45–5.70 fm−1. The calculated position of the zero p 0 is located at the momentum interval 4.60–4.65 fm−1. The position of the zero for one potential coincides regardless of the choice of models and approximations for the nucleon form factors. As the analysis shows, the value of the mean-square charge radius of the deuteron takes the value of r ch = 2.02876–2.14695 fm depending on the chosen deuteron wave function and nucleon form factors.

Properties of Ground-State of 17,19,20,24,26F using the Wave Functions of Harmonic-Oscillator and Spherical Hankel Functions

The nuclear size radii, density distributions and elastic electron scattering charge form factors for Fluorine isotopes (17,19,20,24,26F) were studied using the radial wave functions (WF) of harmonic-oscillator (HO) potential and free mean field described by spherical Hankel functions (SHF) for the core and the valence parts, respectively for all aforementioned isotopes. The parameters for HO potential (size parameter ) and SHF were chosen to regenerate the available experimental size radii. It was found that using spherical Hankel functions in our work improved the calculated results quantities in comparison with empirical data.

Imprints of α clustering in the density profiles of C12 and O16

The $^{4}$He nucleus is a well bound and highly correlated four-nucleon system that is also found in form of $\alpha$-clusters as substructure in nuclear many-body systems. The standard single-particle shell model cannot represent these four-body correlations. It is highly desirable to find a simple way to identify and distinguish these fundamental structures without large-scale computations. In this paper, we investigate with intrinsic Slater determinants as trial states in how far these two competing pictures prevail in the ground states of $^{12}$C and $^{16}$O. The trial states can describe both the $j$-$j$ coupling shell-model and $\alpha$-cluster configurations in a unified way. One-body density distributions of the trial states are calculated and compared to elastic scattering cross section data. The parameters of the trial state are chosen to reproduce the experimental charge radii. A well developed cluster structure is characterized by an enhancement of the differential elastic scattering cross sections, as well as the elastic charge form factors around the first peak positions. The density profiles of the internal regions can also be probed at higher momentum transfer regions beyond the second minimum. With these trial states one can visualize the competition between cluster and shell structure in an intuitive and simple way.

Timelike electromagnetic kaon form factor

We compute the electromagnetic charged kaon form factor in the timelike region by employing a Poincar\'e covariant formalism of the Bethe-Salpeter equation to study quark-antiquark bound states in conjunction with the Schwinger-Dyson equation for the quark propagator. Following a recent kindred calculation of the timelike electromagnetic pion form factor, we include the most relevant intermediate composite particles permitted by their quantum numbers in the interaction kernel to allow for a decay mechanism for the resonances involved. This term augments the usual gluon mediated interaction between quarks. For a sufficiently low energy timelike probing photon, the electromagnetic form factor is saturated by the $\ensuremath{\rho}(770)$ and $\ensuremath{\phi}(1020)$ resonances. We assume $SU(2)$ isospin symmetry throughout. Our results for the absolute value squared of the electromagnetic form factor agree qualitatively rather well and quantitatively moderately so with available experimental data.

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

We present a study of the two-photon-exchange (2upgamma -exchange) corrections to the S-levels in muonic (mu D) and ordinary (D) deuterium within the pionless effective field theory (EFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the EFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon–nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen–deuterium isotope shift. We find the elastic 2upgamma -exchange contribution in mu D larger by several standard deviations than obtained in other recent calculations. This discrepancy ameliorates the mismatch between theory and experiment on the size of 2upgamma -exchange effects, and is attributed to the properties of the deuteron elastic charge form factor parametrisation used to evaluate the elastic contribution. We identify a correlation between the deuteron charge and Friar radii, which can help one to judge how well a form factor parametrisation describes the low-virtuality properties of the deuteron. We also evaluate the higher-order 2upgamma -exchange contributions in mu D, generated by the single-nucleon structure and expected to be the most important terms beyond N3LO. The uncertainty of the theoretical result is dominated by the truncation of the EFT series and is quantified using a Bayesian approach. The resulting extractions of the deuteron charge radius from the mu D Lamb shift, the 2S{-}1S transition in D, and the 2S{-}1S hydrogen–deuterium isotope shift, with the respective 2upgamma -exchange effects evaluated in a unified EFT approach, are in perfect agreement.

A reassessment of nuclear effects in muonic deuterium using pionless effective field theory at N3LO

We provide a systematic assessment of the order-α5 nuclear contributions to the Lamb shift of muonic deuterium, including the accompanying radiative corrections due to vacuum polarisation, up to next-to-next-to-next-to-leading order (N3LO) within the pionless effective field theory (π̸EFT). We also evaluate higher-order corrections due to the single-nucleon structure, which are expected to be the most important corrections beyond N3LO. We find a correlation between the deuteron charge and Friar radii, which can be useful to judge the quality of charge form factor parametrisations. We refine the theoretical description of the 2γ-exchange contribution, especially in the elastic contribution and the radiative corrections, ameliorating the original discrepancy between theory and experiment in the size of 2γ-exchange effects. Based on the experimental Lamb shift of muonic deuterium, we obtain the deuteron charge radius, rd(μD)=2.12763(13)exp(77)theory fm, which is consistent with (but less precise than) the value obtained by combining the H-D isotope shift with the muonic-hydrogen Lamb shift. The theory uncertainty is evaluated using a Bayesian procedure and is dominated by the truncation of the π̸EFT series.

The ground state properties of some exotic nuclei studied by the two-body model

The ground state properties including the density distributions of the neutrons, protons and matter as well as the corresponding root mean square (rms) radii of proton-rich halo candidates 8B, [Formula: see text]N, [Formula: see text]Al and [Formula: see text]P have been studied by the single particle Bear–Hodgson (BH) wave functions with the two-body model of [Formula: see text]. It is found that the rms radii of these proton-rich nuclei are reproduced well by this model and the radial wave functions describe the long tail of the proton and matter density distributions. These results indicate that this model achieves a suitable description of the possible halo structure. The plane wave Born approximation (PWBA) has been used to compute the elastic charge form factors.

Perturbative calculations of deuteron form factors

We calculate the deuteron charge, electric quadrupole, and magnetic form factors up to next-to-next-to-leading order in chiral effective field theory, treating subleading corrections, especially that of chiral nuclear forces, in perturbation theory. We examine the power counting based on naive dimensional analysis by investigating the ultraviolet cutoff variation of these form factors. We find that the N${}^2$LO magnetic form factor shows significant cutoff dependence, suggesting the contact current operator responsible be enhanced. After promotion to N${}^2$LO, it indeed renormalizes the magnetic form factor. This is in agreement with a previous work based on renormalization-group analysis. For the charge and quadrupole moments, perturbative calculation allows us to study how they scale with multiple low-energy parameters such as the pion mass, deuteron binding momentum, and momentum transfer.

ρ meson generalized parton distributions in the Nambu–Jona-Lasinio model

In this paper, both the unpolarized and the polarized $\rho$ meson generalized parton distributions are investigated in the framework of the Nambu--Jona-Lasinio model using proper time regularization scheme. The symmetry properties of $\rho$ meson generalized parton distributions are checked. The three independent distribution functions in deep inelastic scattering, $F_1(x)$, $b_1(x)$ and $g_1(x)$, and the Sachs-like charge, magnetic, and quadruple form factors $G_C(t)$, $G_M(t)$ and $G_Q(t)$, which are the first Mellin moments of unpolarized generalized parton distributions are obtained. In addition, the $u$ quark axial vector form factors $\tilde{F}_1^u(t)$ and $\tilde{F}_2^u(t)$ related to the axial currents from the polarized generalized parton distributions are studied. The impact parameter dependent parton distribution functions, which are the two-dimensional Fourier transform of generalized parton distributions are studied, too. The obtained $\rho$ meson generalized parton distributions satisfy the required properties well.