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DOE OSTI2024

Novel Measurement of the Neutron Magnetic Form Factor from A=3 Mirror Nuclei

The electromagnetic form factors of the proton and neutron encode information on the spatial structure of their charge and magnetization distributions. While measurements of the proton are relatively straightforward, the lack of a free neutron target makes measurements of the neutron's electromagnetic structure more challenging and more sensitive to experimental or model-dependent uncertainties. Various experiments have attempted to extract the neutron form factors from scattering from the neutron in deuterium, with different techniques providing different, and sometimes large, systematic uncertainties. We present results from a novel measurement of the neutron magnetic form factor using quasielastic scattering from the mirror nuclei 3 H and 3 He, where the nuclear effects are larger than for deuterium but expected to largely cancel in the cross-section ratios. We extracted values of the neutron magnetic form factor for low-to-modest momentum transfer, 0.6 < Q 2 < 2.9 GeV 2 , where existing measurements give inconsistent results. The precision and Q 2 range of these data allow for a better understanding of the current world’s data and suggest a path toward further improvement of our overall understanding of the neutron’s magnetic form factor.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Unified model of nucleon elastic form factors and implications for neutrino-oscillation experiments

Precise knowledge of the nucleon’s axial-current form factors is crucial for modeling GeV-scale neutrino-nucleus interactions. Unfortunately, the axial form factor remains insufficiently constrained to meet the precision requirements of upcoming long-baseline neutrino-oscillation experiments. This work studies the nucleon’s axial and vector form factors using the light-front approach to build a quark-diquark model of the nucleon with an explicit pion cloud. The light-front wave functions in both the quark and pion-baryon Fock spaces are first calibrated to existing experimental information on the nucleon’s electromagnetic form factors and then used to predict the axial form factor. The resulting squared charge radius of the axial pseudovector form factor is predicted to be $r$$^{2}_{A}$ = 0.29 ± 0.03 fm 2 , where the small error accounts for the model’s parametric uncertainty. We use our form factor results to explore the (quasi)elastic scattering of neutrinos by (nuclei)nucleons, with the result that the widely implemented dipole ansatz is an inadequate approximation of the full form factor for modeling both processes. Here, the approximation leads to a 5%–10% overestimation of the total cross section, depending on the (anti)neutrino energy. We project overestimations of similar size in the flux-averaged cross sections for the upcoming DUNE long-baseline neutrino-oscillation experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Calculation of the Nucleon Axial Form Factor Using Staggered Lattice QCD

The nucleon axial form factor is a dominant contribution to errors in neutrino oscillation studies. Lattice QCD calculations can help control theory errors by providing first-principles information on nucleon form factors. In these proceedings, we present preliminary results on a blinded calculation of $g_A$ and the axial form factor using HISQ staggered baryons with 2+1+1 flavors of sea quarks. Calculations are done using physical light quark masses and are absolutely normalized. We discuss fitting form factor data with the model-independent $z$ expansion parametrization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

The three-point form factor of Tr ϕ 3 to six loops

We study the three-point form factor of the length-three half-BPS operator (Tr ϕ 3 ) in planar $\mathcal{N}$ = 4 Super-Yang-Mills theory, using analyticity and integrability methods. We find that the functions describing the form factor in perturbation theory live in the same restrictive space of multiple polylogarithms as the one describing the form factor of the stress-tensor operator (Tr ϕ 2 ). Furthermore, we find that the leading-order data in the collinear limit provided by the form factor operator product expansion (FFOPE) is enough to fix the form factor uniquely, at least through six loops. We perform various tests of our results using the subleading FFOPE corrections. We also analyze the form factor in the Regge limit where two Mandelstam invariants are large; we obtain a compact representation for the form factor in this limit which is valid to all orders in the coupling.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Analysis of nucleon electromagnetic form factors from light-front holographic QCD: The spacelike region

We present a comprehensive analysis of the space-like nucleon electromagnetic form factors and their flavor decomposition within the framework of light-front holographic QCD. We show that the inclusion of the higher Fock components $|{qqqq\bar{q}}$ has a significant effect on the spin-flip elastic Pauli form factor and almost zero effect on the spin-conserving Dirac form factor. We present light-front holographic QCD results for the proton and neutron form factors at any momentum transfer range, including asymptotic predictions, and show that our results agree with the available experimental data with high accuracy. In order to correctly describe the Pauli form factor we need an admixture of a five quark state of about 30$\%$ in the proton and about 40$\%$ in the neutron. We also extract the nucleon charge and magnetic radii and perform a flavor decomposition of the nucleon electromagnetic form factors. The free parameters needed to describe the experimental nucleon form factors are very few: two parameters for the probabilities of higher Fock states for the spin-flip form factor and a phenomenological parameter $r$, required to account for possible SU(6) spin-flavor symmetry breaking effects in the neutron, whereas the Pauli form factors are normalized to the experimental values of the anomalous magnetic moments. As a result, the covariant spin structure for the Dirac and Pauli nucleon form factors prescribed by AdS$_5$ semiclassical gravity incorporates the correct twist scaling behavior from hard scattering and also leads to vector dominance at low energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Bootstrapping a stress-tensor form factor through eight loops

We bootstrap the three-point form factor of the chiral stress-tensor multiplet in planar $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory at six, seven, and eight loops, using boundary data from the form factor operator product expansion. This may represent the highest perturbative order to which multi-variate quantities in a unitary four-dimensional quantum field theory have been computed. In computing this form factor, we observe and employ new restrictions on pairs and triples of adjacent letters in the symbol. We provide details about the function space required to describe the form factor through eight loops. Plotting the results on various lines provides striking numerical evidence for a finite radius of convergence of perturbation theory. By the principle of maximal transcendentality, our results are expected to give the highest weight part of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD through eight loops. These results were also recently used to discover a new antipodal duality between this form factor and a six-point amplitude in the same theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Extraction of the neutron electric form factor from measurements of inclusive double spin asymmetries

Background: Measurements of the neutron charge form factor, G$n\atop{E}$, are challenging because the neutron has no net charge. Additionally, measurements of the neutron form factors must use nuclear targets which require accurately accounting for nuclear effects. Extracting G$n\atop{E}$ with different targets and techniques provides an important test of our handling of these effects. Purpose: The goal of the measurement was to use an inclusive asymmetry measurement technique to extract the neutron charge form factor at a four-momentum transfer of 1 (GeV/c) 2 . This technique has very different systematic uncertainties than traditional exclusive measurements and thus serves as an independent check of whether nuclear effects have been taken into account correctly. Method: The inclusive quasielastic reaction 3 $→\atop{He}$ ($→\atop{e}$, e') was measured at Jefferson Laboratory. The neutron electric form factor, G$n\atop{E}$, was extracted at Q 2 = 0.98 ( GeV/c) 2 from ratios of electron-polarization asymmetries measured for two orthogonal target spin orientations. This Q 2 is high enough that the sensitivity to G$n\atop{E}$ is not overwhelmed by the neutron magnetic contribution, and yet low enough that explicit neutron detection is not required to suppress pion production. Results: The neutron electric form factor, G$n\atop{E}$, was determined to be 0.0414 ± 0.0077 ( stat ) ± 0.0022 ( syst ), providing the first high-precision inclusive extraction of the neutron's charge form factor. In conclusion: The use of the inclusive quasielastic 3 $→\atop{He}$ ($→\atop{e}$, e') with a four-momentum transfer near 1 (GeV/c) 2 has been used to provide a unique measurement of G$n\atop{E}$. This new result provides a systematically independent validation of the exclusive extraction technique results and implies that the nuclear corrections are understood. This is contrary to the proton form factor where asymmetry and differential cross section measurements have been shown to have large systematic differences.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Off-shell pion properties: Electromagnetic form factors and light-front wave functions

The off-shell pion electromagnetic form factors are explored with corresponding off-shell light-front wave functions modeled by constituent quark and antiquark. We apply the Mandelstam approach for the microscopic computation of the form factors relating the model parameters with the pion decay constant and charge radius. Analyzing the existing data on the cross sections for the Sullivan process, 1 H(e,e',π + )⁢n, Charged pion form factor between Q 2 = 0.60, and 2.45 GeV 2 . I. Measurements of the cross section for the 1 H⁡(e,e'⁢π + )⁢n reaction, we extract the off-shell pion form factor using the relation derived from the generalized Ward-Takahashi identity for the pion electromagnetic current. They are compared with our previous results from exactly solvable manifestly covariant model of a (3+1)-dimensional fermion field theory. We find that the adopted constituent quark model reproduces the extracted off-shell form factor F 1 ⁡(Q 2 ,t) from the experimental data within a few percent difference and matches well with our previous theoretical simulation which exhibits a variation of about 10% for the extracted off-shell pion form factor g(Q 2 ,t). We also identify the pion valence parton distribution function (PDF) and transverse momentum distribution (TMD) in terms of the light-front wave function and discuss their off-shell properties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Measurement of the Neutron Elastic Electromagnetic Form Factor Ratio at Large Momentum Transfer

Exploring nucleon structure is vital both for understanding its origin and existence as well as for the advancement of the sciences. It helps us answer key questions such as how quark and gluon dynamics create 99% of the nucleon mass. Electron- nucleon scattering has been widely used for precision studies of the nucleon and nuclear structure since the Nobel Prize winning investigations by Robert Hofstadter and collaborators in the 1950s. These studies provide information about the spatial charge and current densities of the nucleon in terms of the electromagnetic form factors. The form factors are functions of four momentum transfer squared (Q2). Extending the electromagnetic form factor measurements to higher Q2 plays a critical role in furthering the understanding of nucleon structure. This motivated the Super BigBite Spectrometer (SBS) program at Jefferson Lab. The open nature of the spectrometers and the direct line of sight from the target to the tracking detector locations in experimental setups such as SBS creates high levels of background at the detectors. This necessitates the use of tracking detectors with high rate capability and good position resolution. Gas Electron Multiplier (GEM) detectors are an excellent choice for tracking detectors in such experiments. Understanding the performance of the GEM detectors is important not just for SBS experiments but also for future high-luminosity experiments. This thesis reports the exploratory results from the measurement of the neutron elastic electromagnetic form factor ratio (Gn E/Gn M) at high momentum transfer. A longitudinally polarized electron beam was scattered off a polarized 3He target, used as an effective polarized neutron target. In this experiment, the polarized 3He target achieved a world record polarization weighted luminosity at a beam current of 45 µA. Double spin asymmetry of the scattered neutron events is used to extract the neutron form factor ratio. Measurements were taken at Q2 = 3.0, 6.8, 9.8 (GeV/c)2. The lowest Q2 measurement is in good agreement with the existing world data, and the higher-Q2 measurements extend the Q2 reach well beyond the existing world data and are expected to remain unmatched for a long time.

Gamage, Vimukthi Haththotuwa [Univ. of Virginia, C↗
DOE OSTI2024

Gravitational form factors of charmonia

We investigate the gravitational form factors of charmonium. Our method is based on a Hamiltonian formalism on the light front known as basis light-front quantization. The charmonium mass spectrum and light-front wave functions were obtained from diagonalizing an effective Hamiltonian that incorporates confinement from holographic QCD and one-gluon exchange interaction from light-front QCD. We proposed a quantum many-body approach to construct the hadronic matrix elements of the energy momentum tensor T + + and T + − , which are used to extract the gravitational form factors A ( Q 2 ) and D ( Q 2 ) . The obtained form factors satisfy the known constraints, e.g., the von Laue condition. From these quantities, we also extract the energy, pressure and light-front energy distributions of the system. We find that hadrons are multilayer systems. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2026

Untangling the heavy-flavor mess: status of the Fermilab-MILC calculation of the $B_{(s)}\to D^{(\ast)}_{(s)}\ellν$ form factors

We present the status of calculations of the form factors of the most relevant heavy-to-heavy and heavy-to-light decay channels. Using seven $N_f = 2+1+1$ HISQ ensembles, with lattice spacings ranging from 0.15 fm down to 0.06 fm, we calculate the form factors of the decays, including correlations among them. More than half of our ensembles feature physical pion masses, and the heavy quarks are simulated at their physical masses using the Wilson-clover action with the Fermilab interpretation. Even though we have recently seen huge qualitative and quantitative leaps in the characterization of heavy-to-heavy decays, these advances have failed to translate into improvements for the inclusive vs exclusive question, or the matter of the Lepton Flavor Universality ratios. In particular, in the $B\to D^{\ast}\ellν$ channel, the current situation of the lattice-QCD form factors is far from clear. Further, the latest lattice-QCD results on the heavy-to-light form factors display unexplained tensions that must urgently be resolved. The work presented here is an attempt to address these issues.

Vaquero, Alejandro [Zaragoza U.]↗
NASA NTRS1992

TRASYS form factor matrix normalization

A method has been developed for adjusting a TRASYS enclosure form factor matrix to unity. This approach is not limited to closed geometries, and in fact, it is primarily intended for use with open geometries. The purpose of this approach is to prevent optimistic form factors to space. In this method, nodal form factor sums are calculated within 0.05 of unity using TRASYS, although deviations as large as 0.10 may be acceptable, and then, a process is employed to distribute the difference amongst the nodes. A specific example has been analyzed with this method, and a comparison was performed with a standard approach for calculating radiation conductors. In this comparison, hot and cold case temperatures were determined. Exterior nodes exhibited temperature differences as large as 7 C and 3 C for the hot and cold cases, respectively when compared with the standard approach, while interior nodes demonstrated temperature differences from 0 C to 5 C. These results indicate that temperature predictions can be artificially biased if the form factor computation error is lumped into the individual form factors to space.

Tsuyuki, Glenn T.↗
DOE OSTI2017

Partonic structure of neutral pseudoscalars via two photon transition form factors

Here, the γγ* → η c,b transition form factors are computed using a continuum approach to the two valence-body bound-state problem in relativistic quantum field theory, and thereby unified with equivalent calculations of electromagnetic pion elastic and transition form factors. The resulting γγ* → η c form factor, G ηc (Q 2 ), is consistent with available data; significantly, at accessible momentum transfers, Q 2 G ηc (Q 2 ) lies well below its conformal limit. These observations confirm that the leading-twist parton distribution amplitudes of heavy-heavy bound states are compressed relative to the conformal limit. A clear understanding of the distribution of valence quarks within mesons thus emerges, a picture which connects Goldstone modes, built from the lightest quarks in nature, with systems containing the heaviest valence quarks that can now be studied experimentally, and highlights basic facts about manifestations of mass within the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Extraction and Parametrization of Isobaric Trinucleon Elastic Cross Sections and Form Factors

By mining data from Jefferson Lab Hall A experiment E08-014 a new 3 He elastic cross section was extracted from a large quasielastic background. This measurement was taken with an initial beam energy of 3.356 GeV and an angle of 20.51°. The cross section was found to be 1.345 × 10 -6 µb/sr ± 0.086 × 10 -6 µb/sr at Q 2 = 34.19 fm -2 . This new data point falls approximately halfway between the first and second diffractive minima of the 3 He form factors. When combined with recent high Q 2 3 He elastic cross section measurements from Jefferson Lab and MIT-Bates this new data point improves our knowledge of the cross section and form factors at large momentum transfers. The new high Q 2 data motivate a reanalysis of the 3 He elastic cross section world data and provide an improved understanding of the magnetic form factor in particular. For this analysis the elastic cross section world data for 3 He, and its mirror nuclei 3 H, were collected. The world data spans a time frame from 1965 to 2016. The dataset contains electron energy ranges from tens of MeV to above 12 GeV for measurements performed at many different facilities. The world data were then fit using a sum of Gaussians parametrization which allowed for the extraction of both targets’ magnetic and electric form factors which were then used to calculate charge densities and radii. The new charge and magnetic form factors for 3 H and the charge form factor for 3 He are in good agreement with the 1994 fits from Amroun et al . However, the addition of the new high Q 2 data has caused the 3 He magnetic form factor’s first diffractive minimum to shift up in Q 2 by 1-3 fm -2 while also decreasing the magnitude of the magnetic form factor above Q2 ≈ 20 fm -2 . The first diffractive minima for 3H are located at Q2 ≈ 13 fm -2 and Q 2 ≈ 23-24 fm -2 for the charge and magnetic form factors respectively. The first diffractive minima for 3 He are located at Q 2 ≈ 11 fm -2 and Q 2 ≈ 17-20 fm -2 for the charge and magnetic form factors respectively. The charge radius for 3 He was found to be 1.90 fm ± 0.00144 fm in reasonable agreement with past measurements, and the charge radius for 3 H was found to be 2.02 fm ± 0.0133 fm which is much larger than past measurements. However, each of these charge radii has an additional uncertainty that must be applied to them due to allowing all parameters to float freely during the sum of Gaussians fitting procedure. This additional uncertainty should be small for 3 He, but it is likely quite significant for 3 H and would help bring this charge radius closer to agreement with past measurements that made different fitting choices. Unfortunately, this analysis was unable to quantify this additional uncertainty. The new form factor fits were compared to modern theoretical predictions from the 2016 paper of Marcucci et al . The ‘conventional’ theoretical approach applied in this paper modelled two and three-body nucleon interactions with relativistic corrections and was reasonably successful at predicting the charge form factors of 3 H and 3 He. χEFT predictions were also often successful. However, while the ‘conventional’ approach still performed best, theory failed to accurately predict the magnetic form factors of either 3 H or 3 He. The first diffractive minimum of the new 3 He magnetic form factor fits actually moved further away from theory. This disagreement between theory and experiment provides motivation for new asymmetry measurements using polarized 3 He and a polarized electron beam. When the beam is scanned in Q 2 on the target the sign of the asymmetry will flip at the form factor minima pinning down their true location.

Barcus, Scott↗
DOE OSTI2023

Extending the thermodynamic form factor bootstrap program: multiple particle-hole excitations, crossing symmetry, and reparameterization invariance

In this study, we further the thermodynamic bootstrap program which involves a set of recently developed ideas used to determine thermodynamic form factors of local operators in integrable quantum field theories. These form factors are essential building blocks for dynamic correlation functions at finite temperatures or non-equilibrium stationary states. In this work we extend this program in three ways. Firstly, we demonstrate that the conjectured annihilation pole axiom is valid in the low energy particle-hole excitations. Secondly, we introduce a crossing relation, which establishes a connection between form factors with different excitation content. Typically, the crossing relation is a consequence of Lorentz invariance, but due to the finite energy density of the considered states, Lorentz invariance is broken. Nonetheless a crossing relation involving excitations with both particles and holes can established using the finite volume representation of the thermodynamic form factors. Finally, we demonstrate that the thermodynamic form factors satisfy a reparameterization invariance, an invariance which encompasses crossing. Reparameterization invariance exploits the fact that the details of the representation of the thermodynamic state are unimportant. In the course of developing these results, we demonstrate the internal consistency of the thermodynamic form factor bootstrap program in a number of ways. Finally, we provide explicit computations of form factors of conserved charges and densities with crossed excitations and show our results can be used to infer information about thermodynamic form factors in the Lieb-Liniger model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Nucleon Isovector Axial Form Factors

We present results for the isovector axial vector form factors obtained using thirteen 2 + 1 + 1-flavor highly improved staggered quark (HISQ) ensembles generated by the MILC collaboration. The calculation of nucleon two- and three-point correlation functions has been done using Wilson-clover fermions. In the analysis of these data, we quantify the sensitivity of the results to strategies used for removing excited state contamination and invoke the partially conserved axial current relation between the form factors to choose between them. Our data driven analysis includes removing contributions from multihadron $Nπ$ states that make significant contributions. Our final results are $g_A$ = 1.292(53) stat (24) sys for the axial charge; $g_S$ = 1.085(50) stat (103) sys and $g_T$ = 0.991(21) stat (10) sys for the scalar and tensor charges; $\langle{r^2_A}\rangle$ = 0.439(56) sta t(34) sys fm 2 for the mean squared axial charge radius, $g^*_P$ = 9.03(47) stat (42) sys for the induced pseudoscalar charge; and $g_{πNN}$ = 14.14(81) stat (85) sys for the pion-nucleon coupling. We also provide a parametrization of the axial form factor $G_A(Q^2)$ over the range 0 ≤ $Q^2$ ≤ 1 GeV 2 for use in phenomenology and a comparison with other lattice determinations. We find that the various lattice data agree within 10% but are significantly different from the extraction of $G_A(Q^2)$ from the $ν$-deuterium scattering data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Nucleon isovector axial form factors

We present results for the isovector axial vector form factors obtained using thirteen 2 + 1 + 1 -flavor highly improved staggered quark (HISQ) ensembles generated by the MILC collaboration. The calculation of nucleon two- and three-point correlation functions has been done using Wilson-clover fermions. In the analysis of these data, we quantify the sensitivity of the results to strategies used for removing excited state contamination and invoke the partially conserved axial current relation between the form factors to choose between them. Our data driven analysis includes removing contributions from multihadron N π states that make significant contributions. Our final results are g A = 1.292 ( 53 ) stat ( 24 ) sys for the axial charge; g S = 1.085 ( 50 ) stat ( 103 ) sys and g T = 0.991 ( 21 ) stat ( 10 ) sys for the scalar and tensor charges; ⟨ r A 2 ⟩ = 0.439 ( 56 ) stat ( 34 ) sys fm 2 for the mean squared axial charge radius, g P * = 9.03 ( 47 ) stat ( 42 ) sys for the induced pseudoscalar charge; and g π N N = 14.14 ( 81 ) stat ( 85 ) sys for the pion-nucleon coupling. We also provide a parametrization of the axial form factor G A ( Q 2 ) over the range 0 ≤ Q 2 ≤ 1 GeV 2 for use in phenomenology and a comparison with other lattice determinations. We find that the various lattice data agree within 10% but are significantly different from the extraction of G A ( Q 2 ) from the ν -deuterium scattering data. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Gravitational form factors of nuclei in the Skyrme model

Here, we compute the gravitational form factor D(t) of various nuclei in the generalized Skyrme model where nuclei are described as solitonic field configurations each with a definite baryon number B. We separately discuss the cases B = 1 (nucleons), B = 2 (deuteron), B = 3 (helium-3 and tritium), and extrapolate to larger B-values. Configurations with B > 1 are in general not spherically symmetric, and we demonstrate how group theory helps to extract the form factor. Numerical results are presented for the configurations with B = 1, 2, 3, 4, 5, 6, 7, 8, 32, 108. We find that the B-dependence is consistent with a power-law D(0) ∝ B β with β = 1.7–1.8. Other gravitational form factors can be calculated in the same framework, and we show the result for the J(t) form factor associated with the angular momentum for the B = 3 solution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗