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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Precision Measurements of the Neutron Magnetic Form Factor to High Momentum Transfer using Durand's Method

Protons and neutrons, collectively known as nucleons, along with electrons, constitute the funda- mental building blocks of the visible universe. Understanding their internal structure is crucial for addressing key scientific questions about our origin and existence. Elastic electron-nucleon scatter- ing provides insights into the spatial distributions of charge and current within nucleons through their electromagnetic form factors. Accurate knowledge of these form factors over a broad range of Q2, the squared four-momentum transfer in the scattering process, reveals details about the nucleon’s internal structure. However, high-Q2 data of the nucleon electromagnetic form factor is scarce due to the challenges associated with such measurements. This thesis reports preliminary results from high-precision measurements of the neutron magnetic form factor (Gn M ) to unprecedented Q2 using Durand’s method, also known as the “ratio” method. Systematic errors are greatly reduced by extracting Gn M from the ratio of neutron-coincident (D(e, e'n)) to proton-coincident (D(e, e'p)) quasi-elastic electron scattering from deuteron. The scattered electrons were detected in the BigBite spectrometer, which features multiple Gas Elec- tron Multiplier (GEM) layers with large active area for high-precision tracking at very high rates. Simultaneous nucleon detection was performed by the Super BigBite spectrometer, which utilizes a dipole magnet with large solid angle acceptance at forward angles and a novel hadron calorimeter with very high and comparable detection efficiencies for both protons and neutrons. This setup could handle very high luminosity, making high-Q2 measurements feasible. Data were collected at five Q2 points: 3, 4.5, 7.4, 9.9, and 13.6 (GeV/c)2. Preliminary results are reported for all, with the lowest two Q2 points in good agreement with existing world data, while the higher points significantly extend the Q2 range in which Gn M is known accurately. The precision of the highest Q2 point is expected to remain unmatched for years to come.

Datta, Provakar↗
DOE OSTI2025

Sullivan Process near Threshold and the Pion Gravitational Form Factors

We propose a novel method to experimentally access the gravitational form factors of the charged pion 𝜋 + through the Sullivan process in electron-proton scattering. We demonstrate that the cross sections of 𝐽/𝜓 photoproduction and 𝜙 electroproduction near the respective thresholds are dominated by the gluon gravitational form factor of the pion to next-to-leading order in perturbative QCD. We predict cross sections for the Electron-Ion Collider and the Jefferson Lab experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Timelike form factor for the anomalous process γ⁎π → ππ

The form factor 𝐹 3𝜋 (𝑠, 𝑡, 𝑢) for the anomalous process 𝛾∗𝜋 → 𝜋𝜋 is calculated in the isospin limit for several values of the light current-quark mass (i.e., the pion mass) using Dyson–Schwinger and Bethe–Salpeter equations. Beyond a quark interaction kernel representing gluon-mediated interactions, leading beyond-rainbow-ladder effects at low energies are incorporated by back-coupling pions as explicit degrees of freedom. Building upon an earlier calculation of the quark-photon vertex that captures the branch cut associated with the two-pion threshold and the ρ-meson resonance, the form factor 𝐹 3𝜋 (𝑠, 𝑡, 𝑢) is determined for timelike Mandelstam s. In particular, predictions are made for the kinematics relevant to the Primakoff reaction studied with COMPASS/AMBER at CERN.

Miramontes, Angel S. [Univ. of Valencia (Spain)] (↗
DOE OSTI2024

Global Data-Driven Determination of Baryon Transition Form Factors

Hadronic resonances emerge from strong interactions encoding the dynamics of quarks and gluons. The structure of these resonances can be probed by virtual photons parametrized in transition form factors. Here, in this study, twelve N* and Δ transition form factors at the pole are extracted from data with the center-of-mass energy from πN threshold to 1.8 GeV, and the photon virtuality 0 ≤ Q 2 /GeV 2 ≤ 8. For the first time, these results are determined from a simultaneous analysis of more than one state, i.e., ~10 5 π⁢N, η⁢N, and K⁢Λ electroproduction data. In addition, about 5×10 4 data in the hadronic sector as well as photoproduction serve as boundary conditions. For the Δ⁡(1232) and N⁡(1440) states our results are in qualitative agreement with previous studies, while the transition form factors at the poles of some higher excited states are estimated for the first time. Realistic uncertainties are determined by further exploring the parameter space.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Two-loop MHV form factors from the periodic Wilson loop

We discuss how to compute maximal-helicity-violating (MHV) form factors for the chiral part of the stress-tensor supermultiplet from periodic light-like polygon Wilson loops in planar $\mathcal{N}$ = 4 super Yang-Mills theory beyond the one-loop level. We show that the periodicity imposes path ordering on points on different edges, which explains the appearance of square roots coming from non-planar Feynman diagrams. Taking such diagrams into account, we provide the integrand of the two-loop n-particle MHV form factor, compute all diagrams, prove the cancellation of divergences and finally compute the two-loop 5-particle and 6-particle form factors as examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

𝐵 → 𝜌⁢ℓ⁢$\bar{v}$ Resonance Form Factors from 𝐵→ 𝜋⁢𝜋⁢ℓ⁢$\bar{v}$ in Lattice QCD

The decay 𝐵 → 𝜌⁢ℓ⁢$\bar{v}$ is an attractive process for determining the magnitude of the smallest Cabibbo-Kobayashi-Maskawa matrix element, |𝑉 𝑢⁢𝑏 |, and can provide new insights into the origin of the long-standing exclusive-inclusive discrepancy in determinations of this standard-model parameter. This requires a nonperturbative QCD calculation of the 𝐵 → 𝜌 form factors 𝑉, 𝐴 0 , 𝐴 1 , and 𝐴 12 . The unstable nature of the 𝜌 resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the 𝐵 → 𝜌 form factors in which the 𝜌 is treated properly as a resonance in 𝑃-wave 𝜋⁢𝜋 scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the 𝐵 → 𝜋⁢𝜋 form factors as a function of both momentum transfer and 𝜋⁢𝜋 invariant mass, and then analytically continue to the 𝜌 resonance pole. This calculation is performed with 2 + 1 dynamical quark flavors at a pion mass of approximately 320 MeV, and demonstrates a clear path toward results at the physical point.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Timelike meson form factors beyond the elastic region from lattice QCD

We present a calculation of the vector-isovector timelike form factors of the pion and the kaon using lattice quantum chromodynamics. We calculate two-point correlation functions with m π ∼ 280 MeV , extracting both the finite-volume spectrum and matrix elements for these states created from the vacuum by a vector current. After determining the coupled-channel π π , K K ¯ scattering amplitudes, we perform the necessary correction for the significant finite-volume effects present in the current matrix elements, leading to the timelike form factors. We find these to be dominated by the presence of the ρ resonance, and we extract its decay constant by an analytic continuation of the amplitudes to the resonance pole. In addition, the spacelike pion form factor is determined on the same lattice configurations, and a dispersive parametrization is used to simultaneously describe the spacelike and elastic timelike regions. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Measurement of the Neutron Electromagnetic Form Factor Ratio at High Momentum Transfer

The inner structure of the nucleon (proton and neutron) remains a topic of great interest in nuclear and particle physics, after many decades of study. For example, understanding the quark-gluon dynamics inside the nucleon would shed light on how 99% of the nucleon mass is created. The neutron electromagnetic form factors, Gn E and Gn M , give important insights into the neutron structure. The Super BigBite Spectrometer (SBS) program at Jefferson Lab (JLab) seeks to extend the form factor measurements for both the proton and the neutron. The neutron electric form actor, Gn E , has been historically difficult to measure due to the short lifetime of the free neutron and the small value of Gn E . The GEn-II experiment is part of the SBS program and seeks to measure Gn E , significantly increasing the high momentum transfer coverage. A newly designed polarized 3He target increased the figure of merit by three times compared to previous measurements. The analysis of this data is especially challenging due to the unprecedented high-rate environment caused by the open nature of the spectrometer with a direct line of sight to the target. This required developing new Gas Electron Multiplier (GEM) particle trackers which can cover large areas demanded by this setup and handle particle rates up to 500 kHz/cm2. Rates this high over a large area is unprecedented in particle tracking systems and came with a number of challenges. Data taken in the SBS program was critical to understanding hardware and software solutions that improved the track reconstruction efficiency to be >97% with a position resolution of 70 ?m. In previous experiments the proton electromagnetic form factors, Gp E and Gp M were measured up to Q2 = 8.5 GeV2 and Q2 = 30 GeV2, respectively, while Gn E has only been measured up to Q2 = 3.4 GeV2. The GEn-II experiment has measured the neutron form factor ratio, Gn E/Gn M, at Q2 values of 2.90, 6.50, and 9.47 GeV2 by scattering a polarized electron beam with a polarized 3He target, used here as an effective polarized neutron target, and measuring the double spin asymmetry of the cross section. Previous Gn E measurements do not extend above Q2 = 3.4 GeV2, and therefore this analysis has extended the world data by almost three times. The background correction is especially difficult at the higher Q2 settings leading to large systematic errors. As very exploratory results from this early analysis of the data, we find for Q2 = 2.90 GeV2, Gn E = 0.0157 ±stat 0.0016 ±sys 0.0011, for Q2 = 6.50 GeV2, Gn E = 0.0067 ±stat 0.0019 ±sys 0.0005, and for Q2 = 9.46 GeV2, Gn E = 0.0046 ±stat 0.0023 ±sys 0.0005. These results are compared to predictions from the Dyson-Schwinger Equations (DSE) model and a Relativistic Constituent Quark Model (RCQM).

Jeffas, Sean↗
DOE OSTI2024

Helium-4 gravitational form factors: Exchange currents

We evaluate the leading exchange corrections to the helium-4 gravitational form factors (GFFs) to momenta of the order of the nucleon mass. We use both the K-harmonic method with simple pair nucleon potential, and a Jastrow trial function using the Argonne 𝑣 14 potential, to evaluate the helium-4 GFFs. The exchange current contributions include the pair interaction, plus the seagull and the pion exchange interactions, modulo the recoil corrections. To estimate the off-shellness of the pion nucleon coupling in this momenta range, we discuss the results using either the pseudoscalar (PS) or pseudovector (PV) pion-nucleon couplings. When the PV coupling is used, the pair diagram contribution is higher order in the nonrelativistic expansion. The results for the helium-4 A-GFF are comparable to those given by the impulse approximation, especially for the PS coupling using both the K-harmonic method and variational method. The exchange current contributions with the PS coupling for the charge form factor of helium-4, yield better agreement with the existing data over a broad range of momenta, especially when the Argonne 𝑣 14 potential including the D-wave admixture is used.

A ≤ 5↗
DOE OSTI2025

Form-factor dependence of neutrino-nucleus cross sections using microscopic methods

To achieve its design goals, the next generation of neutrino-oscillation accelerator experiments requires percent-level predictions of neutrino-nucleus cross sections supplemented by robust estimates of the theoretical uncertainties involved. The latter arise from both approximations in solving the nuclear many-body problem and in the determination of the single- and few-nucleon quantities taken as input by many-body methods. To gauge the sensitivity of realistic nuclear many body methods to these few-nucleon quantities, we compute flux-averaged double-differential cross sections using the Green’s function Monte Carlo and spectral function methods as well as different parameterizations of the nucleon axial form factors based on either deuterium bubble-chamber data or lattice quantum chromodynamics calculations. The cross-section results are compared with available experimental data from the MiniBooNE and T2K collaborations. We also discuss the uncertainties associated with N → Δ transition form factors that enter the two-body current operator. We quantify the relations between neutrino-nucleus cross section and nucleon form factor uncertainties. These relations enable us to determine the form factor precision targets required to achieve a given cross-section precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Precision Measurement of the Neutron Magnetic Form Factor via the Ratio Method at Jefferson Lab Hall A

Protons and neutrons, collectively known as nucleons, are composed of quarks and gluons. The Sachs electromagnetic form factors encode information about the spatial distributions of charge and magnetization in the nucleon, particularly at low momentum transfer. In particular, the neutron magnetic form factor (GMn) provides crucial information about the distribution of magnetization inside the neutron and helps constrain theoretical models of nucleon structure. Quasi-elastic electron scattering from deuterium was measured up to Q^2=13.5 GeV^2 using the Super BigBite Spectrometer in Hall A at Jefferson Lab. In this work, the neutron magnetic form factor GMn was extracted at Q^2 = 3.0 GeV^2 and Q^2=4.5 GeV^2 using the Ratio Method. These results represent a subset of the full dataset collected in this experiment, which extended to significantly higher Q^2. The extracted GMn values agree with the existing global fit within approximately two standard deviations at Q^2=3.0 and show excellent agreement at Q^2=4.5. The measurements achieved systematic uncertainties of about 2% and statistical uncertainties below 0.5%, among the most precise determinations of GMn at these kinematics. These results demonstrate the robustness of the experimental technique and provide an important validation point for future extractions at higher Q^2, where data remain scarce. In addition, the GRINCH heavy gas Cherenkov detector—a key component of the experimental apparatus—was commissioned and achieved an electron detection efficiency of approximately 97%, supporting reliable particle identification. Together, the analysis presented here advances both our understanding of nucleon structure and the validation of the experimental methods and instrumentation used to access it.

Satnik, Maria [College of William and Mary, Willia↗
DOE OSTI2024

Pion gravitational form factors in the QCD instanton vacuum. II

We revisit the hard QCD contributions to the pion gravitational form factors, in terms of the twist-2,3 pion distribution amplitudes (DAs), including novel semihard contributions from the instantons. The pion DAs are evaluated in the QCD instanton vacuum and then properly evolved to higher resolution. The results are compared to our recent results from the QCD instanton vacuum, as well as Bethe-Salpeter calculations and recent lattice data. The interpolated hard and soft contributions to the pion D form factor are used to derive the (gravitational) pressure and shear within the pion, with a clear delineation of their range.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1975

The neutrino charge form-factor

Mathematical analysis and dispersion relations are used to obtain the general functional form of the neutrino charge form-factor. It is shown that if the scale for weak interactions is given by G, where G is the Fermi coupling constant, then for a large range of momentum transfer values, the form-factor may be approximated by a function that is linear in the square of the momentum transfer.

Mickens, R. E.↗
DOE OSTI2024

Quantum Monte Carlo Calculations of Magnetic Form Factors in Light Nuclei

Here, we present Quantum Monte Carlo calculations of magnetic form factors in A = 6-10 nuclei, based on Norfolk two- and three-nucleon interactions, and associated one- and two-body electromagnetic currents. Agreement with the available experimental data for 6 Li, 7 Li, 9 Be and 10 B up to values of momentum transfer q ~ 3 fm -1 is achieved when two-nucleon currents are accounted for. We present a set of predictions for the magnetic form factors of 7 Be, 8 Li, 9 Li, and 9 C. In these systems, two body currents account for ~ 40-60% of the total magnetic strength. Measurements in any of these radioactive systems would provide valuable insights on the nuclear magnetic structure emerging from the underlying many-nucleon dynamics. A particularly interesting case is that of 7 Be, as it would enable investigations of the magnetic structure of mirror nuclei

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Gravitational Form Factors of the Proton from Lattice QCD

The gravitational form factors (GFFs) of a hadron encode fundamental aspects of its structure, including its shape and size as defined from, e.g., its energy density. This Letter presents a determination of the flavor decomposition of the GFFs of the proton from lattice QCD, in the kinematic region 0 ≤−𝑡 ≤2 GeV 2 . The decomposition into up-, down-, strange-quark, and gluon contributions provides first-principles constraints on the role of each constituent in generating key proton structure observables, such as its mechanical radius, mass radius, and 𝐷 term.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

$Ξ$ 𝑏 → $Ξ$ form factors from lattice QCD and standard-model predictions for $Ξ$ 𝑏 → $Ξ$⁢𝜇 + ⁢𝜇 − and $Ξ$ 𝑏 → $Ξ$⁢𝛾 decays

We present the first lattice QCD determination of the $Ξ$ 𝑏 → $Ξ$ vector, axial-vector, and tensor form factors, which are relevant for the theory of rare decays including $Ξ$ 𝑏 → $Ξ$⁢ℓ + ⁢ℓ − and $Ξ$ 𝑏 → $Ξ$⁢𝛾. The calculation is performed with 2+1 flavors of domain-wall fermions at three different lattice spacings and pion masses in the range from approximately 430 to 230 MeV. The bottom quark is implemented using an anisotropic clover action. Three-point functions with a wide range of source-sink separations and model averaging are used to extract the ground-state contributions. We fit the dependence of the form factors on the momentum transfer, the pion mass, and the lattice spacing using modified 𝑧 expansions that account for subthreshold branch cuts, and apply dispersive bounds and asymptotic behavior constraints to achieve controlled uncertainties in the full semileptonic kinematic region. Using our form factor results, we present standard model predictions for the $Ξ$$^{−}_{𝑏}$ → $Ξ$ − ⁢𝛾 and $Ξ$$^{−}_{𝑏}$ → $Ξ$ − ⁢𝜇 + ⁢𝜇 − branching fractions and two angular observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Nucleon tensor form factors at large N c

We investigate nucleon tensor form factors in the large- N c limit. In this picture, the nucleon emerges as a state of the N c valence quarks, which were bound by pion mean fields that were created by the presence of the valence quarks self-consistently. We find that the tensor charge ( g T u − d = 0.99 ) and the anomalous tensor magnetic moment ( κ T u + d = 7.61 ) are dominated by valence quarks, while the tensor quadrupole moment ( Q T u − d = − 7.02 ) shows significant sea quark effects. We examine how these quantities vary as the average size of the pion mean field is changed, showing interpolation between nonrelativistic quark and Skyrme limits. We also observe that g T u − d and κ T u + d depend weakly on the pion mass. In contrast, Q T u − d exhibits strong enhancement near the chiral limit. The numerical results are in good agreement with available lattice quantum chromodynamics (QCD) data and provide predictions for unmeasured quantities. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Consistency of the pion form factor and unpolarized transverse momentum dependent parton distributions beyond leading twist in the light-front quark model

We investigate the interplay among the pion’s form factor, transverse momentum dependent distributions (TMDs), and parton distribution functions (PDFs) extending our light-front quark model (LFQM) computation based on the Bakamjian-Thomas construction for the two-point function [1,2] to the three-point and four-point functions. Ensuring the four-momentum conservation at the meson-quark vertex from the Bakamjian-Thomas construction, the meson mass is taken consistently as the corresponding invariant meson mass both in the matrix element and the Lorentz factor in our LFQM computation. We achieve the current-component independence in the physical observables such as the pion form factor and delve into the derivation of unpolarized TMDs and PDFs associated with the forward matrix element. We address the challenges posed by twist-4 TMDs and exhibit the fulfillment of the sum rule. Effectively, our LFQM successfully handles the light-front zero modes and offers insights for broader three-point and four-point functions and related observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗