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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Mechanical form factors and densities of nonrelativistic fermions

The hadron physics community has been actively debating the interpretation of so-called mechanical properties of hadrons. Nonrelativistic quantum-mechanical systems like the hydrogen atom have been appealed to in these debates as analogies. Since such appeals are likely to continue, it is important to have Galilei-covariant expressions for matrix elements of the energy-momentum tensor. In this work, I obtain Galilei-covariant breakdowns of such matrix elements into mechanical form factors, with a special focus on spin-half states. I additionally study the spatial densities associated with these form factors, using the pilot wave interpretation to guide their breakdown into contributions from internal structure and from quantum-mechanical effects such as wave packet dispersion. For completeness, I also obtain nonrelativistic Breit frame densities.

form factors↗
DOE OSTI2016

Baryon transition form factors at the pole

Electromagnetic resonance properties are uniquely defined at the pole and do not depend on the separation of the resonance from background or the decay channel. Photon-nucleon branching ratios are nowadays often quoted at the pole, and we generalize the considerations to the case of virtual photons. In this paper, we derive and compare relations for nucleon to baryon transition form factors both for the Breit-Wigner and the pole positions. Using the MAID2007 and SAID SM08 partial wave analyses of pion electroproduction data, we compare the $G_M$, $G_E$, and $G_C$ form factors for the $\Delta(1232)$ resonance excitation at the Breit-Wigner resonance and pole positions up to $Q^2=5$ GeV$^2$. We also explore the $E/M$ and $S/M$ ratios as functions of $Q^2$. Finally, for pole and residue extraction, we apply the Laurent + Pietarinen method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Nucleon and N* masses and form factors from a contact interaction

In the Schwinger-Dyson and bound state equation framework, we use a contact interaction that reproduces the low energy interactions of QCD. We use the Faddeev equation to determine masses for the ground and low-lying excited states of the Baryon octet. We then use these amplitudes in a form factor calculation to obtain elastic and transition form factors.

Wilson, David↗
DOE OSTI2022

Status of Lattice QCD Determination of Nucleon Form Factors and Their Relevance for the Few-GeV Neutrino Program

Calculations of neutrino–nucleus cross sections begin with the neutrino–nucleon interaction, making the latter critically important to flagship neutrino oscillation experiments despite limited measurements with poor statistics. Alternatively, lattice quantum chromodynamics (LQCD) can be used to determine these interactions from the Standard Model with quantifiable theoretical uncertainties. Recent LQCD results of g A are in excellent agreement with data, and results for the (quasi-)elastic nucleon form factors with full uncertainty budgets are expected within a few years. We review the status of the field and LQCD results for the nucleon axial form factor, F A ( Q 2 ), a major source of uncertainty in modeling sub-GeV neutrino–nucleon interactions. Results from different LQCD calculations are consistent but collectively disagree with existing models, with potential implications for current and future neutrino oscillation experiments. We describe a road map to solidify confidence in the LQCD results and discuss future calculations of more complicated processes, which are important to few-GeV neutrino oscillation experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Form factors for semileptonic B-decays with HISQ light quarks and clover b-quarks in Fermilab interpretation

We compute the vector, scalar, and tensor form factors for the $B\to \pi$, $B\to K$, and $B_s\to K$ amplitudes, which are needed to describe semileptonic $B$-meson decay rates for both the charged and neutral current cases. We use the highly improved staggered quark (HISQ) action for the sea and light valence quarks. The bottom quark is described by the clover action in the Fermilab interpretation. Simulations are carried out on $N_f = 2+1+1$ MILC HISQ ensembles at approximate lattice spacings from $0.15$ fm down to $0.057$ fm. We present blinded preliminary results for the form factors.

Jeong, Hwancheol↗
DOE OSTI2019

Model-independent form-factor constraints for electromagnetic spin-1 currents

Using local gauge invariance in the form of the Ward-Takahashi identity and the fact that properly constructed current operators must be free of kinematic singularities, it is shown that the magnetic moment μ and the quadrupole moment Q of an elementary spin-1 particle with mass m and charge e are related by 2mμ + m 2 Q = e, thus constraining the normalizations of the Sachs form factors. This relation holds true as a matter of course at the tree level in the standard model, but we prove that it remains true in general for dressed spin-1 states derived from elementary fields. Furthermore, general expressions for spin-1 propagators and currents with arbitrary hadronic dressing are given, which show that the result is independent of any dressing effect or model approach.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

How analytic choices can affect the extraction of electromagnetic form factors from elastic electron scattering cross section data

Scientists often try to incorporate prior knowledge into their regression algorithms, such as a particular analytic behavior or a known value at a kinematic endpoint. Unfortunately, there is often no unique way to make use of this prior knowledge, and thus, different analytic choices can lead to very different regression results from the same set of data. In this paper, to illustrate this point in the context of the proton electromagnetic form factors, we use the Mainz elastic data with its 1422 cross section points and 31 normalization parameters. Starting with a complex unbound non-linear regression, we will show how the addition of a single theory-motivated constraint removes an oscillation from the magnetic form factor and shifts the extracted proton charge radius. We then repeat both regressions using the same algorithm, but with a rebinned version of the Mainz dataset. These examples illustrate how analytic choices, such as the function that is being used or even the binning of the data, can dramatically affect the results of a complex regression. These results also demonstrate why it is critical when using regression algorithms to have either a physical model in mind or a firm mathematical basis

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

$D$-Meson Semileptonic Form Factors at Zero Momentum Transfer in (2+1+1)-Flavor Lattice QCD

We present a calculation of the $D\to K \ell \nu$ and $D\to\pi \ell \nu$ semileptonic form factors at $q^2=0$, which enable determinations of the CKM matrix elements $\lvert{V_{cs}}\rvert$ and $\lvert{V_{cd}}\rvert$, respectively. We use gauge-field configurations generated by the MILC collaboration with four flavors of highly-improved staggered (HISQ) quarks, analyzing several ensembles including those with physical pion masses and approximate lattice spacings ranging from 0.12~fm to 0.042~fm. We also use the HISQ action for the valence quarks. We employ twisted boundary conditions to calculate the form factors at zero momentum transfer directly. We use heavy-light-meson chiral perturbation theory modified for energetic pions and kaons, and supplemented by terms to describe the lattice-spacing dependence, to obtain preliminary results at the physical point and in the continuum limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Gravitational form factors of light mesons

Here, we calculate the gravitational form factors of the pion, $\sigma$ meson, and $\rho$ meson in the Nambu-Jona-Lasinio model of quantum chromodynamics. The canonical energy-momentum tensor (EMT) is used in their derivation, allowing the possibility of an antisymmetric contribution when the hadron has intrinsic spin. We show that the asymmetric graviton vertex arising from the canonical EMT satisfies a simpler Ward-Takahashi identity (WTI) than the symmetric graviton vertex of the Belinfante EMT. The necessity of fully dressing the graviton vertex through the relevant Bethe-Salpeter equation is demonstrated for observing both the WTI and a low-energy pion theorem. Lastly, we calculate static moments of the meson EMT decompositions, obtaining predictions for the meson mass radii. We find light cone mass radii of 0.27 fm for the pion, 0.32 fm for the $\sigma$, and 0.32 fm for the $\rho$. For the pion and rho, these are smaller than the light cone charge radii, respectively 0.51 fm and 0.45 fm, while we have a $\sigma$ charge radius of zero. Our light cone pion mass radius agrees with a phenomenological extraction from KEKB data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Determination of the Axial Nucleon Form Factor from the MiniBooNE Data

Both neutrino and antineutrino charged-current quasi-elastic scattering on a carbon target are studied to investigate the nuclear effect on the determination of the axial form factor F_A(Q^2). A method for extraction of F_A(Q^2) from the flux-integrated $d\sigma/dQ^2$ cross section of (anti)neutrino scattering on nuclei is presented. Data from the MiniBooNE experiment are analyzed in the relativistic distorted-wave impulse approximation, Fermi gas model, and in the Fermi gas model with enhancements in the transverse cross section. We found that the values of the axial form factor, extracted in the impulse approximation and predicted by the dipole approximation with the axial mass M_A~1.37 GeV are in good agreement. On the other hand, the Q^2-dependence of F_A extracted in the approach with the transverse enhancement is found to differ significantly from the dipole approximation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

$$\omega \rightarrow 3\pi $$ and $$\omega \pi ^{0}$$ transition form factor revisited

Abstract In light of recent experimental results, we revisit the dispersive analysis of the $$\omega \rightarrow 3\pi $$ ω → 3 π decay amplitude and of the $$\omega \pi ^0$$ ω π 0 transition form factor. Within the framework of the Khuri–Treiman equations, we show that the $$\omega \rightarrow 3\pi $$ ω → 3 π Dalitz-plot parameters obtained with a once-subtracted amplitude are in agreement with the latest experimental determination by BESIII. Furthermore, we show that at low energies the $$\omega \pi ^0$$ ω π 0 transition form factor obtained from our determination of the $$\omega \rightarrow 3\pi $$ ω → 3 π amplitude is consistent with the data from MAMI and NA60 experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Semileptonic form factors for $$B\rightarrow D^*\ell \nu $$ at nonzero recoil from $$2+1$$-flavor lattice QCD: Fermilab Lattice and MILC Collaborations

Abstract We present the first unquenched lattice-QCD calculation of the form factors for the decay $$B\rightarrow D^*\ell \nu $$ B → D ∗ ℓ ν at nonzero recoil. Our analysis includes 15 MILC ensembles with $$N_f=2+1$$ N f = 2 + 1 flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from $$a\approx 0.15$$ a ≈ 0.15 fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valence b and c quarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element $$|V_{cb}|$$ | V cb | . We obtain $$\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}$$ V cb = ( 38.40 ± 0 . 68 th ± 0 . 34 exp ± 0 . 18 EM ) × 10 - 3 . The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall $$\chi ^2\text {/dof} = 126/84$$ χ 2 /dof = 126 / 84 , which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict $$R(D^*) = 0.265 \pm 0.013$$ R ( D ∗ ) = 0.265 ± 0.013 , which confirms the current tension between theory and experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Studying the Strange Axial Form Factor through Neutral-Current Elastic Scattering in MicroBooNE

The strange quark contribution to the spin of the proton can be determined from neutral-current elastic neutrino-proton scattering. At zero four-momentum transfer the axial form factor in this process becomes a linear combination of the net spin contributions from the individual quark flavors to the spin of the proton. MicroBooNE’s ability to detect low-energy protons allows it to detect these events with negative four-momentum transfer squared as low as Q 2 ≃ 0.1 GeV 2 /c 2 . We present a selection of neutral-current elastic events in a subset of MicroBooNE neutrino data and outline a plan to extract the strange part of the axial form factor from this selection in the full data set.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Measurement of the Neutron Electromagnetic Form Factors at High Momentum Transfer Using a Polarized 3He Target at Jefferson Lab

Ever since the composite structure of nucleons was uncovered, many experiments have been commissioned with the purpose of extracting parameters that shape our understanding of this structure. Form factors are powerful tools that rest at the forefront of the nucleon structure study. In the non-relativistic limit, they describe the magnetic and charge distributions inside the nucleon. The GEn-II experiment, which ran in Hall A of Jefferson Lab as a part of the SuperBigbite Spectrometer (SBS) program, aimed to extract the ratio of the neutron’s electric to magnetic Sachs form factors (GnE/GnM. This was accomplished using the double polarization technique: scattering polarized electrons with initial energies up to 8.45 GeV off high-density polarized 3He targets. The experiment was a coincidence measurement, with the scattered electrons detected in the BigBite Spectrometer and the recoil nucleons in a hadron calorimeter, a part of the SuperBigbite Spectrometer. The convection-style target cells used in this experiment have a 60cm long target chamber, an increase from the 40 cm cell used in the most recent polarized 3He target experiment. In addition, the cells were optically pumped from two sides of the pumping chamber. These improvements in design and functionality introduced world-record-breaking luminosity. This thesis presents preliminary results of the GEn-II experiment for the following 4-momentum transfer (Q2) values: 2.93, 6.76, and 9.78 GeV2, in addition to target performance and preliminary polarimetry results.

Presley, Hunter [Univ. of Virginia, Charlottesvill↗
DOE OSTI2022

Precision Determination of the Neutral Weak Form Factor of Ca 48

In this work, we report a precise measurement of the parity-violating asymmetry $A_{\rm PV}$ in the elastic scattering of longitudinally polarized electrons from $^{48}{\rm Ca}$. We measure $A_{\rm PV} =2668\pm 106\ {\rm (stat)}\pm 40\ {\rm (syst)}$ parts per billion, leading to an extraction of the neutral weak form factor $F_{\rm W} (q=0.8733$ fm$^{-1}) = 0.1304 \pm 0.0052 \ {\rm (stat)}\pm 0.0020\ {\rm (syst)}$ and the charge minus the weak form factor $F_{\rm ch} - F_{\rm W} = 0.0277\pm 0.0055$. The resulting neutron skin thickness $R_n-R_p=0.121 \pm 0.026\ {\rm (exp)} \pm 0.024\ {\rm (model)}$~fm is relatively thin yet consistent with many model calculations. The combined CREX and PREX results will have implications for future energy density functional calculations and on the density dependence of the symmetry energy of nuclear matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Measurement of the form factors of charged kaon semileptonic decays

A measurement of the form factors of charged kaon semileptonic decays is presented, based on 4.4 × 10 6K± → π 0 e ± ν e (K e 3 ± ) and 2.3 × 10 6 K ± → π 0 μ±ν μ (K μ 3 ±) decays collected in 2004 by the NA48/2 experiment. The results are obtained with improved precision as compared to earlier measurements. The combination of measurements in the K e3 ± and K μ3 ± modes is also presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2013

Stackable Form-Factor Peripheral Component Interconnect Device and Assembly

A stackable form-factor Peripheral Component Interconnect (PCI) device can be configured as a host controller or a master/target for use on a PCI assembly. PCI device may comprise a multiple-input switch coupled to a PCI bus, a multiplexor coupled to the switch, and a reconfigurable device coupled to one of the switch and multiplexor. The PCI device is configured to support functionality from power-up, and either control function or add-in card function.

Somervill, Kevin M.↗