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The electromagnetic form factors are the most fundamental observables that encode information about the internal structure of the nucleon. This dissertation explored dependence of R on kinematic variables such as squared four-momentum transfer (Q 2 ) and the virtual photon polarization parameter (ε).
The extraction of matrix elements from baryon three-point functions is complicated by the fact that the signal-to-noise drops rapidly as a function of time. Using a previously discussed method to improve the signal-to-noise for lattice two-point functions, we use this technique to do so for lattice three-point functions, using electromagnetic form factors for the nucleon and Delta as an example.
Recent progress in lattice QCD calculations of nucleon structure will be presented. Calculations of nucleon matrix elements and form factors have long been difficult to reconcile with experiment, but with advances in both methodology and computing resources, this situation is improving. Some calculations have produced agreement with experiment for key observables such as the axial charge and electromagnetic form factors, and the improved understanding of systematic errors will help to increase confidence in predictions of unmeasured quantities. The long-omitted disconnected contributions are now seeing considerable attention and some recent calculations of them will be discussed.
A continuum approach to quark-antiquark bound-states is used to determine the electromagnetic form factors of pion-like mesons with masses m 0- /GeV = 0.14, 0.47, 0.69, 0.83 on a spacelike domain that extends to Q 2 ≲ 10 GeV 2 . The results enable direct comparisons with contemporary lattice-QCD calculations of heavy-pion form factors at large values of momentum transfer and aid in understanding them. Finally, they also reveal, inter alia, that the form factor of the physical pion provides the best opportunity for verification of the factorised hard-scattering formula relevant to this class of exclusive processes and that this capacity diminishes steadily as the meson mass becomes heavier.
The exclusive photoproduction of {Upsilon} has been studied with the ZEUS detector in ep collisions at HERA. The exponential slope, b, of the |t|-dependence of the cross section, where t is the squared four-momentum transfer at the proton vertex, has been measured. This constitutes the first measurement of the |t|-dependence of the {gamma}p{yields}{Upsilon}p cross section. The differential crosssections as a function of t at lower energies of {gamma}p centre-of-mass has been studied in exclusive diffractive photoproduction of J/{psi} mesons with the H1 detector. The exclusive electroproduction of two pions has been measured by the ZEUS experiment. The two-pion invariant-mass distribution is interpreted in terms of the pion electromagnetic form factor, assuming that the studied mass range includes the contributions of the {rho}, {rho} Prime and . {rho}'' vector-meson states.
Recently published measurements of the proton electromagnetic form factor ratio R = μ p G E p /G M p at momentum transfers Q 2 up to 8.5 GeV 2 in Jefferson Lab Hall C deviate from the linear trend of previous measurements in Jefferson Lab Hall A, favoring a slower rate of decrease of R with Q 2 . While statistically compatible in the region of overlap with Hall A, the Hall C data hint at a systematic difference between the two experiments. This possibility was investigated in a reanalysis of the Hall A data. We find that the original analysis underestimated the background in the selection of elastic events. The application of an additional cut to further suppress the background increases the results for R, improving the consistency between Halls A and C.
I review the effects of charge symmetry breaking CSB on electromagnetic form factors and how that influences extraction of information regarding nucleon strangeness content and the weak mixing angle. It seems that CSB effects are very modest and should not impact the analysis of experiments.
Transverse densities describe the distribution of charge and current at fixed light-front time and provide a frame-independent spatial representation of hadrons as relativistic systems. In this paper, we calculate the transverse densities of the octet baryons at peripheral distances b=O(M π -1 ) in an approach that combines chiral effective field theory (χχEFT) and dispersion analysis. The densities are represented as dispersive integrals of the imaginary parts of the baryon electromagnetic form factors in the timelike region (spectral functions). The spectral functions on the two-pion cut at t>4M$2\atop{π}$ are computed using relativistic χEFT with octet and decuplet baryons in the extended on-mass-shell renormalization scheme. The calculations are extended into the ρ-meson mass region using a dispersive method that incorporates the timelike pion form-factor data. The approach allows us to construct densities at distances b>1 fm with controlled uncertainties. Finally, our results provide insight into the peripheral structure of nucleons and hyperons and can be compared with empirical densities and lattice-QCD calculations.
Nucleon properties are modified in the nuclear medium. To understand these modifications and their origin is a central issue in nuclear physics. For example, a wide variety of QCD-based models, including quark-meson coupling and chiral-quark soliton models, predict that the nuclear constituents change properties with increasing density. These changes are predicted to lead to observable changes in the nucleon structure functions and electromagnetic form factors. We present results from a series of recent experiments at MAMI and Jefferson Lab, which measured the proton recoil polarization in the {sup 4}He({rvec e},e{prime}{rvec p}){sup 3}H reaction to test these predictions. These results, with the most precise data at Q{sup 2} = 0.8 (GeV/c){sup 2} and at 1.3 (GeV/c){sup 2} from E03-104, put strong constraints on available model calculations, such that below Q{sup 2} = 1.3 (GeV/c){sup 2} the measured ratios of polarization-transfer are successfully described in a fully relativistic calculation when including a medium modification of the proton form factors or, alternatively, by strong charge-exchange final-state interactions. We also discuss possible extensions of these studies with measurements of the {sup 4}He({rvec e},e{prime}{rvec p}){sup 3}H and {sup 2}H({rvec e},e{prime}{rvec p})n reactions as well as with the neutron knockout in {sup 4}He({rvec e},e{prime}{rvec n}){sup 3}He.
The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools together with key applications. For this, it is first necessary to review previous methods to apply QCD perturbation theory at low spacelike momentum scales, where the influence of the Landau singularities becomes inevitable. Several concepts are considered and their limitations are pointed out. The usefulness of FAPT is discussed in terms of two characteristic hadronic quantities: the perturbatively calculable part of the pion’s electromagnetic form factor in the spacelike region and the Higgs-boson decay into a b b-bar pair in the timelike region. In the first case, the focus is on the optimization of the prediction with respect to the choice of the renormalization scheme and the dependence on the renormalization and the factorization scales. The second case serves to show that the application of FAPT to this reaction reaches already at the four-loop level an accuracy of the order of 1%, avoiding difficulties inherent in the standard perturbative expansion. The obtained results are compared with estimates from fixed-order and contour-improved QCD perturbation theory. Using the brand-new Higgs mass value of about 125 GeV, measured at the Large Hadron Collider (CERN), a prediction for Γ{sub H→b b-bar }= 2.4 ± 0.15 MeV is extracted.
In this work, we present a review of recent applications of nonlocal chiral effective theory to hadron structure studies. Starting from a nonlocal meson-baryon effective chiral Lagrangian, we show how the introduction of a correlation function representing the finite extent of hadrons regularizes the meson loop integrals and introduces momentum dependence in vertex form factors in a gauge invariant manner. We apply the framework to the calculation of nucleon electromagnetic form factors, unpolarized and polarized parton distributions, as well as transverse momentum dependent distributions and generalized parton distributions. Assuming that the nonlocal behavior is a general property of all interactions, we also discuss the application to the lepton anomalous magnetic moment in nonlocal QED.
We measure neutrino charged-current quasielasticlike scattering on hydrocarbon at high statistics using the wideband Neutrinos at the Main Injector beam with neutrino energy peaked at 6 GeV. The double-differential cross section is reported in terms of muon longitudinal ( p ∥ ) and transverse ( p ⊥ ) momentum. Cross section contours versus lepton momentum components are approximately described by a conventional generator-based simulation, however, discrepancies are observed for transverse momenta above 0.5 GeV / c for longitudinal momentum ranges 3–5 and 9 – 20 GeV / c . The single differential cross section versus momentum transfer squared ( d σ / d Q QE 2 ) is measured over a four-decade range of Q 2 that extends to 10 GeV 2 . The cross section turnover and falloff in the Q 2 range 0.3 – 10 GeV 2 is not fully reproduced by generator predictions that rely on dipole form factors. Our measurement probes the axial-vector content of the hadronic current and complements the electromagnetic form factor data obtained using electron-nucleon elastic scattering. These results help oscillation experiments because they probe the importance of various correlations and final-state interaction effects within the nucleus, which have different effects on the visible energy in detectors.
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.
The separate quark flavor contributions to the pion and kaon valence quark distribution functions are studied, along with the corresponding electromagnetic form factors in the space-like region. The calculations are made using the solution of the Bethe-Salpeter equation for the model of Nambu and Jona-Lasinio with proper-time regularization. Both the pion and kaon form factors and the valence quark distribution functions reproduce many features of the available empirical data. The larger mass of the strange quark naturally explains the empirical fact that the ratio u(K) + (x)/u(pi) + (x) drops below unity at large x, with a value of approximately M$2\atop{u}$/Ms$2\atop{s}$ as x → 1. With regard to the elastic form factors we report a large flavor dependence, with the u-quark contribution to the kaon form factor being an order of magnitude smaller than that of the s-quark at large Q 2 , which may be a sensitive measure of confinement effects in QCD. Surprisingly though, the total K + and π + form factors differ by only 10%. Lastly, in general we find that flavor breaking effects are typically around 20%.
We report recent progress in the calculations of the isovector nucleon electromagnetic form factors using 2+1 flavors of domain wall fermions at pion masses of 170 MeV and 250 MeV. The lattice size is fixed at 323 ×64 with a lattice cutoff scale of 1.37(1) GeV. For the calculations with Mp = 170 MeV, we employed the All-Mode-Averaging (AMA) technique, which led to roughly a factor of 20 improvement in computational efficiency and has reduced the statistical errors in our results significantly. We were also able to do calculations at two different source-sink separations, at roughly 1.3 fm and 1.0 fm, without much additional cost by reusing the low eigenmodes stored for the AMA calculations. We will present results for the isovector form factors and their derived quantities, including the Dirac and Pauli radii, anomalous magnetic moment and discuss the effects of possible excited-state contaminations. Connected contributions to the isoscalar Dirac and Pauli form factors will also be shown.
Protons and neutrons, collectively known as nucleons, make up the nuclei at the core of atoms which form our world. The nucleon has been under intensive study for over 100 years, and yet we still do not fully understand the internal dynamics which govern properties like its spin or its mass-which contributes to almost all of the visible mass in the universe. These dynamics are governed by quantum chromodynamics(QCD), the predictions of which are experimentally tested at high energy accelerator facilities such as Jefferson Lab. TheGEN-II experiment (E12-09-016) is one such experiment. GEN-II is part of the Super Bigbite Spectrometer (SBS) experimental form factor pro gramme taking place in Hall A at Jefferson Lab, which aims to make precision measurements of the nucleon electromagnetic form factors(EMFFs)at record high values of squared four momentum transfer ¿2. EMFFs describe the electric and magnetic moment distributions within the nucleon. They can be measured through elastic electron scattering off the nucleon, and describe the recoil response of the target nucleon at a given energy scale. GEN-II is a double polarized semi-exclusive beam target asymmetry (BTA) experiment, seeking to measure the electric form factor of the neutron,¿¿ ¿,at three new values of squared four-momentum transfer¿2 =2.92,6.74and9.82GeV². The latter two points being at record high ¿2. The form factor is determined through measuring the BTA of quasielliptical scattering of a neutron from a polarized nuclear target. The experiment utilized the CEBAF accelerator to produce longitudinally polarized electrons up to ~85% polarization, which were scattered off neutrons within a novel polarized helium-3 (³He) target. This new polarized ³He target was employed by building on the technology of its precursors which existed in similar preceding experiments. This target was designed to operate at the high luminosities typical of Hall A, and reached a record breaking combination of polarization and beam intensity known as figure of merit, three times larger than those predecessors. The SBS collaboration designed and constructed two brand new high acceptance spectrometers for these experiments, an electron arm named Bigbite (BB) and a hadron arm named Super Bigbite. Both spectrometers featured a large acceptance EM dipole magnet, and complementary detector systems. The electron arm contained gaseous electronmultipliers(GEMs) which were used for high precision tracking of the scattered electrons, a heavy gas cherenkov (GRINCH) which was used for PID between electrons and pions, a plastic i ii scintillator timing hodoscope to provide high resolution timing of the start of events, and a pair of EM calorimeters (BBCal) which provided energy measurements of detected particles, and provided the experimental trigger. The hadron arm also contained a system of GEMs which will be utilized for future SBS experiments, and a hadron calorimeter designed to provide position, timing and energy measurements of the recoiling nucleon. The calibration of all detector subsystems, beam and target data is discussed, with a focus on novel timing calibrations to the hodoscope and hadron calorimeter. An analysis of selecting quasielliptical events and suppressing background contributions from a number of sources which contaminate the final event sample is given. The largest irreducible backgrounds are found to be from misidentified protons, timing accidentals and inelastic events. The physical asymmetry is measured and used to extract a value for the form factor ratio ¿¿ ¿/¿¿ ¿. High precision ¿2 data for ¿¿ ¿ is used to then extract ¿¿ ¿. This work finds at ¿2 = 2.92 GeV2 that ¿¿ ¿ = 0.0129+0.0019 -0.0020. This result is in statistical agreement with existing fits to world data, and predictions from the constituent quark model and Dyson–Schwinger equations, in this region of ¿2.
In this overview talk, I will present the current status of lattice QCD calculations of the nucleon form factors. Just recently, Lattice QCD has become capable of realistic calculations of nucleon structure with physical values of light quark masses. Values of nucleon vector (electromagnetic) form factors and nucleon radii have been successfully reproduced on a lattice. I will present this and other results, as well as discuss recent developments and challenges to further improving the systematic precision of nucleon structure calculations.
The Super BigBite Spectrometer (SBS) program in Experimental Hall A of Jefferson Lab is a series of high-precision, large ?2 , electromagnetic form factor experiments. GMn and nTPE were the first two experiments of the SBS program and ran from Oc?tober 2021 through February 2022. Both experiments detect neutron-tagged ?(?, ???) and proton-tagged ?(?, ???) quasi-elastic electrons scattering from a deuterium tar?get. The GMn experiment is a measurement of the magnetic form factor of the neutron, ?? ?, via the ratio method over a ?2 range of 3.5 to 13.5 (GeV/c)2 . The nTPE experiment ran in-parallel with the GMn experiment and shared an overlap?ping kinematic point with GMn. nTPE extends the GMn experiment to assess the differences between Rosenbluth Slop and the single-photon exchange approximation. The nTPE experiment had two kinematic settings corresponding to different electron scatting angles at a fixed ?2 of 4.5 (GeV/c)? . Comparisons of nucleon form factor ratio measurements acquired through polarization transfer and LT separation reveal discrepancies as ?2 increases. Two-photon exchange is strongly favored as the reason for this discrepancy. ?? ? has been extracted at two kinematic settings corresponding to ?2 values of 3.0 and 4.5 (GeV/c)2 . Additionally, I will present an assessment of the differences between Rosenbluth Separation and single-photon exchange measure?ments.