Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm

We present a new measurement of the positive muon magnetic anomaly, a_{μ}≡(g_{μ}-2)/2, from the Fermilab Muon g-2 Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω[over ˜]_{p}^{'}, and of the anomalous precession frequency corrected for beam dynamics effects, ω_{a}. From the ratio ω_{a}/ω[over ˜]_{p}^{'}, together with precisely determined external parameters, we determine a_{μ}=116 592 057(25)×10^{-11} (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a_{μ}(FNAL)=116 592 055(24)×10^{-11} (0.20 ppm). The new experimental world average is a_{μ}(exp)=116 592 059(22)×10^{-11} (0.19 ppm), which represents a factor of 2 improvement in precision.

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm

We present the first results of the Fermilab National Accelerator Laboratory (FNAL) Muon g-2 Experiment for the positive muon magnetic anomaly a_{μ}≡(g_{μ}-2)/2. The anomaly is determined from the precision measurements of two angular frequencies. Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency ω_{a} between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring. The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ω[over ˜]_{p}^{'} in a spherical water sample at 34.7 °C. The ratio ω_{a}/ω[over ˜]_{p}^{'}, together with known fundamental constants, determines a_{μ}(FNAL)=116 592 040(54)×10^{-11} (0.46 ppm). The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement. After combination with previous measurements of both μ^{+} and μ^{-}, the new experimental average of a_{μ}(Exp)=116 592 061(41)×10^{-11} (0.35 ppm) increases the tension between experiment and theory to 4.2 standard deviations.

Revealing Color Forces with Transverse Polarized Electron Scattering

The Spin Asymmetries of the Nucleon Experiment measured two double spin asymmetries using a polarized proton target and polarized electron beam at two beam energies, 4.7 and 5.9 GeV. A large-acceptance open-configuration detector package identified scattered electrons at 40° and covered a wide range in Bjorken x (0.3<x<0.8). Proportional to an average color Lorentz force, the twist-3 matrix element, d[over ˜]_{2}^{p}, was extracted from the measured asymmetries at Q^{2} values ranging from 2.0 to 6.0  GeV^{2}. The data display the opposite sign compared to most quark models, including the lattice QCD result, and an unexpected scale dependence. Furthermore, when combined with the neutron data in the same Q^{2} range the results suggest a flavor independent average color Lorentz force.

A glimpse of gluons through deeply virtual compton scattering on the proton

The internal structure of nucleons (protons and neutrons) remains one of the greatest outstanding problems in modern nuclear physics. By scattering high-energy electrons off a proton we are able to resolve its fundamental constituents and probe their momenta and positions. Here we investigate the dynamics of quarks and gluons inside nucleons using deeply virtual Compton scattering (DVCS)-a highly virtual photon scatters off the proton, which subsequently radiates a photon. DVCS interferes with the Bethe-Heitler (BH) process, where the photon is emitted by the electron rather than the proton. We report herein the full determination of the BH-DVCS interference by exploiting the distinct energy dependences of the DVCS and BH amplitudes. In the regime where the scattering is expected to occur off a single quark, measurements show an intriguing sensitivity to gluons, the carriers of the strong interaction.

Rosenbluth Separation of the π^{0} Electroproduction Cross Section

We present deeply virtual π^{0} electroproduction cross-section measurements at x_{B}=0.36 and three different Q^{2} values ranging from 1.5 to 2  GeV^{2}, obtained from Jefferson Lab Hall A experiment E07-007. The Rosenbluth technique is used to separate the longitudinal and transverse responses. Results demonstrate that the cross section is dominated by its transverse component and, thus, is far from the asymptotic limit predicted by perturbative quantum chromodynamics. Nonetheless, an indication of a nonzero longitudinal contribution is provided by the measured interference term σ_{LT}. Results are compared with several models based on the leading-twist approach of generalized parton distributions (GPDs). In particular, a fair agreement is obtained with models in which the scattering amplitude includes convolution terms of chiral-odd (transversity) GPDs of the nucleon with the twist-3 pion distribution amplitude. This experiment, together with previous extensive unseparated measurements, provides strong support to the exciting idea that transversity GPDs can be accessed via neutral pion electroproduction in the high-Q^{2} regime.

Measurement of the Target-Normal Single-Spin Asymmetry in Quasielastic Scattering from the Reaction (3)He(↑)(e,e')

We report the first measurement of the target single-spin asymmetry, A(y), in quasielastic scattering from the inclusive reaction (3)He(↑)(e,e') on a (3)He gas target polarized normal to the lepton scattering plane. Assuming time-reversal invariance, this asymmetry is strictly zero for one-photon exchange. A nonzero A(y) can arise from the interference between the one- and two-photon exchange processes which is sensitive to the details of the substructure of the nucleon. An experiment recently completed at Jefferson Lab yielded asymmetries with high statistical precision at Q(2)=0.13, 0.46, and 0.97  GeV(2). These measurements demonstrate, for the first time, that the (3)He asymmetry is clearly nonzero and negative at the 4σ-9σ level. Using measured proton-to-(3)He cross-section ratios and the effective polarization approximation, neutron asymmetries of -(1-3)% were obtained. The neutron asymmetry at high Q(2) is related to moments of the generalized parton distributions (GPDs). Our measured neutron asymmetry at Q(2)=0.97  GeV(2) agrees well with a prediction based on two-photon exchange using a GPD model and thus provides a new, independent constraint on these distributions.

Measurement of double-polarization asymmetries in the quasielastic (3)He[→](e[→],e(')d) process

We present a precise measurement of double-polarization asymmetries in the ^{3}He[over →](e[over →],e^{'}d) reaction. This particular process is a uniquely sensitive probe of hadron dynamics in ^{3}He and the structure of the underlying electromagnetic currents. The measurements have been performed in and around quasielastic kinematics at Q^{2}=0.25(GeV/c)^{2} for missing momenta up to 270  MeV/c. The asymmetries are in fair agreement with the state-of-the-art calculations in terms of their functional dependencies on p_{m} and ω, but are systematically offset. Beyond the region of the quasielastic peak, the discrepancies become even more pronounced. Thus, our measurements have been able to reveal deficiencies in the most sophisticated calculations of the three-body nuclear system, and indicate that further refinement in the treatment of their two-and/or three-body dynamics is required.

Precision measurement of the neutron twist-3 matrix element d(2)(n): probing color forces

Double-spin asymmetries and absolute cross sections were measured at large Bjorken x  (0.25≤x≤0.90), in both the deep-inelastic and resonance regions, by scattering longitudinally polarized electrons at beam energies of 4.7 and 5.9 GeV from a transversely and longitudinally polarized (3)He target. In this dedicated experiment, the spin structure function g(2)((3)He) was determined with precision at large x, and the neutron twist-3 matrix element d(2)(n) was measured at ⟨Q(2)⟩ of 3.21 and 4.32  GeV(2)/c(2), with an absolute precision of about 10(-5). Our results are found to be in agreement with lattice QCD calculations and resolve the disagreement found with previous data at ⟨Q(2)⟩=5  GeV(2)/c(2). Combining d(2)(n) and a newly extracted twist-4 matrix element f(2)(n), the average neutron color electric and magnetic forces were extracted and found to be of opposite sign and about 30  MeV/fm in magnitude.

Probing the repulsive core of the nucleon-nucleon interaction via the (4)He(e,e'pN) triple-coincidence reaction

We studied simultaneously the (4)He(e,e'p), (4)He(e,e'pp), and (4)He(e,e'pn) reactions at Q(2)=2(GeV/c)(2) and x(B)>1, for an (e,e'p) missing-momentum range of 400 to 830  MeV/c. The knocked-out proton was detected in coincidence with a proton or neutron recoiling almost back to back to the missing momentum, leaving the residual A=2 system at low excitation energy. These data were used to identify two-nucleon short-range correlated pairs and to deduce their isospin structure as a function of missing momentum, in a region where the nucleon-nucleon (NN) force is expected to change from predominantly tensor to repulsive. The abundance of neutron-proton pairs is reduced as the nucleon momentum increases beyond ∼500  MeV/c. The extracted fraction of proton-proton pairs is small and almost independent of the missing momentum. Our data are compared with calculations of two-nucleon momentum distributions in (4)He and discussed in the context of probing the elusive repulsive component of the NN force.

Measurements of parity-violating asymmetries in electron-deuteron scattering in the nucleon resonance region

We report on parity-violating asymmetries in the nucleon resonance region measured using inclusive inelastic scattering of 5-6 GeV longitudinally polarized electrons off an unpolarized deuterium target. These results are the first parity-violating asymmetry data in the resonance region beyond the Δ(1232). They provide a verification of quark-hadron duality-the equivalence of the quark- and hadron-based pictures of the nucleon-at the (10-15)% level in this electroweak observable, which is dominated by contributions from the nucleon electroweak γZ interference structure functions. In addition, the results provide constraints on nucleon resonance models relevant for calculating background corrections to elastic parity-violating electron scattering measurements.

Measurement of the neutron radius of 208Pb through parity violation in electron scattering

We report the first measurement of the parity-violating asymmetry A(PV) in the elastic scattering of polarized electrons from 208Pb. A(PV) is sensitive to the radius of the neutron distribution (R(n)). The result A(PV)=0.656±0.060(stat)±0.014(syst) ppm corresponds to a difference between the radii of the neutron and proton distributions R(n)-R(p)=0.33(-0.18)(+0.16) fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.