A polarized neutron beam and the Nab spectrometer (pNAB) at the Spallation Neutron Source will enable simultaneous measurements of the beta (A) and neutrino (B) asymmetries in free neutron decay. Combined Nab and pNAB measurements of the correlation parameters a, A, and B will determine the axial-vector to vector coupling ratio in the weak interaction with a precision of about 0.025%. Neutrons are polarized with supermirror polarizers and analyzed with polarized 3He. Together with precise neutron lifetime measurements, these results will provide the most stringent test of Cabibbo-Kobayashi-Maskawa (CKM) matrix unitarity from free neutron decay.

The past five years have brought significant new results on the muon magnetic anomaly, a_μ= (g_μ- 2)/2, and on the hadronic vacuum polarization (HVP) contribution dominating the uncertainty Δa_μ. Serious tension has emerged between the experimental and standard model(SM) values for a_μ, as well as between the SM and the first precise lattice QCD values. We review the current experimental and theoretical status of a_μ, along with the prospects for new results,focusing on MUonE,a new experiment at CERN, aiming to evaluate the leading order contribution to a(HVP) in a direct measurement of muonic Bhabha scattering.

The current three sigma tension in the unitarity test of the Cabbibo-Kobayashi-Maskawa (CKM) matrix is a notable problem with the Standard Model of elementary particle physics. A long-standing goal of the study of free neutron beta decay is to better determine the CKM element Vud through measurements of the neutron lifetime and a decay correlation parameter. The Nab collaboration intends to measure a, the neutrino-electron correlation, with accuracy sufficient for a competitive evaluation of Vud based on neutron decay data alone. This paper gives a status report and an outlook.

Fundamental neutron physics, combining precision measurements and theory, probes particle physics at short range with reach well beyond the highest energies probed by the LHC. Significant US efforts are underway that will probe BSM CP violation with orders of magnitude more sensitivity, provide new data on the Cabibbo anomaly, more precisely measure the neutron lifetime and decay, and explore hadronic parity violation. World-leading results from the US Fundamental Neutron Physics community since the last Long Range Plan, include the world's most precise measurement of the neutron lifetime from UCN$\tau$, the final results on the beta-asymmetry from UCNA and new results on hadronic parity violation from the NPDGamma and n-${^3}$He runs at the FNPB (Fundamental Neutron Physics Beamline), precision measurement of the radiative neutron decay mode and n-${}^4$He at NIST. US leadership and discovery potential are ensured by the development of new high-impact experiments including BL3, Nab, LANL nEDM and nEDM@SNS. On the theory side, the last few years have seen results for the neutron EDM from the QCD $\theta$ term, a factor of two reduction in the uncertainty for inner radiative corrections in beta-decay which impacts CKM unitarity, and progress on {\it ab initio} calculations of nuclear structure for medium-mass and heavy nuclei which can eventually improve the connection between nuclear and nucleon EDMs. In order to maintain this exciting program and capitalize on past investments while also pursuing new ideas and building US leadership in new areas, the Fundamental Neutron Physics community has identified a number of priorities and opportunities for our sub-field covering the time-frame of the last Long Range Plan (LRP) under development. This white paper elaborates on these priorities.

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.

This whitepaper presents the research priorities decided on by attendees of the 2022 Town Meeting for Fundamental Symmetries, Neutrons and Neutrinos, which took place December 13-15, 2022 in Chapel Hill, NC, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 275 scientists registered for the meeting. The whitepaper makes a number of explicit recommendations and justifies them in detail.

We report a measurement of two energy-weighted gamma cascade angular distributions from polarized slow neutron capture on the Cl-35 nucleus, one parity-odd correlation proportional to (s) over right arrown.(k) over right arrow (gamma) and one parity-even correlation proportional to (s) over right arrown.(k) over right arrown x (k) over right arrow (gamma). A parity-violating asymmetry can appear in this reaction due to the weak nucleon-nucleon interaction, which mixes opposite parity S-and P-wave levels in the excited compound Cl-36 nucleus formed upon slow neutron capture. If parity-violating (PV) and parity-conserving (PC) terms both exist, the measured differential cross section can be related to them via d sigma sigma/d Omega proportional to 1 +A(gamma,PV) cos theta +A(gamma,PC) sin theta. The PV and PC asymmetries for energy-weighted gamma cascade angular distributions for polarized slow neutron capture on Cl-35 averaged over the neutron energies from 2.27-9.53 meV were measured to be A(gamma,PV) = (-23.9 +/- 0.7) x 10(-6) and A(gamma,PC) = (0.1 +/- 0.7) x 10(-6). These results are consistent with previous experimental results. Systematic errors were quantified and shown to be small compared to the statistical error. These asymmetries in the angular distributions of the gamma rays emitted from the capture of polarized neutrons in Cl-35 were used to verify the operation and data analysis procedures for the NPDGamma experiment, which measured the parity-odd asymmetry in the angular distribution of gamma s from polarized slow neutron capture on protons.

The physics motivation and the conceptual design of the PIONEER experiment, a next-generation rare pion decay experiment testing lepton flavor universality and CKM unitarity, are described. Phase I of the PIONEER experiment, which was proposed and approved at Paul Scherrer Institut, aims at measuring the charged-pion branching ratio to electrons vs.\ muons, $R_{e/\mu}$, 15 times more precisely than the current experimental result, reaching the precision of the Standard Model (SM) prediction at 1 part in $10^4$. Considering several inconsistencies between the SM predictions and data pointing towards the potential violation of lepton flavor universality, the PIONEER experiment will probe non-SM explanations of these anomalies through sensitivity to quantum effects of new particles up to the PeV mass scale. The later phases of the PIONEER experiment aim at improving the experimental precision of the branching ratio of pion beta decay (BRPB), $\pi^+\to \pi^0 e^+ \nu (\gamma)$, currently at $1.036(6)\times10^{-8}$, by a factor of three (Phase II) and an order of magnitude (Phase III). Such precise measurements of BRPB will allow for tests of CKM unitarity in light of the Cabibbo Angle Anomaly and the theoretically cleanest extraction of $|V_{ud}|$ at the 0.02\% level, comparable to the deduction from superallowed beta decays.

A next-generation rare pion decay experiment, PIONEER, is strongly motivated by several inconsistencies between Standard Model (SM) predictions and data pointing towards the potential violation of lepton flavor universality. It will probe non-SM explanations of these anomalies through sensitivity to quantum effects of new particles even if their masses are at very high scales. Measurement of the charged-pion branching ratio to electrons vs. muons Re/μ is extremely sensitive to a wide variety of new physics effects. At present, the SM prediction for Re/μ is known to 1 part in 104, which is 15 times more precise than the current experimental result. An experiment reaching the theoretical accuracy will test lepton flavor universality at an unprecedented level, probing mass scales up to the PeV range. Measurement of the rare process of pion beta decay, π+ → π0e+ν(γ), with 3 to 10-fold improvement in sensitivity, will determine |Vud| in a theoretically pristine manner and test CKM unitarity, which is very important in light of the recently emerged tensions. In addition, various exotic rare decays involving sterile neutrinos and axions will be searched for with unprecedented sensitivity. The experiment design benefits from experience

We present the first measurement of dihadron angular correlations in electron-nucleus scattering. The data were taken with the CLAS detector and a 5.0 GeV electron beam incident on deuterium, carbon, iron, and lead targets. Relative to deuterium, the nuclear yields of charged-pion pairs show a strong suppression for azimuthally opposite pairs, no suppression for azimuthally nearby pairs, and an enhancement of pairs with large invariant mass. These effects grow with increased nuclear size. The data are qualitatively described by the gibuu model, which suggests that hadrons form near the nuclear surface and undergo multiple scattering in nuclei.These results show that angular correlation studies can open a new way to elucidate how hadrons form and interact inside nuclei.

In 2018, a test run with muons in the North Area at CERN was performed, running parasitically downstream of the COMPASS spectrometer. The aim of the test was to investigate the elastic interactions of muons on atomic electrons, in an experimental configuration similar to the one proposed by the project MUonE, which plans to perform a very precise measurement of the differential cross-section of the elastic interactions. COMPASS was taking data with a 190 GeV π beam, stopped in a tungsten beam dump: the muons from these π decays passed through a setup including a graphite target followed by 10 planes of Si tracker and a BGO crystal electromagnetic calorimeter placed at the end of the tracker. The elastic scattering events were selected and analysed, and compared to expectations from MonteCarlo simulation. The agreement found was satisfactory and demonstrated that measuring the angles of the outgoing particles, a clean sample of elastic interaction could be identified.

In common with a number of simple processes involving elementary particles, charged pion decays are profoundly shaped by applicable Standard Model (SM) symmetries and properties. Given the highly precise SM theoretical description, pion decays are used as selective probes of SM parameters, and of possible SM extensions. The PEN experiment at PSI is studying the \pi^+ \to e^+\nu_e(\gamma)π+→e+νe(γ), or \pi_{e2(\gamma)}πe2(γ) decay. The primary goal is to reach the relative precision of 5 \times 10^{-4}5×10−4 in R_{e/\mu}^\piRe/μπ, the branching ratio for \pi_{e2(\gamma)}πe2(γ) decay. We review the PEN research program, its present status, and prospects.

As the lightest meson, pion offers unique opportunities for measuring parameters and testing limits of the Standard Model (SM). The PiBeta experiment, carried out at PSI, focused on SM tests accessible through the pion beta, \pi^+ \to \pi^0e^+\nu_e(\gamma)π+→π0e+νe(γ), and electronic radiative, \pi^+ \to e^+\nu_e\gammaπ+→e+νeγ, decay channels. We review the PiBeta experiment, and update the pion beta decay branching ratio B^{\text{exp}}_{\pi\beta}=1.038(6)_{\text{tot}}\times10^{-8}Bπβexp=1.038(6)tot×10−8, along with the corresponding derived value of the Cabibbo-Kobayashi-Maskawa matrix element V_{ud} = 0.9738(28)Vud=0.9738(28).

The international PEN collaboration aims to obtain the branching ratio for the pion electronic decay π → eνe(γ), aka πe2, to a relative precision of 5 × 10−4 or better. The PEN apparatus comprises a number of detection systems, all contributing vital information to the PEN event reconstruction. This paper discusses the design, performance, and Monte Carlo simulation of the mini time projection chamber (mTPC) used for pion, muon, and positron beam particle tracking. We also review the use of the extracted trajectory coordinates in the analysis, in particular in constructing observables critical for discriminating background processes, and in maximizing the fiducial volume of the target in which decay event vertices can be accepted for branching ratio extraction without introducing bias.

Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is one of the methods that have been used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described, and it is briefly compared with other commonly used frequency extraction methods. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytically. A method of mitigating the artifacts in the extracted phase function of an FID is discussed. Correlations between noises of the phase function samples are studied for different noise spectra. We discovered that the error covariance matrix for the extracted phase function is nearly singular and improper for constructing the χ2 used in the fitting routine. A down-sampling method for fixing the singular covariance matrix has been developed, so that the minimum χ2-fit yields properly the statistical uncertainty of the extracted frequency. Other practical methods of obtaining the statistical uncertainty are also discussed.

A first measurement of the longitudinal beam spin asymmetry ALU in the semi-inclusive electroproduction of pairs of charged pions is reported. ALU is a higher-twist observable and offers the cleanest access to the nucleon twist-3 parton distribution function e(x). Data have been collected in the Hall-B at Jefferson Lab by impinging a 5.498 GeV electron beam on a liquid-hydrogen target, and reconstructing the scattered electron and the pion pair with the CLAS detector. One-dimensional projections of the sin(phiR) moments of ALU are extracted for the kinematic variables of interest in the valence quark region. The understanding of di-hadron production is essential for the interpretation of observables in single hadron production in semi-inclusive DIS, and pioneering measurements of single spin asymmetries in di-hadron production open a new avenue in studies of QCD dynamics.

The ratio of the electric and magnetic form factor of the proton, $\mu_p G_E^p/G_M^p$, has been measured for elastic electron-proton scattering with polarized beam and target up to four-momentum transfer squared, $Q^2=5.66$ (GeV/c)$^2$ using the double spin asymmetry for target spin orientation aligned nearly perpendicular to the beam momentum direction. This measurement of $\mu_p G_E^p/G_M^p$ agrees with the $Q^2$ dependence of previous recoil polarization data and reconfirms the discrepancy at high $Q^2$ between the Rosenbluth and the polarization-transfer method with a different measurement technique and systematic uncertainties uncorrelated to those of the recoil-polarization measurements. The form factor ratio at $Q^2$=2.06 (GeV/c)$^2$ has been measured as $\mu_p G_E^p/G_M^p = 0.720 \pm 0.176_{stat} \pm 0.039_{sys}$, which is in agreement with an earlier measurement with the polarized target technique at similar kinematics. The form factor ratio at $Q^2$=5.66 (GeV/c)$^2$ has been determined as $\mu_p G_E^p/G_M^p=0.244\pm0.353_{stat}\pm0.013_{sys}$, which represents the highest $Q^2$ reach with the double spin asymmetry with polarized target to date.

A single calorimeter station for the Muon $g-2$ experiment at Fermilab includes the following subsystems: a 54-element array of PbF$_{2}$ Cherenkov crystals read out by large-area SiPMs, bias and slow-control electronics, a suite of 800 MSPS waveform digitizers, a clock and control distribution network, a gain calibration and monitoring system, and a GPU-based frontend read out through a MIDAS data acquisition environment. The entire system performance was evaluated using 2.5 - 5 GeV electrons at the End Station Test Beam at SLAC. This paper includes a description of the individual subsystems and the results of measurements of the energy response and resolution, energy-scale stability, timing resolution, and spatial uniformity. All measured performances meet or exceed the $g-2$ experimental requirements. Based on the success of the tests, the complete production of the required 24 calorimeter stations has been made and installation into the main experiment is complete. Furthermore, the calorimeter response measurements determined here informed the design of the reconstruction algorithms that are now employed in the running $g-2$ experiment.

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.

The Nab experiment will measure the ratio of the weak axial-vector and vector coupling constants λ = gA/gV with precision δλ/λ ∼ 3 × 10− 4 and search for a Fierz term bF at a level ΔbF < 10− 3. The Nab detection system uses thick, large area, segmented silicon detectors to very precisely determine the decay proton’s time of flight and the decay electron’s energy in coincidence and reconstruct the correlation between the antineutrino and electron momenta. Excellent understanding of systematic effects affecting timing and energy reconstruction using this detection system are required. To explore these effects, a series of ex situ studies have been undertaken, including a search for a Fierz term at a less sensitive level of ΔbF < 10− 2 in the beta decay of 45Ca using the UCNA spectrometer.