Accessing interior magnetic field vector components in neutron electric dipole moment experiments via exterior measurements, I. Boundary-value techniques

We propose a new concept for determining the interior magnetic field vector components in neutron electric dipole moment experiments. If a closed three-dimensional boundary surface surrounding the fiducial volume of an experiment can be defined such that its interior encloses no currents or sources of magnetization, each of the interior vector field components and the magnetic scalar potential will satisfy a Laplace equation. Therefore, if either the vector field components or the normal derivative of the scalar potential can be measured on the surface of this boundary, thus defining a Dirichlet or Neumann boundary-value problem, respectively, the interior vector field components or the scalar potential (and, thus, the field components via the gradient of the potential) can be uniquely determined via solution of the Laplace equation. We discuss the applicability of this technique to the determination of the interior magnetic field components during the operating phase of neutron electric dipole moment experiments when it is not, in general, feasible to perform direct in situ measurements of the interior field components. We also study the specifications that a vector field probe must satisfy in order to determine the interior vector field components to a certain precision. The technique we propose here may also be applicable to experiments requiring monitoring of the vector magnetic field components within some closed boundary surface, such as searches for neutron-antineutron oscillations along a flight path or measurements in storage rings of the muon anomalous magnetic moment $g-2$ and the proton electric dipole moment.

Comparison of magnetic field uniformities for discretized and finite-sized standard $costheta$, solenoidal, and spherical coils

A significant challenge for experiments requiring a highly uniform magnetic field concerns the identification and design of a discretized and finite-sized magnetic field coil of minimal size. In this work we compare calculations of the magnetic field uniformities and field gradients for three different standard (i.e., non-optimized) types of coils: $costheta$, solenoidal, and spherical coils. For an experiment with a particular requirement on either the field uniformity or the field gradient, we show that the volume required by a spherical coil form which satisfies these requirements can be significantly less than the volumes required by $costheta$ and solenoidal coil forms.

Framework for maximum likelihood analysis of neutron beta decay observables to resolve the limits of the V-A law

We assess the ability of future neutron beta decay measurements of up to O(10^{-4}) precision to falsify the standard model, particularly the V-A law, and to identify the dynamics beyond it. To do this, we employ a maximum likelihood statistical framework which incorporates both experimental and theoretical uncertainties. Using illustrative combined global fits to Monte Carlo pseudodata, we also quantify the importance of experimental measurements of the energy dependence of the angular correlation coefficients as input to such efforts, and we determine the precision to which ill-known second-class hadronic matrix elements must be determined in order to exact such tests.

Measurement of the neutron $beta$-asymmetry parameter $A_0$ with ultracold neutrons

We present a detailed report of a measurement of the neutron $beta$-asymmetry parameter $A_0$, the parity-violating angular correlation between the neutron spin and the decay electron momentum, performed with polarized ultracold neutrons (UCN). UCN were extracted from a pulsed spallation solid deuterium source and polarized via transport through a 7-T magnetic field. The polarized UCN were then transported through an adiabatic-fast-passage spin-flipper field region, prior to storage in a cylindrical decay volume situated within a 1-T $2 times 2pi$ solenoidal spectrometer. The asymmetry was extracted from measurements of the decay electrons in multiwire proportional chamber and plastic scintillator detector packages located on both ends of the spectrometer. From an analysis of data acquired during runs in 2008 and 2009, we report $A_0 = -0.11966 pm 0.00089_{-0.00140} ^{+0.00123}$, from which we extract a value for the ratio of the weak axial-vector and vector coupling constants of the nucleon, $lambda = g_A/g_V = -1.27590 pm 0.00239_{-0.00377}^{+0.00331}$. Complete details of the analysis are presented.

Impact of motion along the field direction on geometric-phase-induced false electric dipole moment signals

Geometric-phase-induced false electric dipole moment (EDM) signals, resulting from interference between magnetic field gradients and particle motion in electric fields, have been studied extensively in the literature, especially for neutron EDM experiments utilizing stored ultracold neutrons and co-magnetometer atoms. Previous studies have considered particle motion in the transverse plane perpendicular to the direction of the applied electric and magnetic fields. We show, via Monte Carlo studies, that motion along the field direction can impact the magnitude of this false EDM signal if the wall surfaces are rough such that the wall collisions can be modeled as diffuse, with the results dependent on the size of the storage cells dimension along the field direction.

A solenoidal electron spectrometer for a precision measurement of the neutron $beta$-asymmetry with ultracold neutrons

We describe an electron spectrometer designed for a precision measurement of the neutron $beta$-asymmetry with spin-polarized ultracold neutrons. The spectrometer consists of a 1.0-Tesla solenoidal field with two identical multiwire proportional chamber and plastic scintillator electron detector packages situated within 0.6-Tesla field-expansion regions. Select results from performance studies of the spectrometer with calibration sources are reported.