A New Experiment to Measure the Electron-Antineutrino (a) Coefficient in Neutron Decay

Collaborators

M.S. Dewey, A.K. Thompson - NIST
A.K. Komives - DePauw University
F.E. Wietfeldt, C. Trull - Tulane University
B.G. Yerozolimsky, L. Goldin - Harvard University
Yu. Mostovoy, S. Balashov - Kurchatov Institute (Moscow)
G. Jones, R. Anderman, B. Collett - Hamilton College
M. Leuschner - University of New Hampshire

Left to right; A. Day-Nitkin(student intern, Wootton H.S), M.S. Dewey, F.E. Wietfeldt, R. Anderman, S. Balashov,
B. Yerozolimsky, Y. Mostovoy, L. Goldin

A New Experiment to Measure the Electron-Antineutrino (a) Coefficient in Neutron Decay

A free neutron will beta decay, with a lifetime of about 900 seconds, into a proton, electron, and antineutrino. This is one of the most fundamental processes in particle physics and it provides a rich laboratory for exploring the fundamental forces of nature. The coefficients that describe the angular correlations between the emitted electron and antineutrino determine the weak coupling constants g_A and g_V. They are sensitive to new physical forces and phenomena that have been theoretically proposed but not yet discovered, such as supersymmetric particles, scalar and tensor weak forces, and right-handed weak forces.

The observable of interest in this experiment is the electron-antineutrino angular correlation coefficient, also known as the "a" coefficient. It quantifies the correlation of the form:

$dN=F(E_e) [1+a \frac{\textstyle{p_e\cdot p_\nu}}{\textstyle{E_e E_\nu}}]$

Various tests of the Standard Model can be made using the neutron decay parameters. For example, their values can be related to the strength of hypothetical right-handed weak forces and scalar and tensor forces. At the present level of precision there is no evidence for these forces, but as the experimental technology improves and more precise measurements are made, a discrepancy may eventually emerge from these results, indicating the presence of new physics. So the neutron decay system acts as a low-energy frontier of particle physics which is complementary to the high-energy frontier of supercollider physics.

The coefficient a has been the most difficult to measure, and therefore is the least precisely-known, of the neutron decay parameters The antineutrino cannot be detected, but the influence of its momentum can be felt on the other particles (electron and proton) which are detected. The most obvious way to determine the value of a is to measure the recoil proton energy spectrum. The proton energies are very low (maximum is 751 eV), so a precise determination of the shape of the energy spectrum is very difficult and prone to systematic error. The best measurement so far, by Stratowa, Dobrozemsky, and Weinzierl was published in 1978. The result was a = -0.102 ± 0.005. The quoted uncertainty is dominated by the estimated systematic error. This result required the proton energy spectral shape to be measured to a precision of less than 0.5 %, a phenomenal technical feat. The fact that this measurement has not been improved over the last twenty years is a testament to its difficulty.

Description of the Experiment

We have recently devised a new approach to the measurement of a. It relies on the construction of an asymmetry that directly yields a, without requiring precise spectroscopy. Therefore, it is systematically much cleaner and has the potential for a much improved determination of a. The basic scheme of this new method is shown in Figure 1. A proton detector and electron detector are positioned on either side of a highly-collimated cold neutron beam. A long solenoid, aligned to the axis of the detectors, is located between the beam and proton detector. Coincidence detection of the electron and proton is possible for neutrons that decay in the indicated decay region. The solenoid produces a central magnetic field B. Inside the solenoid are a series of precisely aligned circular apertures of radius r. A proton's trajectory inside the solenoid is helical, with radius R proportional to its transverse momentum. Only those decay protons with transverse momentum below (eBr/c), or less depending on the position of the decay vertex, can pass unobstructed through the solenoid and be detected. A pair of fine wire grids produce an electric field in the decay region, directing all decay protons toward the proton detector regardless of their initial axial momenta.

Figure 1

The determination of a from this scheme is best illustrated by the momentum-space diagram shown in Figure 2. The lower dashed line indicates the solenoid-detector axis, and the large black dot is the position of the neutron decay. To simplify this illustration I will assume that the decay position was on axis, although in general this will not be the case. The cold neutron's kinetic energy is very small (about 0.003 eV) so it can be treated as decaying from rest. A typical decay electron's momentum is shown as p_e. Consider the decay proton momentum. The solenoid and aperture arrangement will allow any proton whose transverse momentum is less than (eBr/2c) to be detected. The electric field ensures that any value of the axial momentum will be accepted. Therefore the proton's momentum acceptance is described by the lower circular cylinder shown in the figure. Any proton whose momentum vector terminates inside this cylinder is detected. Now consider the antineutrino. It is not detected, but conservation of transverse momentum requires that the antineutrino momentum vector (p) terminate in a second cylinder (shaded in the figure) which is identical to the lower cylinder and translated by -p_e. Also, the decay proton's kinetic energy can be neglected, so conservation of energy fixes the length of the antineutrino momentum vector to be $|p_\nu|= Q/c - \sqrt{p_e^2 + m_e^2c^2}$ . Therefore, for any neutron decay where both the electron and proton are detected, the possible antineutrino momenta must fall into one of two kinematically distinct groups, indicated in the figure by the regions labeled I and II. These two regions are formed by the intersections of the upper cylinder with a spherical shell of radius |p|. The detection solid angles subtended by the two regions are equal in size, so if a is zero there is equal probability for the antineutrino to be in either group. Any significant difference between the number of events in each group must be due to the electron-antineutrino correlation given by a. For those events where the decay vertex is off axis, the cylinders have elliptical, rather than circular, cross-sections, but the above analysis and its conclusions are the same.

Figure 2

The two groups of coincidence events, corresponding to regions I and II, can be experimentally distinguished in a very simple way. The decay electrons have velocities close to the speed of light, and so are detected a few nanoseconds after the neutron decays. The protons however are much slower and require several microseconds to reach the proton detector. The time between electron and proton detection can be easily measured using standard time-of-flight methods. Furthermore, the protons associated with group I events are distinctly faster than those of group II events, due to conservation of momentum. So by recording for each event the electron energy and the proton time-of-flight we obtain, after many decays, N_I events in group I and N_II events in group II for each electron energy. It is then straightforward to show that a is given by:

$a(E_e) = \frac{\textstyle{\rm I}}{\textstyle{\nu_e}} \, K(E_e) \frac{\textstyle{N_{\rm I}-N_{\rm II}}}{\textstyle{N_{\rm I}+N_{\rm II}}}$

where _e is the electron velocity corresponding to energy E_e. The values of a obtained for each energy E_e are then statistically combined to obtain the final value of a. The quantity K(E_e) is an instrumental constant that depends on the shape of the magnetic field and arrangement of the apertures. In this experiment we hope to measure a to a precision better than 1 %.

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Inquiries or comments: david.gilliam@nist.gov
Online: October 2003