Neutron Decay

We examine the structure of the charged weak interaction using cold, polarized and free neutrons. These decay into an electron, a proton and an anti-electronneutrino with a mean lifetime of about 15 minutes. In contrast to nuclear decays, this process is not influenced by nuclear effects. Consequently this system allows measurements with very small theoretical corrections.

The Feynman-diagram of neutron beta decay is shown in the figure to the right. A down-quark changes its flavour to an up-quark emitting a W-boson. Hence, the process is sensitive to the first quark-mixing-matrix element V_ud. The full Cabibbo-Kobayashi-Maskawa (CKM) matrix is of great interest in particle physics. Its elements are obtained from beta decay (V_ud) or in high-energy physics experiments using particle accelerators. In contrast to this, neutron decay with a maximum electron energy of 782 keV is an excellent example of a system for low-energy particle physics.

For a review of the field of precision experiments on neutron decay, see Dubbers and Märkisch, Annual Review of Nuclear and Particle Science 71, 139-163 (2021), DOI: 10.1146/annurev-nucl-102419-043156 .

The transition probability of the beta decay of polarized neutrons can be parametrized using measurable quantities, the so called correlation coefficients. These correlate properties such as the momentum and spin of different particles. Some of the coefficients are (see figure on the right):

• a: correlates the momenta of electron and neutrino
• A: correlates neutron spin and electron momentum
• B: correlates neutron spin and neutrino momentum
• C: correlates neutron spin and proton momentum
• D: correlates neutron spin and the cross-product of the lepton momenta

Note that A, B and C are parity violating and a non-vanishing coefficient D would imply a broken time reversal invariance. When taking the electron spin into account, there are about a dozen such observable correlations in neutron decay.

The electron asymmetry is directly connected to λ, the ratio of the axial-vector-coupling constant g_a and the vector-coupling g_v. This is a very important quantity, governing many weak processes from particle physics to cosmology. A measurement of the beta-asymmetry correlation coefficient A combined with the the neutron lifetime gives access to the first element V_ud of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix, which is assumed to be unitary within the standard model of particle physics.

Another interesting observalble is the electron spectrum of the (polarized) decay itself: From a high precision measurement one can obtain information about small effects such as the weak magnetism (as predicted by the Conserved Vector Current (CVC) hypothesis), the Fierz interference term, or radiative corrections.