# 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 .

## Correlation Coefficients

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*. This is a very important quantity, governing many weak processes from particle physics to cosmology. A measurement of the beta-asymmetry correlation coefficient

_{v}*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.

## Standard Model Tests with PERKEO and PERC

In 2000, *V*_{ud} was determined from a PERKEO II measurement with high precision and found a 2.6 sigma deviation from unitarity (Abele 02). Since then we have performed an improved measurement with PERKEO II, verifying our result (Mund 13). The deviation from unitarity was resolved by updated values for the neutron lifetime and the CKM matrix element *V*_{us}. A measurement with current spectrometer PERKEO III eliminated leading sources of systematic error by using a pulsed neutron beam while at the same time increasing the available statistics by an order of magnitude (Märkisch 2009). The results of this measurement are currently undergoing internal review before publication.

The weak interaction is maximally parity violating (fully left handed) which is not motivated by the Standard Model. The neutrino-asymmetry coefficient *B and *the proton asymmetry coefficient *C* are sensitive to possible right-handed currents that are proposed by some theoretical models. A measurement of the neutrino asymmetry coefficient B and the proton asymmetry coefficient *C* was performed at the Institut Laue-Langevin (ILL) with the instrument PERKEO II (Schumann 07, Schumann 08). In 2014/2015 PERKEO III was again installed at the ILL with the aim to measure the proton asymmetry C in neutron beta decay, including its dependece on the proton energy.

PERKEO's successor is the Proton Electron Radiation Channel Experiment (PERC) which is currently being set-up together with the new MEPHISTO beam line for particle physics at the research reactor FRM II of the MLZ.