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4.5 Fundamental Interactions
of maximal parity violation in low energy β decay. The
combination of the neutron lifetime, τ n , with the electron
asymmetry, A n , and the neutrino asymmetry, B n , in neutron
decay has now reached a comparable sensitivity. All
measured quantities have reached a level of precision
of a few parts in 10 -3 and all measurements so far are
consistent with the SM predictions.
Within general left-right symmetric extensions of the
SM, results obtained from low-energy β decays, from
muon decay and from direct searches for new heavy
charged bosons at colliders complement each other
due to their different sensitivities to the parameters.
Moreover, parity restoration mechanisms which involve
quark–lepton interactions cannot directly be probed in
the purely leptonic muon decay. In such a context any
new effort at low energies to search for the effects of
new bosons in the mass range between 500 GeV/c 2 and
1 TeV/c 2 , is highly valuable.
In neutron decay the most recent results for the β and
neutrino asymmetries obtained with PERKEO-II feature
several times smaller corrections than previous results
and new measurements are being prepared (e.g. with
the new PERC facility). Efforts are also ongoing and
planned in the US, at LANSCE (Los Alamos), NIST and
the SNS (Oak Ridge). Solving the current issue of the
neutron lifetime is therefore of crucial importance for
establishing more stringent limits for new physics.
In nuclear β decay the precision of β asymmetry
measurements is improving and a first measurement
of the neutrino asymmetry has recently been made. In
both cases still higher precision and more precise determination
of the nuclear polarisation are highly desirable.
As demonstrated earlier the use of atom and ion traps
could contribute significantly to this as effects of scattering
are strongly reduced.
This would then allow measurements of the longitudinal
polarisation of positrons from polarized nuclei
also to be made, which can be very sensitive to V+A
interactions. For well chosen transitions sensitivities to
right-handed bosons with a mass of about 500 GeV/c 2
and beyond are feasible, but are presently hampered
by scattering effects on insufficient nuclear polarisation.
Further efforts and new initiatives oriented towards the
production and storage in atom or ion traps of highly
polarised, high intensity and high purity sources are thus
to be pursued. In this context, new and more accurate
methods to precisely determine the nuclear polarisation
should be developed as well.
β decay correlation coefficients
In β decay the neutron or nuclear with spin J emits an electron (or positron) with momentum p and spin sigma
and an electron (anti)neutrino with momentum q. The decay probability can be written as
d 2 W p̅ · q̑ m e p̅ p̅ x q̑ p̅ p̅
⎯⎯ ∼ 1 + a ⎯⎯ + bΓ ⎯ + 〈J〉 · [ A ⎯ + B q̑ + D ⎯ ] + 〈σ〉 · [ G ⎯ + Q〈J〉 + R〈J〉 x ⎯ ]
dΩ e dΩ v E E E E E E
where the correlation coefficients, i.e. a, b, A, B, D, G, Q and R, depend on the coupling constants and on the
nuclear matrix elements. For pure Fermi or Gamow-Teller β transitions these coefficients are independent of the
matrix elements and thus, to first order, of nuclear structure effects, and depend only on the spin of the initial
and final states. The description of β decay, and of the weak interaction in general, in terms of exclusively vector
(V) and axial-vector (A) interactions, i.e. the V-A theory as part of the SM, found its origin in measurements of the
beta-neutrino correlation coefficient a. The discovery of parity violation was made from the observation that the
beta asymmetry correlation coefficient A is non-zero. In the SM the Fierz interference term b vanishes, while the
time reversal violating correlations characterized by the D and R coefficients should be zero, apart from small
and calculable final state effects. Selecting the appropriate initial and final states one can select either the V or
A interaction in Fermi or Gamow-Teller β transitions, respectively, allowing one to search for as yet unobserved
scalar (S) or tensor (T) contributions by observing the characteristic decay.
In practice the neutrino momentum q cannot be measured. It is therefore necessary
to measure the recoil momentum of the nucleus to determine the full correlation. The
accuracy of such measurements is hampered by the low kinetic energies, E recoil , of the
recoiling nucleus. This has become possible recently by using atom and ion traps to
store the radioactive nuclei in vacuum, allowing one to accurately measure the direction
and energy of the recoil.
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