Parity Nonconserving Interaction Research Articles

On the renormalization of a parity non-conserving interaction

An exact formulation is given of the renormalization method in a parity non-conserving theory. Equations determining the renormalization constants are obtained and, among other things, the internal consistency of the theory is examined.

Parity conservation in strong interactions

The recent discovery that parity is not conserved in certain weak interactions has opened the question of the degree to which it is conserved in the strong interactions (internucleonic and electromagnetic). Parity non-conservation in such interactions may be detected by: (i) The violation of a selection rule which is absolute if parity is conserved. (ii) The presence of circular polarization of γ-rays or longitudinal polarization of heavy particles in reactions involving unpolarized initial systems and where the apparatus itself defines no screw sense. (iii) The presence of odd powers of cos θ in the angular distribution of radiations coming from well-defined nuclear states. Two experiments have been performed in class (i). The radiative capture 4 He(d, γ) 6 Li through the 0 + state at 3·57 MeV has been sought and its absence corresponds to F 2 < 1 X 10 -7 ( F is the relative strength of the parity non-conserving interaction). The reaction 7 Be( n , α)α with thermal neutrons has been sought and the limit on the cross-section corresponds to F 2 < 1 X 10 -7 .

Chirality of Tensors and Parity-Nonconserving Interactions

In this letter it is shown that there necessarily exist two independent chirality operators, X, Y, in tensor calculus, and that any Lagrangian has to be invariant under the combined transformation X-Y-P, where P is the parity operator. (A.C.)

On the spin of the muon

The distribution in angle and energy of the electron arising from the decay of a longitudinally polarized muon of spin 3/2 is calculated, using the most general parity nonconserving direct interaction. The result depends upon three parameters (functions of the coupling constants) which cannot be adjusted to give agreement with experiment.

On the Longitudinal and Transverse Polarization of Positrons in µ+-Meson Decay

We have calculated the density matrix which characterizes the polarization state of positrons emitted from µ+-meson decays at rest, using general parity non-conserving interactions, the mass of electron beig neglected. From the density matrix, we can tell the degree and direction of polarization of the positrons. Detection of transverse polarization perpendicular to the plane spanned by the polarization vector of the initial µ+-meson and the propagation vector of the positron, will provide a test for whether invariance under Wigner's time reversal is valid or not.

Parity Nonconservation and the Group-Space of the Proper Lorentz Group

As a means of incorporating isotopic spin into the foundations of the theory of spin \textonehalf{} particles, a slight modification of the free-particle Dirac equations has previously been proposed which follows from a consideration of the group-space of the proper Lorentz group. Further considerations of the group-space suggest two additional modifications which may contribute, in a mutually complementary way, toward establishing a new symmetry principle applicable to parity-nonconserving interactions.

Polarization of Electrons in Muon Decay with General Parity-Nonconserving Interactions

The polarization of electrons in muon decay is studied in the case of the four-component neutrino theory with general parity-nonconserving interactions. The spectrum for each of the two states of longitudinal polarization is described by a set of three parameters of which only two are independent. By observing the electron polarization in arbitrary directions, one can determine ten parameters of which six are related to the two longitudinal polarizations and the rest to the transverse part. It is seen that the prediction of the two-component neutrino theory about the electron polarization in muon decay is quite specific and can be distinguished from that of the general case, if the latter involves the interactions of the $S$, $T$, $P$ types in charge-retention order. However, from the study of the polarization of electrons, it is impossible to distinguish the two-component theory from the four-component theory which involves only the vector-type interactions. It is noticed that the $\mathrm{TCP}$ theorem determines a detailed correspondence between the polarization dependence of the spectra for the ${\ensuremath{\mu}}^{+}$ and ${\ensuremath{\mu}}^{\ensuremath{-}}$ decays. This provides us with an opportunity to determine experimentally whether weak interactions actually obey the $\mathrm{TCP}$ theorem or not.

Asymmetry of Low-Energy Positrons from Muon Decay

An investigation of the angular asymmetry of lowenergy positrons from the decay of polarized muons coming to rest in a propane bubble chamber is reported. The energy dependence of the asymmetry parimeter alpha is predicted by the two-component theory of the neutrino, while according to the four- component theory, with arbitrary parity-nonconserving interactions, this parameter can have a wide range of energy variations depending on the values of the interaction constants. Berley et al., have recently investigated the energy dependence of the asymmetry parameter for the upper half of the energy spectrum by an absorption technique and found approximate agreement with the prediction of the two-component theory. The results of the present work support this view. (A.C.)

Muon Decay with Parity Nonconserving Interactions and Radiative Corrections in the Two-Component Theory

The decay of a polarized muon is studied in the case of the general four-component neutrino theory with the most general parity-nonconserving interaction. A three-parameter formula for the decay-electron distribution is obtained as a generalization of the Michel formula for an unpolarized muon. This general formula is examined to determine to what extent the observed spectrum enables one to decide whether any particular theory is correct or not. It is seen, among other things, that by the observation of the muon decay spectrum alone one cannot test the validity of the two-component neutrino theory. To facilitate a possible accurate experimental test of the two-component neutrino theory, the radiative correction for the decay of a polarized muon is worked out to the lowest order in $\ensuremath{\alpha}$. Although the correction is rather complicated, it can still be expressed approximately by the three-parameter formula mentioned above. It is found, in particular, that the corrected Michel parameter for the two-component theory is ${0.70}_{6}$ when a neutrino and an antineutrino are emitted in the final state, which is 6% smaller than the value 0.75 predicted by the simple theory.