PARITY AND CHARGE CONJUGATION

BETA DECAY OF Cobalt-60

Cobalt-60 -> Zinc-60 + electron + anti-neutrino
 

Beta decay of cobalt-60 as seen in a right handed coordinate system. In the diagram on the right a current, I, is driven through a coil to produce a magnetic field B. The electrons which cause the current are indicated as small blue spheres which travel in the opposite direction to the conventional current I. This current I produces a magnetic field B which, by the right hand rule is pointing up. The cobalt-60 nucleus is positively charged. We can imagine it to be spinning in the direction as indicated. The classically spinning charged sphere has a magnetic moment given by the right hand rule. The nucleus behaves similarly. The magnetic moment of the nucleus points along the spin direction S. The torque exerted by B on the tiny nuclear magnet causes S to line up with B.

What happens when we make the observation of beta decay from the left handed coordinate system? Lee and Yang, 1956, suggested that beta decay may not exhibit reflection symmetry.

In the experiment of C. S. Wu et al, 1957, cobalt-60 nuclei were cooled to very low temperatures, about 0.01K, and their magnetiv moments S were aligned by imposing an external magnetic field B produced by current I in a coil. In the right handed coordinate system (rh) the observation is that electrons (blue circles) are preferentially emitted in a direction opposite the magnetic moment S in a ratio about 150/100. In the left handed coordinate system the observation is that electrons are preferentially emitted in the same direction as S. The observations about the nature of the beta decay process then depends on which coordinate system is used. This results shows that there is no "reflection" symmetry for the weak force that causes beta decay. Another way of saying this is that " parity" is not conserved in beta decay.

What happens if we transform all particles into their anti particles. This is called the "Charge Conjugation" transformation. The electrons that are moving through the wires to produce the current I now become positrons, ( the anti - electron). The current I then points in the direction shown. This produces a magnetic field B by the right hand rule, pointing down. The nucleus becomes anti-cobalt60. It is now a negatively charged rotating sphere. Using the right hand rule to obtain the spin direction and noting that the negatively charged rotating body has a magnetic moment opposite to its angular momentum, the magnetic moment S still points along B. Our anti-universe observer concludes that the charged leptons( positrons) are preferentially emitted in the direction of S. This again is different from the observation in the matter universe.

From this experiment we see that beta decay violates reflection symmetry and matter/antimatter symmetry.
 

What would happen if our anti-matter observer used a left handed coordinate system? In this case B would point up by the left hand rule. The magnetic moment of the anti-cobalt60 nucleus also points up because of the negatively charged nucleus. This observer would conclude that the charged leptons(positrons) are preferentially emitted in the direction opposite the magnetic moment of the nucleus. Hence, his observation is the same as that of the righthanded observer in the matter universe. From these results we conclude that the weak force responsible for beta decay is symmetric under the combined transformations of reflection (parity, P) and charge conjugation(C), or we say the beta decay is CP invariant.  While this appears to be true for beta decay we must note that there is a small but significant violation of CP invariance for the weak decay of the neutral kaon.

Suppose we we run time backwards after we have changed to a LH coordinate system and done the charge conjugation. The directions of all velocities must change. Then the residual nucleus, zinc-60, becomes a target which preferentially absorbs electrons coming against the magnetic moment. The combined transformation PCT yields the same conclusion as the original panel at the top. The beta decay process produces an asymmetric emission/absorption of electrons. Electrons are preferentially emitted/absorbed when they travel in a direction opposite to the magnetic moment of the decaying/absorbing nucleus.

 

Very general arguments require that the combined transformations of reflection and charge conjugation and time reversal, PCT, must be a symmetry for all physical forces!

Direct observation of neutrinos from beta decay was made by Reines et al. in 1953

Neutrons can decay in free space and inside nuclei into protons and electrons and anti neutrinos. It has been discovered that the anti neutrinos emitted in beta decay have their spin vectors pointing in the direction of their momentum. We call the anti neutrinos from beta decay "right-handed" because their spin direction can be define to be along the momentum direction if a right hand rule is use to define spin dirction.

Protons inside a nucleus can decay into a neutron, a positron, and a neutrino. Neutrinos emitted in positron decay have their spin vectors pointed oppositely to their momentum vectors. We call the neutrinos from beta decay "left-handed" because their spin direction can be defined to be in same same direction as their momentum if a left hand rule is used to define spin direction.

We note that anti neutrinos with their spin anti parallel to momentum have never been seen. Neutrinos with their spin parallel to their momentum have also never been seen.

The Modern theory of the weak interactions was developed by Weinberg, Glashow, and Salam. This theory unites the electromagnetic force and the weak force.

Internal Symmetries