Questions: Parity Violation in the Weak Interaction

Question 1

In the Wu experiment with polarized cobalt-60 nuclei, what was observed?

• A. Electrons were emitted equally in all directions
• B. Electrons were emitted preferentially opposite to the direction of the nuclear spin
• C. Electrons were emitted only along the nuclear spin
• D. No electrons were emitted at low temperature

Answer: (B)

An asymmetry between the directions along and against the spin means the mirror-image experiment, in which that relation is reversed, would give a different result. Parity is not conserved.

Question 2

Which quantity changes sign under a parity transformation and so can reveal parity violation if its average is nonzero?

• A. The energy of a particle
• B. The spin of a particle
• C. The product of spin and momentum, σ·p
• D. The magnitude of momentum

Answer: (C)

Momentum reverses under parity, while spin does not, so σ·p (helicity) changes sign. A nonzero average helicity cannot occur in a parity-symmetric world.

Question 3

Under a parity transformation, the spin of a particle reverses direction.

• T. True
• F. False

Answer: False

Spin, like orbital angular momentum r × p, is an axial vector. Both r and p reverse, so their cross product does not.

Question 4

The pion decays to a muon and neutrino far more often than to an electron and neutrino, even though the electron channel releases more energy. Explain using helicity.

Model answer: The spin-0 pion must produce the charged lepton and neutrino with opposite momenta and opposite spins, which forces the charged antilepton into the 'wrong' helicity for the weak interaction. The amplitude for that helicity is proportional to the lepton's mass, so the very light positron is strongly suppressed.

The measured ratio of π⁺ → e⁺νₑ to π⁺ → μ⁺ν_μ is about 1.2 × 10⁻⁴, in agreement with this helicity suppression.