Parity Violation and Weak Interaction

Parity Violation and Weak Interaction

and after all particle interactions. The processes in which parity is not conserved would look different in the mirror image (+ 180o rotation) world. With some hints from experimental results, T. D. Lee and C. N. Yang pointed out that conservation of parity may be violated in weak interaction. A test was arranged by C. S. Wu to observe the beta decay of cobalt-60 in a magnetic field. It shows a preferred direction for the emitting electrons (the left-handed electrons) and thus validates the hypothesis of parity violation for weak interaction -- the mirror world behaves differently from the real world (see Figure 15-05l). Two Chinese physicists shared the 1957 Nobel Prize (not including Wu) for their efforts in identifying this peculiar behaviour about weak interaction.

Figure 15-05l Parity Violation [view large image]

Note that parity will be conserved if there are equal number of electrons in both directions. It is a useful tool to predict permissible process when parity is conserved.

What is parity violation () in the weak interaction of elementary particles?

ChatGPT said:
Excellent question - this goes right to the heart of how the weak interaction differs fundamentally from all other forces.
Let's break it down clearly and step by step:
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1. What parity means
In physics, parity (P) refers to the symmetry of spatial inversion - the idea that the laws of physics should be the same in a mirror-reflected universe.
Mathematically, parity changes the sign of spatial coordinates:
(x,y,z) to (-x, -y, -z)
If the laws of physics are unchanged by this operation, parity is conserved.
For most forces (gravitational, electromagnetic, strong), this is indeed true: a process and its mirror image occur with equal probability.
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2. The discovery of parity violation
In the 1950s, theoretical physicists Tsung-Dao Lee and Chen-Ning Yang suggested that parity might not be conserved in the weak interaction (the force responsible for beta decay, for example).
Until then, everyone assumed all forces obeyed parity symmetry.
Their idea was tested in 1957 by Chien-Shiung Wu and her team, in the famous Wu experiment on cobalt-60 nuclei.

They aligned the spins of cobalt-60 nuclei in a magnetic field and measured the direction of emitted electrons from beta decay.
Result:
More electrons were emitted opposite to the direction of the nuclear spin.
If parity were conserved, there should have been equal emission in both directions.
This was stunning - parity was violated in weak interactions.
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3. What parity violation means physically
It means that the weak force distinguishes between left and right.
In other words:
" Nature's laws for weak processes are not mirror symmetric.
" The weak force only couples to left-handed particles and right-handed antiparticles.
Here:
" "Left-handed" means the particle's spin direction is opposite to its motion.
" "Right-handed" means the spin is aligned with its motion.
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4. Mathematical formulation

That's the mathematical expression of parity violation - only one "handedness" participates.
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5. Consequences
" Neutrinos are produced only left-handed (and antineutrinos right-handed).
" The weak interaction defines an absolute direction in space - a built-in "arrow" that distinguishes left from right.
" This asymmetry underlies CP violation (charge + parity violation) observed in kaons and B mesons - an ingredient necessary to explain why our universe is matter-dominated.
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6. Summary

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Would you like me to show how the Wu experiment quantitatively demonstrated parity violation - e.g. with the asymmetry formula for electron emission?

ChatGPT said:
Yes - exactly right.
For all other fundamental forces - gravity, electromagnetism, and the strong interaction - left-handed and right-handed particles behave identically. These forces are parity-symmetric, meaning they make no distinction between a particle's handedness.
Let's summarize clearly:
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?? Electromagnetic force
" Described by Quantum Electrodynamics (QED).
" Couples equally to left- and right-handed electrons, since the photon is vector-like (it couples to charge, not chirality).
" Mirror image behaves identically ? parity conserved.
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?? Strong force
" Described by Quantum Chromodynamics (QCD).
" Gluons couple to color charge, not to spin orientation.
" Hence, left and right quarks feel the same force ? parity conserved.
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?? Gravitational force
" In general relativity, gravity depends on mass-energy, not spin orientation.
" Both handedness states experience identical curvature of spacetime ? parity conserved.
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?? Weak force
" The only exception.
" Mediated by W^+/- and Z⁰ bosons.
" Couples only to left-handed fermions (and right-handed antifermions).
" Thus, it violates parity maximally - not just a small difference, but a total exclusion of one handedness.
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ChatGPT said:
Excellent follow-up - this goes to the heart of where the weak interaction actually shows up in nature.
Although it's far weaker than the electromagnetic or strong forces, it's absolutely crucial for how matter evolves, decays, and even shines in stars.
Let's look at the main physical phenomena governed by the weak interaction, grouped by context:
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?? 1. Beta decay (radioactivity)
The classic example of the weak force.
" Process:
A neutron transforms into a proton, emitting an electron and an antineutrino:

" This changes one element into another - the basis of radioactive beta decay.
" Mechanism:
A down quark inside the neutron changes into an up quark via emission of a virtual W^- boson, which quickly decays into

" Importance:
Enables natural radioactivity, nuclear dating, and the generation of internal heat in planets (via radioactive decay chains).
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?? 2. Nuclear fusion in stars
The weak force makes stars shine.
" In the Sun's proton-proton chain, two protons fuse:

" One proton must convert into a neutron to form deuterium - and this conversion happens only through the weak interaction.
Without this step, fusion wouldn't start - no Sun, no starlight, no life.
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?? 3. Neutrino interactions
Neutrinos are extremely light and interact only via the weak force (and gravity).
Examples:

Because their weak cross-section is tiny, neutrinos can pass through light-years of lead unscathed - yet they play key roles in supernova explosions and neutrino astronomy.
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?? 4. Quark flavor changes
The weak force changes one flavor of quark into another - something no other force can do.
Examples:

This is encoded in the CKM matrix, which quantifies the probability of each flavor transition.
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?? 5. CP and parity violation
The weak interaction alone breaks parity and, in certain meson decays, also violates CP symmetry (combined charge-parity).
This tiny asymmetry between matter and antimatter is believed to be one ingredient behind the matter dominance of our universe.
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?? 6. Muon and other lepton decays
Weak force governs the decay of heavier leptons:

and similarly for the tau lepton.
Again, this involves a W boson exchange.
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Would you like me to include a diagram showing these processes - e.g., Feynman-style sketches of weak interactions via W and Z bosons?

ChatGPT said:
Excellent and very deep question - you're now asking why nature's weak force prefers one handedness, not merely how it manifests.
Let's unpack this carefully, from the empirical fact to the theoretical reason within the Standard Model, and then what we don't yet know fundamentally.
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?? 1. The empirical fact
Experiments (like the Wu experiment, 1957) show that the weak interaction acts only on left-handed particles and right-handed antiparticles.
This is not a small asymmetry - it's maximal parity violation.
So:
" Left-handed neutrinos interact; right-handed ones do not.
" Right-handed antineutrinos interact; left-handed ones do not.
This is a direct observation, not something derived from deeper principles (yet).
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?? 2. Theoretical structure in the Standard Model
In the Standard Model (SM), the weak force is described by a non-Abelian gauge symmetry:
SU(2)_L X U(1)_Y
That subscript L is crucial - it means that only left-handed fermions transform as doublets under SU(2)_L.
How it works:

This asymmetric assignment is built into the structure of the Standard Model.
Thus, the weak interaction Lagrangian includes a "V-A" (vector minus axial vector) term:

The operator projects out only the left-handed components of the field.
That's the mathematical cause of parity violation - the weak gauge field simply doesn't couple to right-handed particles.
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?? 3. Why only SU(2)_L?
This is the real mystery.
There is no deeper explanation within the Standard Model - it's a foundational asymmetry built into the gauge structure.
In other words:
The weak force violates parity because the laws of nature assign different transformation properties to left- and right-handed particles.
No fundamental reason is known why the symmetry group is SU(2)_L and not SU(2)_R, or both.
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?? 4. Attempts at deeper understanding
a. Left-Right Symmetric Theories
Proposed extensions (like the Pati-Salam or SO(10) grand unified theories) introduce a full structure :

In these models:
" Parity is initially conserved at high energy.
" It becomes spontaneously broken when the universe cools - only SU(2)_L remains active at low energy.
This would make parity violation an emergent phenomenon, not a fundamental asymmetry.
b. Neutrino masses and right-handed neutrinos
The discovery of neutrino oscillations implies neutrinos have small masses - possibly linked to heavy right-handed neutrinos that don't participate in weak interactions.
These right-handed neutrinos might restore symmetry at high energy (in so-called "seesaw mechanisms").
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In short:
?? Parity violation occurs because the weak interaction couples only to left-handed fields, as encoded in the Standard Model's SU(2)_L structure.
Why nature chose this asymmetric setup remains one of the most profound open questions in physics.
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Would you like me to illustrate this with a diagram showing the SU(2)_L structure - left-handed doublets vs right-handed singlets and how they connect to W and Z bosons?

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