P, CP and CPT symmetry in neutrino oscillation? (quick question)

In summary, the conversation discusses the application of operators for P, CP, and CPT in neutrino oscillation calculations. It is noted that while charge conjugation and time reversal operations have specific effects on the oscillation probability, the incorporation of parity transformation is unclear. The expert explains that this is due to the fact that weak force violates P maximally and the existence of left-handed anti-neutrinos would require the existence of right-handed neutrinos. The conversation also mentions the expected violation of CP in the neutrino sector and the exact symmetry of CPT.
  • #1
Doofy
74
0
Just a quick question about notation really here. In neutrino oscillation we can calculate a probability of an oscillation occurring between two flavour eigenstates - invariably denoted [itex] P(\nu_{\alpha} \rightarrow \nu_{\beta}) [/itex]. I've got some confusion about what happens to this when we apply operators for P, CP and CPT.

Charge conjugation turns particles to anti-particles, so I'm thinking this transformation would be denoted [itex] P(\nu_{\alpha} \rightarrow \nu_{\beta}) \rightarrow P(\overline{\nu_{\alpha}} \rightarrow \overline{\nu_{\beta}}) [/itex]

Time reversal would presumably be [itex] P(\nu_{\alpha} \rightarrow \nu_{\beta}) \rightarrow P(\nu_{\beta} \rightarrow \nu_{\alpha}) [/itex]

The combination of C and T operations would therefore be [itex] P(\nu_{\alpha} \rightarrow \nu_{\beta}) \rightarrow P(\overline{\nu_{\beta}} \rightarrow \overline{\nu_{\alpha}}) [/itex]

My question is how would the parity transformation be incorporated here?

ie. how would one write [itex] \hat{P} P(\nu_{\alpha} \rightarrow \nu_{\beta}), \hat{C}\hat{P} P(\nu_{\alpha} \rightarrow \nu_{\beta}) [/itex] and [itex] \hat{C}\hat{P}\hat{T} P(\nu_{\alpha} \rightarrow \nu_{\beta}) [/itex] ?
 
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  • #2
The application of P will switch the chirality of a fermion. For neutrinos, this would be rather problematic, as, so far as we know, there are no right-handed neutrinos. (This is related to the fact that the weak force violates P maximally.) C, on the other hand, will reverse all charges, but will not reverse chirality; so, it will take you from a left-handed neutrino to a left-handed anti-neutrino. But, as you can check for yourself, the anti-neutrino state which must be included to allow spin-conservation in gauge interactions involving a left-handed neutrino is actually the right-handed anti-neutrino. (Equivalently, the existence of a left-handed anti-neutrino would require the existence of a right-handed neutrino.) So, again, we have a maximal violation, this time of C. It's only if we apply CP (turning a left-handed neutrino into a right-handed anti-neutrino) that we should expect to get a meaningful conjugation.

Now, as it happens, we already know that the weak force slightly violates CP, as well; and, it's expected that there should be some CP violation in the neutrino sector; but, this ought to be a small effect compared to the size of the oscillation effects.

CPT, on the other hand, should be an exact symmetry. There's a good deal of work showing that a violation of CPT necessarily entails a violation of local Lorentz symmetry.
 

What is P, CP, and CPT symmetry in neutrino oscillation?

P, CP, and CPT symmetry are properties of particles and their interactions in the field of particle physics. They refer to the conservation of parity (P), charge conjugation-parity (CP), and combined charge-parity-time (CPT) invariance in physical processes, specifically in the phenomenon of neutrino oscillation.

How do P, CP, and CPT symmetries affect neutrino oscillation?

In neutrino oscillation, the symmetries of P, CP, and CPT play a crucial role in determining the behavior of neutrinos. For example, P symmetry states that the laws of physics remain the same if the coordinates of a system are inverted, while CP symmetry states that the laws of physics remain the same if a particle is replaced with its antiparticle. CPT symmetry combines these two and states that the laws of physics remain the same if a particle's coordinates are inverted, and it is replaced with its antiparticle. Neutrino oscillation experiments have shown that these symmetries may not always hold, leading to the discovery of neutrino oscillation.

Why is the violation of these symmetries important in neutrino oscillation?

The violation of P, CP, and CPT symmetries in neutrino oscillation is significant because it indicates that neutrinos have a non-zero mass. According to the Standard Model of particle physics, neutrinos are considered massless particles, and the violation of these symmetries challenges this fundamental theory. Therefore, studying the violation of these symmetries in neutrino oscillation can provide crucial insights into the nature of neutrinos and their properties.

Can P, CP, and CPT symmetries be restored in neutrino oscillation?

While the current evidence shows that P, CP, and CPT symmetries are violated in neutrino oscillation, it is still possible that these symmetries can be restored in certain conditions. For example, some theories suggest that the symmetries may be restored in the high-energy regime of neutrinos. However, more research and experiments are needed to confirm these theories and understand the behavior of neutrinos fully.

How does the violation of P, CP, and CPT symmetries impact our understanding of the universe?

The violation of P, CP, and CPT symmetries in neutrino oscillation has significant implications for our understanding of the universe and the laws of physics. It challenges the Standard Model and opens up new possibilities for theories beyond it. Furthermore, understanding the properties and behavior of neutrinos can help us unravel mysteries such as the existence of dark matter and the dominance of matter over antimatter in the universe.

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