CPT Invariance & Neutrinos: Exploring the Violation

[touqra]

On page 3 of the following pdf:
http://pdg.lbl.gov/2005/reviews/numixrpp.pdf

the paragraph after equation 13.12, there's a line that says:
"Thus, if U is not real, the neutrino... When CPT holds, any difference between these probabilities indicates a violation of CP invariance."

I don't understand how it should be a violation of CP invariance, and not CPT invariance that is violated.

 

[CarlB]

It's correct, but confusing. When the author writes "any difference between these probabilities", by "these probabilities" he refers to the probabilities calculated in equation (13.8), not the probabilities calculated in (13.12).

 

[sir-pinski]

The statement in the paragraph is referring to the concept of CPT (Charge-Parity-Time) invariance, which is a fundamental symmetry principle in particle physics. This principle states that the laws of physics should be the same if the charge of a particle is reversed (C), the spatial coordinates are inverted (P), and time is reversed (T). If this principle holds true, then the probabilities of certain processes occurring should be the same for particles and their antiparticles.

In the context of neutrinos, the paragraph is discussing the phenomenon of neutrino oscillations, where a neutrino can change from one flavor (electron, muon, or tau) to another as it travels through space. This process is described by a mathematical matrix called the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix, denoted by U. This matrix contains both real and imaginary components, and it is these imaginary components that are related to the violation of CP invariance.

To explain this further, let's consider the process of a neutrino oscillating from one flavor to another. If CPT holds true, then the probabilities for this process should be equal for both neutrinos and antineutrinos. However, if the PMNS matrix U is not real, then the probabilities for this process will be different for neutrinos and antineutrinos, indicating a violation of CP invariance. This means that the laws of physics are not the same for particles and their antiparticles, and thus, the CPT symmetry is violated.

In summary, the statement in the paragraph is discussing how the violation of CP invariance is related to the imaginary components of the PMNS matrix, and it is this violation that signifies a violation of CPT invariance.