QFT anomaly in electromagnetic, neutral Pion decays

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Discussion Overview

The discussion revolves around the electromagnetic decay of the neutral pion, specifically addressing the conservation laws of parity and charge conjugation in the context of quantum field theory (QFT) anomalies. Participants explore the implications of these conservation laws on the decay process and question the validity of certain assumptions made in the analysis.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Exploratory

Main Points Raised

  • One participant describes the decay of the neutral pion into two photons, detailing the conservation of angular momentum and the implications for charge conjugation (C) and parity (P) conservation.
  • Another participant suggests that the original questions might be better suited for a different section of the forum, indicating a potential misplacement of the topic.
  • A participant asserts that parity is not violated in the electromagnetic decay of the neutral pion, referencing an external link for further context.
  • Another participant challenges the initial analysis, pointing out errors in the calculation of charge conjugation for two photons and questioning the application of angular momentum conservation.
  • This same participant argues that the conservation of parity for the neutral pion decay requires a different orbital angular momentum state than initially proposed, referencing historical experiments that measured the parity of the pion.
  • A later reply expresses confusion regarding the identification of the anomaly in the context of the discussion.

Areas of Agreement / Disagreement

Participants express disagreement on the interpretation of conservation laws in the context of the neutral pion decay, with some asserting that parity is violated while others argue it is not. The discussion remains unresolved regarding the existence and implications of the QFT anomaly.

Contextual Notes

Participants highlight potential errors in the initial analysis, including misunderstandings of charge conjugation and angular momentum conservation. The discussion reflects varying interpretations of quantum field theory principles without reaching a consensus.

Cinquero
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The electromagnetic neutral pion decay is a three-point interaction: it decays into two virtual and charged Kaons or Protons, of which one then radiates a photon and then annihalates with the other to produce a second photon. (Obviously, a neutral particle cannot radiate photons directly)

Questions:

1.) Let's go into the CMS of the neutral Pion. There, it neither has spin nor orbital momentum. The total angular momentum is therefore J=L+S=0 (where + denotes the spin addition). The Pion is a P=-1 eigenstate of parity and a C=+1 eigenstate of the charge conjugation operator. The C value of the two photons is C=(-1)(-1)(-1)^(l+s). Because of momentum conservation, it is L=0 and therefore l=0. Conservation of J then requires that the two photon spins are antiparallel, which requires S=0 and therefore s=0, where s is the spin-3-component. This shows that the two-Photon decay agrees with C-conservation. Using a similar argumentation, the one-Photon decay contradicts C-conservation.

Let's have a look at parity conservation. The two photons have intrinsic parity -1 each, which "adds" up to +1. Orbital angular momentum must be zero according to classical conservation laws. So we have a violation of parity. Is that correct?

2.) Has that to do with the (a?) QFT anomaly, namely Ward-Identities as a substitution for classical conservation laws which get broken by the process of quantization? If yes, could someone please give an overview of what is actually happening here?
 
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You may want to consider posting your series of questions in the Nuclei and Particles section, which I think is more relevant.

Zz.
 
You are right. Did not see it at first. Seems like I'm not allowed to move it. Who is?
 
Cinquero said:
You are right. Did not see it at first. Seems like I'm not allowed to move it. Who is?

Oh, don't worry about it. When one of the moderators sees this, it'll get moved. Till then, you should just continue as usual with the existing threads.

Zz.
 
There are some errors in your analysis.
1. C for two photons is just (-1)(-1)=+1. There is no (-1)^{l+s) because the photon is its own antiparticle.
2. I don't understand "Because of momentum conservation, it is L=0 and therefore l=0." Angular momentum conservation applies to J and not to L
3. Conservation of parity from a pseudoscalar \pi^0 requires L=1 for the two photon state, and then the two photons must be in total spin S=1+1=1. This spin state of the photons was verified by looking at their relative polarization. This argument, in reverse, was originally proposed by Yang in the 50's to measure the parity of the pi0. The experiment found crossed polarizations for the photons, showing they were in a spin one state.
4. The above results just depends on conservation laws, and have nothing to do with more detailed theory.
 
Thx. But where is the anomaly? :-)
 

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