# QFT anomaly in electromagnetic, neutral Pion decays

• Cinquero
In summary, the electromagnetic neutral pion decay is a three-point interaction where it decays into two virtual and charged Kaons or Protons. This then leads to the production of two photons, with the two photons having a total spin of 1 and crossed polarizations. This decay process agrees with C-conservation, but violates parity conservation. This can be explained by conservation laws and does not involve any QFT anomalies.
Cinquero
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?

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? :-)

## 1. What is a QFT anomaly in electromagnetic, neutral Pion decays?

A QFT anomaly is a violation of a symmetry in a quantum field theory. In the context of electromagnetic, neutral Pion decays, it refers to a violation of the conservation of the electromagnetic current, which is a fundamental symmetry in the Standard Model of particle physics.

## 2. How does the QFT anomaly affect neutral Pion decays?

The QFT anomaly affects neutral Pion decays by causing the decay rate to deviate from the expected value based on the conservation of the electromagnetic current. This leads to a discrepancy between experimental measurements and theoretical predictions.

## 3. What is the significance of studying QFT anomaly in neutral Pion decays?

Studying QFT anomaly in neutral Pion decays is important because it provides a deeper understanding of the fundamental symmetries and interactions in the Standard Model. It also helps to test the validity of the theory and can potentially lead to new insights and discoveries in particle physics.

## 4. Are there any experimental observations of QFT anomaly in electromagnetic, neutral Pion decays?

Yes, there have been several experimental observations of QFT anomaly in electromagnetic, neutral Pion decays. These include the measurements of the branching ratio of the decay and the polarization of the decay products, which have shown deviations from the theoretical predictions.

## 5. What are some current research efforts focused on QFT anomaly in electromagnetic, neutral Pion decays?

Current research efforts include further experimental measurements to better understand the QFT anomaly in neutral Pion decays, as well as theoretical studies to explain the observed discrepancies and potentially extend the Standard Model to incorporate this phenomenon. There is also ongoing research to study the implications of QFT anomaly in other decay processes and interactions.

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