C-parity π+ π- π0: Is (-1)^L (+1) Correct?

In summary, the C-parity of π+ π- alone is simply (-1)^L, where L is the angular momentum quantum number for the system. For π+ π- π0, it is calculated as (-1)(-1)^L, indicating opposite CP eigenvalues for two pions and three pions. This provides evidence for CP violation when observing both K_{0 L} to two pions and three pions decays. To calculate C eigenvalue directly, one can use the multiplicative quantum number C and perform C^n for n pions system. The C and P eigenvalues of a single particle, such as pion, can be determined by setting them for basic particles like proton and electron, and studying
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TL;DR Summary
C-parity of π+ π- π0 compared to π+ π-
The C-parity of π+ π- alone is simply (-1)^L, where L is the angular momentum quantum number for the system. But then what is C-parity of π+ π- π0? Is it simply (-1)^L (+1), where L is the angular momentum quantum number for the π+ π- subsystem (which isn't necessarily the angular momentum of the whole three pion system)?
 
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π+ π- π0's CP is(-1)(-1)^(L). So, two pions and three pions have opposite CP eigenvalues. Therefore, observation of both K_{0 L} to two pions and three pions decays is clue of CP violation.
 
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SBoh said:
π+ π- π0's CP is(-1)(-1)^(L). So, two pions and three pions have opposite CP eigenvalues. Therefore, observation of both K_{0 L} to two pions and three pions decays is clue of CP violation.
This implies C = +1 which seems right. But how do you calculate C eigenvalue directly?
 
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C is multiplicative quantum number. So, once you know C of a single pion, you just need to perform C^n for n pions system. It is same for P. So, C(pion)^n P(pion)^n (-1)^L is total CP eigenvalue.
If you ask how we can know C or P eigenvalue of single particle such as pion, I would answer that we need to set C and P eigenvalues to several basic particles such as proton and electron. Then, we can study C and P quantum number of other particles (i.e. pions) using physical process such as pion + deutron to two neutrons.
 
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FAQ: C-parity π+ π- π0: Is (-1)^L (+1) Correct?

1. What is C-parity?

C-parity is a quantum number that describes the behavior of a particle under charge conjugation, which is the process of changing a particle into its antiparticle.

2. What is the significance of C-parity in particle physics?

C-parity is important in understanding the symmetry of particles and their interactions. It helps to classify particles and determine their properties.

3. What does (-1)^L (+1) mean in relation to C-parity?

In particle physics, L represents the orbital angular momentum of a particle. The equation (-1)^L (+1) is used to determine the C-parity of a particle based on its orbital angular momentum.

4. How is C-parity determined experimentally?

C-parity can be determined experimentally by studying the decay products of a particle and analyzing their properties, such as their spin and charge.

5. Is (-1)^L (+1) the only way to determine C-parity?

No, there are other methods for determining C-parity, such as studying the behavior of a particle under other symmetries like parity and time reversal.

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