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

ln(
Messages
42
Reaction score
0
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)?
 
Physics news on Phys.org
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.
 
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?
 
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.
 
Thread 'Why is there such a difference between the total cross-section data? (simulation vs. experiment)'
Well, I'm simulating a neutron-proton scattering phase shift. The equation that I solve numerically is the Phase function method and is $$ \frac{d}{dr}[\delta_{i+1}] = \frac{2\mu}{\hbar^2}\frac{V(r)}{k^2}\sin(kr + \delta_i)$$ ##\delta_i## is the phase shift for triplet and singlet state, ##\mu## is the reduced mass for neutron-proton, ##k=\sqrt{2\mu E_{cm}/\hbar^2}## is the wave number and ##V(r)## is the potential of interaction like Yukawa, Wood-Saxon, Square well potential, etc. I first...
Back
Top