# Kaon decay parity if pion parity is redefined as +1

I am reading in Neeman’s book, The particle hunter, second edition, page 169, about the “theta-tau riddle.” He writes that

You might suggest that we define the parity of the pion as $$+1$$, but this would not be of any help to us — in this case too the parity of the three pions produced by the kaon decay would be $$-1$$ (because of the angular momentum of the system).

What does he mean? I thought the kaon angular momentum is zero.

• A system of particles in addition to their intrinsic spin can have angular momentum, as is the case of the rho0 to pi+pi- ( see my answer physics.stackexchange.com/questions/689025/… ). I agree that it seems a wrong statement . imo it just reverses the puzzle. Jan 18 at 5:46
• So, would redefining the pion parity as +1 solve parity violation for this decay? Jan 18 at 6:03
• I don’t know what you mean by reverse, since both the two pion and three pion states would have the same parity of +1. I am thinking that there is no freedom in redefining the pion parity. I searched for how they deduce the pion parity and find the pion capture by a deuteron as an example. Even if I reverse parity for the neutrons and the proton in the deuteron, the parity of the pion still comes out -1. So, maybe there is no such freedom in redefining its parity? Jan 18 at 7:24
• @annav, are you suggesting that two scalar particles in an $s$-wave would have negative parity? I don’t follow that.
– rob
Jan 18 at 14:22
• @rob I have to rethink this. Reversing the parity of the pion, would reconcile the tau and theta parity state, except for the observation that the parity of the pion is fixed experimentally as noted by cipocip. It is the zero spin of the tau theta that does not allow the statement "because of the angular momentum of the system", to be used as an argument for keeping on the puzzle,( conservation of angular momentum), and not accept it shows parity violation in the decays of one particle instead of two. Jan 18 at 14:42

I think the quoted statement may be an error in the book. I’m pretty comfortable stating that any number of scalar mesons sharing an $$s$$-wave state should have positive parity.
However, as you write in a comment, assigning positive parity to the pion moves the puzzles of parity nonconservation from the strangeness-changing weak decays to strong interactions like $$\rm \pi^- d\to nn$$ or to electromagnetic interactions like $$\pi^0\to\gamma\gamma$$.