Decay of Roe Meson: Conservation Laws Explained

[K8181]

I just started a class in particle physics this semester, and I really need help on one of our first homework problems. We are supposed to show that while the following decays are allowed:

roe(+) --> pi(0)pi(+)
roe(-) --> pi(0)pi(-)
roe(0) --> pi(+)pi(-)

the following decay is not allowed:

roe(0) --> pi(0)pi(0)

I am pretty sure the reason is that it violates a conservation law, but I don't know which one. We have barely touched on what quantities are conserved in lecture. I can see that charge is conserved in all cases, so no problem there.

We are also told that the roe meson is a spin 1 particle, so I think that should play a role. However, the part of quantum mechanics that dealt with angular momentum and spin was a bit treacherous for me. Any help is greatly appreciated.

 

[Integral]

This all sounds pretty fishy to me... Oh perhaps you mean $\rho$ that is rho!

You might benifit by reading This thread.

 

[K8181]

Fantastic! I am already familiar with LaTex.

 

[K8181]

For anyone reading this thread, that link was just about using LaTex for math symbols...I still REALLY need help with this problem!

 

[vincebs]

I'm not an expert in particle physics, but have you checked

1.) spin
2.) parity

I think rho mesons have both their quark and antiquark aligned, whereas pions have them antiparallel so one rho can't make two pions.

 

[K8181]

From what I have deduced, I think the culprit is parity. Could you explain what you know about parity? I have always found it a mysterious concept.

 

[Astronuc]

For some simple discussions on parity see - http://hyperphysics.phy-astr.gsu.edu/hbase/particles/parint.html#c4

And a discussion on mesons

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/hadron.html

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/meson.html (table of mesons)

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/meson2.html (eta, rho, etc)

I would hazard a guess and say that it probably has to do with the quark configuration.