# Tau decays

• I
Hello! Tau decay has a branching ratio to a charged pion + neutral pion + tau neutrino much bigger than to a charged pion and a tau neutrino. Based on consideration of available phase space, I would imagine that adding an extra pion would decrease the branching ratio. Why is this happening? Thank you!

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The decay is actually $\tau \rightarrow \rho \nu$ followed by $\rho^\pm \rightarrow \pi^\pm \pi^0$. The reason is that the virtual W couples more strongly to the rho than the pion, but I don't think there is an I-level explanation for why. There's not even a single simple A-level explanation: it's multiple factors.

The decay is actually $\tau \rightarrow \rho \nu$ followed by $\rho^\pm \rightarrow \pi^\pm \pi^0$. The reason is that the virtual W couples more strongly to the rho than the pion, but I don't think there is an I-level explanation for why. There's not even a single simple A-level explanation: it's multiple factors.
Thanks a lot! So the W boson decays into an up/down pair, but for some reason that pair has a higher probability to form a rho meson than a pion? Iso ne of the reason related to the fact that the rho is a vector while the pion is a scalar, while W is a vector?

vanhees71
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Iso ne of the reason related to the fact that the rho is a vector while the pion is a scalar, while W is a vector?
It's not that simple. I don't think there is an I-level explanation for why. There's not even a single simple A-level explanation: it's multiple factors.

vanhees71