# Does tau decay to rho meson + tau neutrino?

In the particle data group table: http://pdg.lbl.gov/2020/tables/rpp2020-sum-leptons.pdf ,only $$\tau \rightarrow \pi + \nu_{\tau}$$ is documented. But does $$\tau \rightarrow \rho + \nu_{\tau}$$ as well? I don't see any conservation laws that could forbid such decay to happen.

• The decay to the $\rho$ will be phase space suppressed by the heavy $\rho$ mass Jul 6 '20 at 17:48

The $$\rho$$ has the quantum numbers of $$\pi\pi$$ coupled to $$I=1$$. If they only list particles stable under the strong interaction then $$\tau^-\to\rho^-\nu$$ is the same as $$\tau^-\to\pi^-\pi^0\nu$$, which indeed has a branching ratio of 25%. The table is more helpful than that: It lists the non-resonant (non $$\rho$$) part of $$\tau\to \pi^-\pi^0\nu$$, which is very small. So the branching ratio is about 25%.