Tau Decay: More Pions, Less Ratio?

[BillKet]

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!

 

[Vanadium 50]

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.

 

[BillKet]

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]

https://arxiv.org/abs/1310.7922

 

[Vanadium 50]

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]

While the purely leptonic decays are quite easy to understand by just using perturbation theory to the electroweak standard model, QFD, the semi-leptonic decays involving hadrons and the strong interaction, is not so easy to understand from simple analytic principles. An important theoretical tool is to use the approximate chiral symmetry of QCD in the light-quark sector to derive effective hadronic models. Finally there are also some phenomenological models. In connection with the electromagnetic (and maybe also for the weak) interaction of hadrons, particularly pions, the socalled vector-meson-dominance model is quite successful. If I remember right, for the decay via vector and axial-vector currents you need both, direct decays as well as decays vial $\rho$ and $a_1$ mesons. Above, I've quoted a review paper which seems to me pretty up to date concerning $\tau$ physics.