# Why is the hadronic $\tau$ branching ratio into 2 pions prefered?

In the PDG the $$\tau$$ branching ratios are listed and Br$$(\tau^- \rightarrow \pi^-\pi^0 \nu_\tau)\approx 25$$ %, while Br$$(\tau^- \rightarrow \pi^-\nu_\tau)\approx 11$$ %. How can this be since the Feynman diagrams are of higher order for the former decay channel. Does this happen due to some discrete symmetry, angular momentum conservation or the chiral nature of the weak interaction?

• Look at this. Strong diagrams don't dominate each other as you are conjecturing! Why the decay prefers the ρ- to the π- , basically, one needs to think about... Oct 2 '21 at 17:59
• Superb question; perhaps there is no facile, cogent answer, of the type you are imagining. On p 166, table V-3 of Dynamics of the Standard Model Donoghue, Golowich, & Holstein (Camb Univ Press) make these accurate predictions by comparing $F_\pi$ for the π to $g_\rho$ for the ρ decay channels, the constants being determined phenomenologically. Why these decay constants are what they are, I don't know; but it's worth asking what lattice simulations produce for them. Oct 2 '21 at 19:11
• Table 1 of this gets you most of the way there! $g_\rho/F_\pi\sim 1.65$. Must be a feature of the vector versus axial quark currents. Oct 3 '21 at 0:30