We test the low-energy theorems of broken chiral and conformal invariance by use of the experimental $\pi \pi$ phases up to $m_{\pi \pi }=1\mathrm{}$ GeV. Our method differs considerably from a previous treatment by Renner and Staunton. Nevertheless, in the (3, ¯3) ⊕ (¯3, 3) model considered by these authors we recover their result that no consistent solution exists. The same result is obtained for the (8, 8). In a mixed model a consistent solution is found. This model has been introduced previously by the authors in order to be able to cope with a large $\pi \pi$ scattering length $a_0^{\mathrm{}\left(0\right)\mathrm{}}$. Our assumptions include that $\delta$ is a $c$ number and that $u$ has dimension two, in agreement with the low-energy theorems we use.

• Received 12 August 1974

DOI:https://doi.org/10.1103/PhysRevD.11.1856