Decayη′→ηππas a Test of Chiral Symmetry Breaking

Abstract

The width $\Gamma$ of the decay ${\eta }^{\prime }\to \eta \pi \pi$ is estimated in the (8, 8) model of chiral symmetry breaking. Under plausible additional assumptions we find $\Gamma >0.27\mathrm{}$ MeV together with an experimentally uninteresting upper limit. In particular, the (8, 8) model is - at least under present extrapolation errors in the Dalitz plot of the decay - consistent with any $\Gamma$ above our lower limit and below the experimental upper limit $\Gamma <2.7\mathrm{}$ MeV. The actual width may be expected to be around 1 MeV in perfect agreement with the (8, 8) model. Our assumptions include that the dimension $l_u$ of the chiral-symmetry-breaking Hamiltonian density has the particularly attractive value 2. For this value, the conventional (3, ¯3) ⊕ (¯3, 3) model predicts $\Gamma <0.065\mathrm{}$ MeV. Despite the large extrapolation errors the decay ${\eta }^{\prime }\to \eta \pi \pi$ therefore clearly distinguishes between the two models and might be decisive. For any given extrapolation the estimated $\Gamma$ of the (8, 8) model is at least 13 times bigger than the prediction of the (3, ¯3) ⊕ (¯3, 3) model for $l_u=2\mathrm{}$. For $l_u=3\mathrm{}$ a prediction can also be obtained in the (3, ¯3) ⊕ (¯3, 3) model with a $c$-number $\delta$. It reads $\Gamma <0.25\mathrm{}$ MeV and is roughly compatible with the expected width. The ${\eta }^{\prime }\mathrm{}\left(958\right)\mathrm{}$ is taken to be a possible ninth pseudoscalar meson throughout. It is however emphasized that nonexistence of an SU(3) scalar meson might be a plausible alternative in the (8, 8) model.