Crouching Sigma, Hidden Scalar in $γγ\toπ^0π^0$

Abstract

There has long been speculation about the nature of the $σ$-resonance. For three decades Jaffe has argued for a tetraquark composition, while others have claimed it is largely a glueball. A key pointer to its nature is its coupling to two photons. Consequently, there have been recent proposals to observe this important scalar hiding in $γγ\toπ^0π^0$. We show here that the $σ$ is already crouching in this cross-section exactly as measured twenty years ago. What is new is that precise knowledge of the position of the $σ$-pole, provided by the analysis of the Roy equations, now allows its two photon coupling to be accurately fixed. Its two photon width is found to be $(4.1 \pm 0.3)$ keV, a value far too large for a gluonic, or even a tetraquark, state.