The interaction and resonances in photon–photon scattering

Junxu Lu; B. Moussallam

doi:10.1140/epjc/s10052-020-7969-8

EPJ

The $\pi \eta$ interaction and $$a_0$$

resonances in photon–photon scattering

Junxu Lu¹^,2 and B. Moussallam¹^*

¹ Pôle Théorie, IJCLab (CNRS/IN2P3, UMR9012), Université Paris-Saclay, 91406, Orsay, France
² School of Physics, Beihang University, Beijing, 102206, China

Received: 17 February 2020
Accepted: 24 April 2020
Published online: 18 May 2020

Abstract

We revisit the information on the two lightest $$a_0$$

resonances and S-wave $\pi \eta$ scattering that can be extracted from photon–photon scattering experiments. For this purpose we construct a model for the S-wave photon–photon amplitudes which satisfies analyticity properties, two-channel unitarity and obeys the soft photon as well as the soft pion constraints. The underlying I=1 hadronic T-matrix involves six phenomenological parameters and is able to account for two resonances below 1.5 GeV. We perform a combined fit of the $\gamma \gamma \rightarrow \pi \eta$ and $\gamma \gamma \rightarrow K_SK_S$ high statistics experimental data from the Belle collaboration. Minimisation of the $\chi ^2$ is found to have two distinct solutions with approximately equal $\chi ^2$ . One of these exhibits a light and narrow excited $$a_0$$

resonance analogous to the one found in the Belle analysis. This however requires a peculiar coincidence between the $$J=0$$

and

resonance effects which is likely to be unphysical. In both solutions the $$a_0(980)$$

resonance appears as a pole on the second Riemann sheet. The location of this pole in the physical solution is determined to be $m-i\varGamma /2=1000.7^{+12.9}_{-0.7} -i\,36.6^{+12.7}_{-2.6}$ MeV. The solutions are also compared to experimental data in the kinematical region of the decay $\eta \rightarrow \pi ^0\gamma \gamma$ . In this region an isospin violating contribution associated with ${\pi ^+}{\pi ^-}$ rescattering must be added for which we provide a dispersive evaluation.

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EPJ

The $\pi \eta$ interaction and resonances in photon–photon scattering

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