Determination of the $e^+ e^- \to \gamma \gamma(\gamma)$ cross-section at centre-of-mass energies ranging from 189 GeV to 202 GeV

A test of the QED process \eeintogg(\fot) is reported. The data analysed were collected with the DELPHI detector in 1998 and 1999 at the highest ener\-gies achieved at LEP, reaching 202 GeV in the centre-of-mass. The total integrated luminosity amounts to 375.7 pb$^{-1}$. The differential and total cross-sections for the process $e^+e^- \to \gamma \gamma$ were measured, and found to be in agreement with the QED prediction. 95\% Confidence Level (C.L.) lower limits on the QED cut-off parameters of $\rm \Lambda_+ $ 330 GeV and $\rm \Lambda_{-}>$ 320 GeV were derived. A 95\% C.L. lower bound on the mass of an excited electron of 311 $\rm GeV/c^2$ (for $\lambda_{\gamma}$ =1) was obtained. s-channel virtual graviton exchange was searched for, resulting in 95\% C.L. lower limits on the string mass scale, $\rm M_S$: $\rm M_S 713 \, GeV/c^2$ ( $\lambda=1$) and $\rm M_S 691 \,GeV/c^2$ ($\lambda = -1$).