Light-by-light scattering in ultraperipheral collisions of heavy ions with future FoCal and ALICE 3 detectors

We discuss possible future studies of photon-photon (light-by-light) scattering using a planned FoCal and ALICE 3 detectors. We include different mechanisms of $\gamma\gamma\to\gamma\gamma$ scattering, such as double-hadronic photon fluctuations, $t/u$-channel neutral pion exchange or resonance excitations ($\gamma \gamma \to R$) and deexcitation ($R \to \gamma \gamma$). The broad range of (pseudo)rapidities and lower cuts on transverse momenta open a necessity to consider not only dominant box contributions but also other subleading contributions. Here we include low mass resonant $R = \pi^0$, $\eta$, $\eta'$ contributions. The resonance contributions give intermediate photon transverse momenta. However, these contributions can be eliminated by imposing windows on di-photon invariant mass. We study and quantify individual box contributions (leptonic, quarkish). The electron/positron boxes dominate at low $M_{\gamma \gamma}<1$ GeV di-photon invariant masses. The PbPb$\to$PbPb$\gamma \gamma$ cross section is calculated within equivalent photon approximation in the impact parameter space. Several differential distributions are presented and discussed. We consider four different kinematic regions. We predict cross section in the (mb-b) range for typical ALICE 3 cuts, a few orders of magnitude larger than for the current ATLAS or CMS experiments. We also consider the two-$\pi^0$ background which can, in principle, be eliminated at the new kinematical range for the ALICE 3 measurements by imposing dedicated cuts on di-photon transverse momentum and\or so-called vector asymmetry.Comment: 20 pages, 19 Figures, 3 Tables; misprint corrected, 1 figure adde

A remark on the dimension of the Bergman space of some Hartogs domains

Let D be a Hartogs domain of the form D={(z,w) \in CxC^N : |w| < e^{-u(z)}} where u is a subharmonic function on C. We prove that the Bergman space of holomorphic and square integrable functions on D is either trivial or infinite dimensional.Comment: 12 page

INVESTIGATION OF BURRIED INTERFACE (Si3N4/Ga As) BY EXAFS IN TOTAL REFLECTION AND DISPERSIVE MODE

Etudier l'interface sous un film de passivation est souvent impossible. La spectroscopie d'absorption X par reflectivité totale permet de réaliser une telle approche si le film déposé est de densité plus faible que le substrat. C'est le cas de Si3 N4 sur Ga As. Les deux méthodes de préparation utilisées conduisent à des interfaces de structure différente. La méthode PECVD donne une interface homogène tandis que la méthode du plasma réactif produit également en faible quantité des liaisons GaN. Dans ce dernier cas un modèle d'îlots de GaN serait en accord avec l'étude XPS.To reach a burried interface below the passivating film is often out of the capability of experimental technique. The X-ray absorption, spectroscopy using the total reflection scheme allows such investigation if the deposited film has a lower electronic density than the substrate one. This requirement is fulfilled with Si3 N4 on Ga As. Two considered processes leads to interfaces with large differences. PECVD keeps well-defined reflecting surface, while the cathodic reactive sputtering gives rise to an island-type one, this results agree with XPS measurements