Constraints on variation of fine structure constant from joint SPT-SZ and XMM-Newton observations

We search for a variation of the electromagnetic fine structure constant ($\alpha \equiv e^2/\hbar c$) using a sample of 58 SZ selected clusters in the redshift range ($0.2<z<1.5$) detected by the South Pole Telescope, along with X-ray measurements using the XMM-Newton observatory. We use the ratio of the integrated SZ Compto-ionization to its X-ray counterpart as our observable for this search. We first obtain a model-independent constraint on $\alpha$ of about 0.7%, using the fact that the aforementioned ratio is constant as a function of redshift. We then look for a logarithmic dependence of $\alpha$ as a function of redshift: $\Delta \alpha/\alpha = -\gamma \ln(1+z)$, as this is predicted by runaway dilaton models. We find that $\gamma$ = $-0.046 \pm 0.1$, which indicates that there is no logarithmic variation of $\alpha$ as a function of redshift. We also search for a dipole variation of the fine structure constant using the same cluster sample. We do not find any evidence for such a spatial variation.