  The recent measurements of the Cosmic Microwave Background anisotropies at
arcminute angular scales performed by the ACT and SPT experiments are probing
the damping regime of CMB fluctuations. The analysis of these datasets
unexpectedly suggests that the effective number of relativistic degrees of
freedom is larger than the standard value of Neff = 3.04, and inconsistent with
it at more than two standard deviations. In this paper we study the role of a
mechanism that could affect the shape of the CMB angular fluctuations at those
scales, namely a change in the recombination process through variations in the
fine structure constant. We show that the new CMB data significantly improve
the previous constraints on variations of {\alpha}, with {\alpha}/{\alpha}0 =
0.984 \pm 0.005, i.e. hinting also to a more than two standard deviation from
the current, local, value {\alpha}0. A significant degeneracy is present
between {\alpha} and Neff, and when variations in the latter are allowed the
constraints on {\alpha} are relaxed and again consistent with the standard
value. Deviations of either parameter from their standard values would imply
the presence of new, currently unknown physics.
