  We investigate the phase shifts of low-energy alpha-alpha scattering under
variations of the fundamental parameters of the Standard Model, namely the
light quark mass, the electromagnetic fine-structure constant as well as the
QCD theta-angle. As a first step, we recalculate alpha-alpha scattering in our
Universe utilizing various improvements in the adiabatic projection method,
which leads to an improved, parameter-free prediction of the S- and D-wave
phase shifts for laboratory energies below 10 MeV. We find that positive shifts
in the pion mass have a small effect on the S-wave phase shift, whereas
lowering the pion mass adds some repulsion in the two-alpha system. The effect
on the D-wave phase shift turns out to be more pronounced as signaled by the
D-wave resonance parameters. Variations of the fine-structure constant have
almost no effect on the low-energy alpha-alpha phase shifts. We further show
that up-to-and-including next-to-leading order in the chiral expansion,
variations of these phase shifts with respect to the QCD theta-angle can be
expressed in terms of the theta-dependent pion mass.
