Alpha-alpha scattering in the Multiverse

We investigate the phase shifts of low-energy α-α 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 θ-angle. As a first step, we recalculate α-α 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 α-α 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 θ-angle can be expressed in terms of the θ-dependent pion mass.