Abstract
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.
Highlights
Near-threshold S-wave results from a state with (JP, I) = (0+, 0) at an energy ER 0.1 MeV above the threshold, see e.g. the review [2], with a tiny width of ΓR 6 eV
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
We will use the same chiral EFT at next-to-next-to-leading order combined with the socalled Adiabatic Projection Method (APM), that allows for ab initio calculations of nuclear reactions, as developed in refs. [12,13,14]
Summary
While the investigation of the resonance enhancement in the 3α process due to the Hoyle state already sets rather stringent limits on the possible variations of the light quark mass and the fine-structure constant, one has to be aware that these results are afflicted with some inherent uncertainties, as in the corresponding stellar simulations only the distance of the Hoyle state to the 3α-threshold is varied Translating this into a dependence on, say, the light quark mass assumes that only the nuclei directly involved in the 3α process are subject to these changes, but one should perform the complete stellar simulations (reaction networks) with appropriately modified masses and reaction rates. It is of interest to study the reaction rate of the fundamental α-α scattering process as a function of θ, as will be done here
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