We employ an effective field theory ( EFT ) that exploits the separation of scales in the p -wave halo nucleus ^ { 8 } \mathrm { B } to describe the process ^ { 7 } \mathrm { Be } ( p, \gamma ) ^ { 8 } \mathrm { B } up to a center-of-mass energy of 500 keV .
The calculation , for which we develop the lagrangian and power counting in terms of velocity scaling , is carried out up to next-to-leading order ( NLO ) in the EFT expansion .
The Coulomb force between ^ { 7 } Be and proton plays a major role in both scattering and radiative capture at these energies .
The power counting we adopt implies that Coulomb interactions must be included to all orders in \alpha _ { em } .
We do this via EFT Feynman diagrams computed in time-ordered perturbation theory , and so recover existing quantum-mechanical technology such as the Lippmann-Schwinger equation and the two-potential formalism for the treatment of the Coulomb-nuclear interference .
Meanwhile the strong interactions and the E1 operator are dealt with via EFT expansions in powers of momenta , with a breakdown scale set by the size of the ^ { 7 } Be core , \Lambda \approx 70 MeV .
Up to NLO the relevant physics in the different channels that enter the radiative capture reaction is encoded in ten different EFT couplings .
The result is a model-independent parametrization for the reaction amplitude in the energy regime of interest .
To show the connection to previous results we fix the EFT couplings using results from a number of potential model and microscopic calculations in the literature .
Each of these models corresponds to a particular point in the space of EFTs .
The EFT structure therefore provides a very general way to quantify the model uncertainty in calculations of ^ { 7 } \mathrm { Be } ( p, \gamma ) ^ { 8 } \mathrm { B } .
We provide details of this projection of models into the EFT space and show that the resulting EFT parameters have natural size .
We also demonstrate that the only N ^ { 2 } LO corrections in ^ { 7 } \mathrm { Be } ( p, \gamma ) ^ { 8 } \mathrm { B } come from an inelasticity that is practically of N ^ { 3 } LO size in the energy range of interest , and so the truncation error in our calculation is effectively N ^ { 3 } LO .
The key LO and NLO results have been presented in our earlier papers .
The current paper provides further details on these studies .
We also discuss the relation of our extrapolated S ( 0 ) to the previous standard evaluation .