  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, is
carried out up to next-to-leading order (NLO) in the EFT expansion. The power
counting we adopt implies that Coulomb interactions must be included to all
orders in $\alpha_{\rm em}$. We do this via EFT Feynman diagrams computed in
time-ordered perturbation theory, and so recover existing quantum-mechanical
technology such as 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 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. We also discuss the relation of our extrapolated $S(0)$ to the
previous standard evaluation.
