We report a leading-order ( LO ) calculation of ^ { 7 } \mathrm { Be } ( p, \gamma ) ^ { 8 } \mathrm { B } in a low-energy effective field theory . ^ { 8 } \mathrm { B } is treated as a shallow proton + { } ^ { 7 } \mathrm { Be } core and proton + { } ^ { 7 } \mathrm { Be } ^ { * } ( core excitation ) p -wave bound state .
The couplings are fixed using measured binding energies and proton- ^ { 7 } \mathrm { Be } s -wave scattering lengths , together with ^ { 8 } \mathrm { B } asymptotic normalization coefficients from ab initio calculations .
We obtain a zero-energy S -factor of 18.2 \pm 1.2 ~ { } ( { ANC~ { } only } ) eV b .
Given that this is a LO result it is consistent with the recommended value S ( 0 ) = 20.8 \pm 1.6 eV b .
Our computed S ( E ) compares favorably with experimental data on ^ { 7 } \mathrm { Be } ( p, \gamma ) ^ { 8 } \mathrm { B } for E < 0.4 MeV .
We emphasize the important role of proton- ^ { 7 } \mathrm { Be } scattering parameters in determining the energy dependence of S ( E ) , and demonstrate that their present uncertainties significantly limit attempts to extrapolate these data to stellar energies .