  Expressions for the potentials appearing in the nonrelativistic effective
field theory description of doubly heavy baryons are known in terms of operator
insertions in the Wilson loop. However, their evaluation requires
nonperturbative techniques, such as lattice QCD, and the relevant calculations
are often not available. We propose a parametrization of these potentials with
a minimal model dependence based on an interpolation of short- and
long-distance descriptions. The short-distance description is obtained from
weakly-coupled pNRQCD and the long-distance one is computed using an effective
string theory. The effective string theory coincides with the one for pure
gluodynamics with the addition of a fermion field constrained to move on the
string. We compute the hyperfine contributions to the doubly heavy baryon
spectrum. The unknown parameters are obtained from heavy quark-diquark symmetry
or fitted to the available lattice QCD determinations of the hyperfine
splittings. Using these parameters we compute the double charm and bottom
baryon spectrum including the hyperfine contributions. We compare our results
with those of other approaches and find that our results are closer to lattice
QCD determinations, in particular for the excited states. Furthermore, we
compute the vacuum energy in the effective string theory and show that the
fermion field contribution produces the running of the string tension and a
change of sign in the L\"uscher term.
