  We provide a non-perturbative expression for the hadron production in
electron-positron annihilation at zero temperature in a strongly coupled,
large-Nc SU(Nc) field theory with Nf << Nc quark flavors. The resulting
expressions are valid to leading order in the electromagnetic coupling constant
but non-perturbatively in the SU(Nc) interactions and the mass of the quark. We
obtain this quantity by computing the imaginary part of the hadronic vacuum
polarization function Pi_q using holographic techniques, providing an
alternative to the known method that uses the spectrum of infinitely stable
mesons determined by the normalizable modes of the appropriated fields in the
bulk. Our result exhibits a structure of poles localized at specific real
values of q^2, which coincide with the ones found using the normalizable modes,
and extends it offering the unique analytic continuation of this distribution
to a function defined for values of q^2 over the complex plane. This analytic
continuation permits to include a finite decay width for the mesons. By
comparison with experimental data we find qualitatively good agreement on the
shape of the first pole, when using the rho meson parameters and choosing a
proper normalization factor. We then estimate the contribution to the anomalous
magnetic moment of the muon finding an agreement within 25%, for this choice of
parameters.
