Hadron production in electron-positron annihilation computed from the gauge-gravity correspondence

We provide a nonperturbative expression for the hadron production in electron-positron annihilation at zero temperature in a strongly coupled, large-N-c SU(N-c) field theory with N-f < N-c quark flavors. The resulting expressions are valid to leading order in the electromagnetic coupling constant but nonperturbatively in the SU(N-c) 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