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

TL;DR

This paper derives a non-perturbative holographic expression for hadron production in electron-positron annihilation, incorporating finite meson decay widths and comparing favorably with experimental data and muon magnetic moment estimates.

Contribution

It introduces a holographic method to compute hadron production non-perturbatively, extending previous models by including finite meson decay widths and complex q^2 analysis.

Findings

Qualitative agreement with experimental data on the rho meson shape.

Estimated contribution to muon g-2 within 25%.

Provided a novel analytic continuation of the polarization function.

Abstract

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.