Low Energy Pion-Pion Elastic Scattering in Sakai-Sugimoto Model

TL;DR

This paper uses the Sakai-Sugimoto holographic QCD model to derive pion-pion scattering amplitudes, incorporating higher-order corrections, and finds good agreement with experimental phase shift data.

Contribution

It derives the four-derivative pion contact terms from the holographic model and evaluates low-energy scattering amplitudes including these corrections.

Findings

Derived phenomenological pion Lagrangian from holographic model

Calculated pion-pion scattering amplitudes with corrections

Achieved satisfactory agreement with experimental data

Abstract

We have considered the holographic large $N_c$ QCD model proposed by Sakai and Sugimoto and evaluated the non-Abelian DBI-action on the D8-brane upto $(\alpha')^4$ terms. Restricting to the pion sector, these corrections give rise to four derivative contact terms for the pion field. We derive the Weinberg's phenemenological lagrangian. The coefficients of the four derivative terms are determined in terms of $g_{YM}^2$. The low energy pion-pion scattering amplitudes are evaluated. Numerical results are presented with the choice of $M_{KK}=0.94 GeV$ and $N_c=11$. The results are compared with the amplitudes calculated using the experimental phase shifts. The agreement with the experimental data is found to be satisfactory.