High-Energy Fixed-Angle Meson Scattering and the Constituent Counting Rule in Holographic QCD

We investigate the high-energy fixed-angle scattering of pions and $\rho$-mesons in a bottom-up holographic QCD model. To this end, we generalise the approach of Polchinski and Strassler arXiv:hep-th/0109174 to write an ansatz for meson scattering amplitudes based on superstring scattering amplitudes in asymptotically AdS space. We demonstrate that our generalisation of the Polchinski–Strassler proposal is necessary to describe $\rho$-meson scattering consistently with the Nambu–Goldstone boson equivalence theorem. Our results for pion and $\rho$-meson scattering amplitudes are in agreement with the constituent counting rule found in QCD. Moreover, our proposal for 2-to-2 scattering amplitudes provides a method for computing scattering angle dependence.