High-Energy Pion Scattering in Holographic QCD: A Comparison with Experimental Data

Following Polchinski and Strassler [1] and our previous work [2], we study high-energy pion scattering in the holographic QCD hard-wall model. In particular, we focus on comparing our predictions for the angular dependence of $π^{+} π^{-} \to π^{+} π^{-}$ scattering with experimental data extracted from the process $π^{-} p \to π^{+} π^{-} n$. Having previously shown that our approach reproduces the constituent counting rule found in QCD, we now observe qualitative agreement between our predictions and the extracted data in the high-energy fixed-angle regime. We also provide predictions for all other 2-to-2 pion scattering processes. Our approach can be extended to a broader range of meson and glueball scattering processes in various holographic QCD models.

💡 Research Summary

In this work the authors revisit high‑energy pion‑pion scattering within the framework of holographic QCD, employing the hard‑wall (hard‑cutoff) model of a five‑dimensional asymptotically AdS (AAdS) space. Building on the seminal proposal of Polchinski and Strassler, they formulate an explicit ansatz for the four‑point pion scattering amplitude that incorporates the full tower of string states through a super‑string 4‑point amplitude S. By replacing the flat‑space metric with the AAdS metric, substituting the five‑dimensional momenta with the physical four‑momenta of the external pions, and using the pion wave‑function ψπ(w)∝(−g k)−½∼|w|−3, they obtain an integral expression (eq. 2.12) for the amplitude.

The crucial observation is that, in the high‑energy fixed‑angle limit (s→∞ with t/s held fixed), the dominant s‑dependence of the integral comes solely from the UV region of the geometry (w→±∞). The exponential softness of the underlying string amplitude is suppressed, leaving a power‑law behaviour A∼s−2 f(θ), precisely the constituent‑counting rule expected from perturbative QCD for a process involving two pions (m=2). The authors verify this scaling analytically by rescaling the radial coordinate w→w∗=w/(R5√α′s) and performing the w‑integral with a UV cutoff; the result is independent of the IR cutoff provided it is finite.

To make contact with experiment, the authors extract π+π−→π+π− scattering data indirectly from measurements of the reaction π−p→π+π−n reported in Ref.