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

TL;DR

The paper investigates high-energy pion scattering in a holographic QCD hard-wall model, testing whether the angular dependence matches the QCD constituent counting rule. Using a Polchinski-Strassler-inspired ansatz in a 5D AdS hard-wall background, the authors derive a 4-point pion scattering amplitude whose leading s-dependence is governed by the UV region. They compare indirect experimental data (π−p → π+π−n) with the holographic predictions in the high-energy fixed-angle regime and find qualitative agreement, while noting Regge regime discrepancies. They also provide predictions for all other 2→2 pion channels and discuss extensions to other meson and glueball processes. The work highlights the potential of holographic QCD to capture hard-scattering scaling and angular structures in hadronic processes, while outlining major limitations and avenues for refinement.

Abstract

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.

Figures (10)

• Figure 1: Angular dependence of the two independent amplitudes $(\tilde{\alpha}^{\prime} s)^2 {\cal A}(s, t)$ and $(\tilde{\alpha}^{\prime} s)^2 {\cal A}(t, u)$. The amplitudes are evaluated as functions of the scattering angle $\theta$ at various values of $\tilde{\alpha}^{\prime} s$ using equations \ref{['eq:2_A1_y']} and \ref{['eq:2_A2_y']} with the methods described above. The graphs show three lines: a dotted line for $\tilde{\alpha}^{\prime} s = 10.5$, a dashed line for $\tilde{\alpha}^{\prime} s = 50.5$, and a solid line for $\tilde{\alpha}^{\prime} s = 100.5$. In panel (b), all three lines are superimposed.
• Figure 2: Illustrations of the scattered particle momenta in the Gottfried--Jackson frame, obtained by boosting from the lab frame to the outgoing $\pi \pi$ rest frame. In this frame, the $z$-axis is along the incoming $\pi^{-}$ direction, $\hat{z} = \vec{q}^{\,\,(1)}/|\vec{q}^{\,\,(1)}|$, and the $y$-axis is given by $\hat{y} = \vec{q}^{\,\,(2)} \times \vec{q}^{\,\,(1)} / |\vec{q}^{\,\,(2)} \times \vec{q}^{\,\,(1)}|$, where the momenta $\vec{q}^{\,\,(1)}$ and $\vec{q}^{\,\,(2)}$ are defined in \ref{['fig:q_def']}. The scattering angles $\theta$ and $\varphi$ are defined such that $-1 \leq \cos \theta \leq 1$ and $-\pi \leq \varphi \leq \pi$.
• Figure 3: Schematic diagram of the process $\pi^{-} p \to \pi^{+} \pi^{-} n$ showing the four-momentum assignments for external particles, with all momenta taken as incoming by convention.
• Figure 4: Mechanisms contributing to the process $\pi^{-} p \to \pi^{+} \pi^{-} n$ at low $|t_{pn}|$.
• Figure 5: Fits for the 175 GeV dataset. The solid black line represents the best fit using the PMA model, while the grey band corresponds to one standard deviation of the fitting parameters in the PMA model. The dashed black like corresponds to a best fit using 1PE model. Data points shown in red were excluded from the fit. The experimental data were digitised from Figure 29 in reference Bromberg:1983he; it is worth noting that we were not able to recover all data points or errors faithfully, although such cases were rare. The $s$-values indicated above correspond to the binned $s$-values included in the experimental measurements, whereas our fits are made only to the average of these binned values.