HadroTOPS: A Monte Carlo Event Generator For Hadron Production In Two-Photon Scattering In Electron Positron Collisions

TL;DR

HadroTOPS provides a comprehensive Monte Carlo generator for hadronic two-photon production in $e^+e^-$ collisions, delivering exact LO QED couplings with a uniform phase-space decay and enabling partial-wave analyses across energy and photon-virtuality ranges. It combines exclusive, dispersively constrained amplitudes for $\pi\pi$ and $\pi^0\eta$ channels with data-driven inputs for $K\bar K$ and $\eta\eta$, and includes the $f_1(1285)\to\eta\pi^+\pi^-$ mode to cover a broad spectrum of hadronic final states. The framework supports both inclusive and exclusive processes, uses an efficient Schuler-based phase-space generator, and provides modular input schemes, precise vector handling, and ROOT-compatible outputs, making it suitable for BESIII/Belle II studies and PWAs. Validation against analytic luminosity functions and comparisons with existing generators demonstrate accurate, flexible modeling of two-photon processes and their azimuthal dependences, with practical applications to hadron spectroscopy and hadronic light-by-light contributions to $(g-2)_\mu$.

Abstract

We present a Monte Carlo event generator specifically developed for the study of hadronic two-photon fusion events in two-photon scattering at electron-positron colliders. The code enables the generation of events with exact leading-order QED coupling and a flat phase space decay of the hadronic state into an arbitrary number of final state particles as selected by the user. Thus, this generator is well-suited for the use of partial wave analyses tools to study the two-photon production of higher-multiplicity final states across a wide range of energies and photon virtualities. Furthermore, the code integrates both experimental and theoretical inputs on the two-photon couplings of hadrons to simulate two-photon production processes. Motivated by the investigations of the BESIII collaboration, the final states $π^+π^-$, $π^0π^0$, $π^0η$, $K^+K^-$, $K^0_SK^0_S$, $ηη$, and $f_1(1285)\to ηπ^+π^-$ via $a_0^\pm(980)π^\mp$ and $f_0(500)η$ are currently included. The code is sufficiently flexible to easily add additional final states as well as quickly change the already included channels.

Figures (20)

• Figure 1: The $e^+e^- \to e^+e^- \pi_1 \pi_2$ process in the $\gamma^*\gamma^*$ c.m. frame
• Figure 2: The azimuthal angles $\tilde{\phi}_1$ and $\tilde{\phi}_2$ in the $\gamma^\ast \gamma^\ast$ c.m. frame between the lepton planes and the hadron plane. The latter is chosen as the $xz$-plane. The momenta $\vec{p}_1$ and $\vec{q}_1$ define the $x_1 z$-plane, whereas the momenta $\vec{p}_2$ and $\vec{q}_2$ define the $x_2 z$-plane.
• Figure 3: Flowchart of the four-vector generation of the $e^+e^-X$ final state
• Figure 4: Top row of panels: prediction for $\sigma_{TT}$ for $\gamma \gamma \to \pi^0 \pi^0$ compared with data. Lower panels: predictions for $\sigma_{0}$, $\sigma_{2}$, and $\sigma_{LL}$ for $\gamma^* \gamma^* \to \pi^0 \pi^0$ with $Q_1^2 = 0.25 \,\text{GeV}^2$ and $Q_2^2 = 0, 0.25, 0.5, 0.75, 1.0 \,\text{GeV}^2$, shown for full angular coverage ($|\cos\theta| \leq 1$).
• Figure 5: Predictions for $\sigma_{TL}$, $\sigma_{LT}$, $\tau_{0}$, and $\tau_{1}$ for $\gamma^* \gamma^* \to \pi^0 \pi^0$ with $Q_1^2 = 0.25 \,\text{GeV}^2$ and $Q_2^2 = 0, 0.25, 0.5, 0.75, 1.0 \,\text{GeV}^2$, shown for full angular coverage ($|\cos\theta| \leq 1$).