Data-Driven Predictions for Dark Photon and Millicharged Particle Production

TL;DR

The paper tackles the challenge of predicting light, weakly coupled particles in fixed-target experiments by tying signal production to measured dilepton (virtual photon) distributions via electromagnetic amplitudes. It introduces a data-driven framework that normalizes dark photon and millicharged particle yields to the observed SM $dσ_γ/dm_γ^2 d^3 q$ and trains a conditional normalizing flow to generate fully differential kinematics for fast, realistic Monte Carlo samples. Using a NA60-like mock dataset, the authors demonstrate faithful reproduction of yields and kinematic distributions, with KL-divergence validation and the ability to interpolate across $m_{A'}$ and $m_χ$ values. The approach reduces dependence on uncertain hadronic form factors and can be extended to other vector bosons, enabling more accurate signal acceptance estimates for long-lived dark-sector searches in upcoming experiments.

Abstract

Accurate signal predictions are essential for interpreting and optimizing fixed-target searches for new physics. Even in minimal models such as the dark photon ($A'$) or millicharged particles (mCPs), theoretical uncertainties in hadronic production can be substantial. We introduce a data-driven framework that predicts both the rate and kinematic distributions of $A'$ and mCP production directly from measured dilepton events, without relying on specific theoretical production models. This method uses the close correspondence between amplitudes for emission of $A'$ or mCPs, and for off-shell Standard Model photon production, the latter being experimentally measurable in full differential form. We demonstrate that normalizing flow models can learn these distributions from data and serve as a fast, realistic Monte Carlo generator for dark sector signal simulations.

Figures (8)

• Figure 1: Validation of our mock data set (obtained by reweighing Pythia 8.3 samples) against dimuon invariant mass (left) and vector meson transverse momentum distributions observed by NA60 from their Pb target. In the right panel, the coloured bands indicate $1\sigma$ ranges of the NA60 $p_T$ spectrum fit parameters.
• Figure 2: Data-driven estimate of $A'$ yield (black line) for an NA60-like beam and target configuration as a function of $m_{A'}$. The mock data includes only meson decays, and not bremsstrahlung (red curve). The data-driven result accounts for the effects of detector resolution. The red band corresponds to variations of a proton form-factor parameter, in the bremsstrahlung calculation by a factor of 2. Note that both curves correspond to the full phase space without any angular cuts.
• Figure 3: Data-driven estimate of mCP ($\chi$) yield (black line) for an NA60-like beam and target configuration as a function of $m_{\chi}$. The mock data includes only meson decays needed to describe the NA60 result and not bremsstrahlung (red curve), which may not account for all relevant production channels in a given mass window. For example, for NA60, contributions from $\pi^0 \to \gamma \bar{\chi}\chi$ and $J/\psi\to\bar{\chi}\chi$ (shown as coloured lines), are not included due to experimental selections.
• Figure 4: Kullback-Leibler divergence between normalizing flow model trained on mock data and the data itself, as a function of the virtual photon invariant mass $m_{\gamma}$. The green (yellow) bands show 68% (95%) confidence limits for KL divergence between different realizations of the data. The black dotted lines indicate the $95\%$ uncertainty bands due to finite sample size drawn from the NF model. The NF model is compatible with the data distribution up to statistical uncertainties, which are more severe at larger invariant masses because of smaller sample sizes.
• Figure 5: Comparison of the normalized $q_T$ (left column) and $E_{A'}=E_\gamma$ (right column) dark photon distributions sampled from the NF model and the mock data for different $m_{A'} = m_\gamma$ values. In each row the data is a subset of the full data set with virtual photon invariant masses within 30 MeV of the corresponding $m_{A'}$. The NF model successfully interpolates the distributions to arbitrary $m_{A'}$; the quality of interpolation degrades at larger mass because the training data sample is small in that region of phase space.