Road map for the tuning of hadronic interaction models with accelerator-based and astroparticle data

TL;DR

Global tuning of hadronic interaction models using data from both accelerator-based and astroparticle experiments addresses longstanding tensions in interpreting high-energy data. The paper outlines a two-loop tuning framework that integrates conventional particle-physics event generators with air-shower simulations, supported by a Rivet-like translator for astroparticle observables. It highlights automatic tuning strategies (gradient-based and Bayesian) and presents early astro-tuning efforts, demonstrating feasibility while identifying bottlenecks such as forward physics constraints and computational costs. The work argues that successful global tuning would reduce model uncertainties, clarify non-perturbative QCD effects, and improve predictive power for both collider analyses and cosmic-ray physics.

Abstract

In high-energy and astroparticle physics, event generators play an essential role, even in the simplest data analyses. As analysis techniques become more sophisticated, e.g. based on deep neural networks, their correct description of the observed event characteristics becomes even more important. Physical processes occurring in hadronic collisions are simulated within a Monte Carlo framework. A major challenge is the modeling of hadron dynamics at low momentum transfer, which includes the initial and final phases of every hadronic collision. QCD-inspired phenomenological models used for these phases cannot guarantee completeness or correctness over the full phase space. These models usually include parameters which must be tuned to suitable experimental data. Until now, event generators have been developed and tuned mainly on the basis of data from high-energy physics experiments at accelerators. The wealth of data available from the latest generation of astroparticle experiments has not yet been fully exploited, and in many cases is not satisfactorily described. Both kinds of data sets are complementary as astroparticle experiments provide sensitivity especially to hadrons produced nearly parallel to the collision axis and cover center-of-mass energies up to several hundred TeV, well beyond those reached at colliders so far. In this report, we provide an overview of state-of-the-art event generators and their tuning, including the most relevant inputs from high-energy accelerator and astroparticle experiments. We present a road map that shows, for the first time, how the unified tuning of event generators with accelerator-based and astroparticle data can be performed.

Figures (5)

• Figure 1: Effect of changing basic parameters of hadronic interactions on the means and standard deviations of the logarithm of the muon number $N_\mu$ (top row) and the depth $X_\text{max}$ of the shower maximum (bottom row) for a $10^{19.5}$ eV proton shower simulated with Conex using Sibyll2.1 as the baseline model. The left and right columns show relative shifts from the mean and fluctuations, respectively. The data, originally based onUlrich:2010rg, are shown as a function of the modification in the nucleon-nucleon system at a CM-energy $\sqrt{s_\text{NN}}\xspace = 13$ TeV, which is extrapolated logarithmically towards higher energies. The shaded bands highlight a $\pm 10\,\%$ and $\pm 30\,\%$ modification, respectively (Plot taken from Albrecht:2021cxw).
• Figure 2: Muon content of air showers encoded in $\Delta z$-values (see text) as a function of the shower energy $E$ from different experiments. Only experiments with little (red-brown) or no (black) muon contribution to the energy estimator are shown. The $\Delta z$ value shows the deviation of the muon content from the expectation based on the data driven GSF model Dembinski:2017zsh and the event generator EPOS LHC. The gray band indicates the expectation when the mass is inferred from Auger $X_\text{max}$ measurements instead of GSF. Error bars show statistical and systematic uncertainties added in quadrature. Figure adapted from Ref. ArteagaVelazquez:2023fda
• Figure 3: A schematic of classic tuning. The classic tuning loop proceeds as follows: 1) A new vector of parameter values $\vec{A_0}$ is used to configure the event generator. 2) The event generator is used to simulate all collision systems fitting the required initial conditions of the Rivet plugins. 3) The Rivet plugins compute predictions comparable to their respective HEP data from the raw event sample. 4) A chi-square value is computed from all Rivet plugins and fed back into the tuning algorithm. 5) The tuning algorithm computes a new vector of parameter values based on this input.
• Figure 4: A schematic of global tuning. The global tuning loop proceeds as follows: 1) An initial vector of parameter values $\vec{A_0}$ is used to configure the event generator. 2a) The event generator is used to simulate all collision systems fitting the required initial conditions of the Rivet plugins. 2b) The event generator runs inside the air shower simulation code Corsika to simulate air showers, or simulates all collision systems required to build interaction tables for Conex or MCEq, which are then used to simulate air showers. 3) The energy spectrum and mass composition of the primary cosmic rays follow a cosmic ray flux model. 4a) The Rivet plugins compute predictions comparable to their respective HEP data from the raw HEP event sample. 4b) Rivet-like translators compute predictions comparable to their respective EAS data based on the raw air shower sample. 5) A chi-square value is computed from all Rivet plugins and the translator plugins and fed back into the tuning algorithm. 6) The tuning algorithm computes a new vector of parameter values based on these inputs. Note that the Rivet-like translator still needs to be developed.
• Figure 5: Muon content of air showers encoded in z-values (see text) as function of shower energy E from different experiments. The event generator used to compute the predicted muon content is shown in the upper left corner of each plot. The colors indicate how much muons contribute to the estimate of the shower energy E. The dashed line indicated the expected z-value based on the GSF model Dembinski:2017zsh, while the gray band shows the expectation from Auger $X_\text{max}$ measurements. Error bars show statistical and systematic uncertainties added in quadrature. Figure taken from Ref. ArteagaVelazquez:2023fda