Angantyr: Heavy-Ion Extension of PYTHIA8

• Angantyr is a heavy-ion extension of PYTHIA8 that extrapolates proton–proton frameworks to simulate p–A and A–A collisions with minimal tuning.
• It employs a Glauber-model for nuclear geometry, integrating wounded nucleon fluctuations, multi-parton interactions, and diffractive excitation in sub-collision events.
• Angantyr serves as a non-collective baseline, enabling researchers to isolate QGP-medium effects and test the limits of pp-based descriptions in nuclear collisions.

Searching arXiv for Angantyr papers and related applications to ground the article in the literature. arxiv_search(query="Angantyr PYTHIA heavy-ion model", max_results=10, sort_by="relevance") arxiv_search(query="Angantyr model heavy-ion PYTHIA8 applications", max_results=10, sort_by="relevance") Angantyr is the heavy-ion extension of PYTHIA8: a model for generating complete exclusive hadronic final states in proton–nucleus and nucleus–nucleus collisions by extrapolating the pp event-generation framework of PYTHIA8 to pA and AA systems with as few new assumptions and tunings as possible (Bierlich et al., 2018). It is built around a Glauber-model description of nuclear geometry, wounded-nucleon and Fritiof-inspired ideas, and explicit treatment of multi-parton interactions and diffractive excitation in each nucleon–nucleon sub-collision (Bierlich et al., 2018). Across later phenomenology, Angantyr is repeatedly used as a baseline model without a hot thermalized medium, hydrodynamic flow, or jet quenching, so that deviations between data and simulation can be interpreted as signatures of collectivity, QGP-medium effects, critical fluctuations, or other dynamics absent from the model (Zuman et al., 2023).

1. Origins and conceptual role

Angantyr was introduced to bridge a large part of the gap between high-energy hadron phenomenology and heavy-ion phenomenology by constructing heavy-ion events as a direct extrapolation of high-energy pp collisions as described by PYTHIA (Bierlich et al., 2018). The core motivation is twofold: to provide a realistic non-collective baseline for heavy-ion observables, and to test how far a pp-based description can go before genuinely collective physics must be added (Bierlich et al., 2018).

In the model’s own framing, heavy-ion collisions are not generated through an explicit QGP stage or hydrodynamic evolution. Instead, Angantyr generalizes the usual pp framework to pA and AA collisions by combining many nucleon–nucleon-like sub-collisions into one nuclear event (Bhowmick et al., 2024). This places it in a distinct methodological category relative to hybrid approaches such as SMASH-vHLLE or transport-based models such as AMPT: Angantyr is designed to capture geometry, fluctuating nucleon substructure, multiple scattering, parton showers, and Lund-string hadronization, while omitting a de-confined medium and collective expansion (Constantin et al., 6 Sep 2025).

The baseline status of Angantyr is central to its later use. The model is described as suitable for understanding fluctuations expected from geometry, hadronic production, and acceptance effects alone, and as a reference model without deconfined QGP formation (Bhowmick et al., 2024). This suggests that Angantyr is best interpreted not as a complete theory of heavy-ion dynamics, but as a controlled null hypothesis for observables sensitive to collectivity, medium response, or criticality.

2. Event construction and nuclear geometry

Angantyr constructs a pA or AA event as a superposition of multiple nucleon–nucleon sub-collisions determined by Glauber geometry and event-by-event nucleon fluctuations (Bierlich et al., 2018). In practical descriptions across the literature, nucleons are distributed inside nuclei according to Woods–Saxon profiles, the collision geometry is handled with a Glauber-model picture, and the number of wounded nucleons is determined with Gribov-corrected Glauber fluctuations (Bhowmick et al., 2024).

At the formal level, the nuclear S-matrix is written as

$$S^{AB}(b) = \prod_{\mu=1}^A \prod_{\nu=1}^B S^{(N_\mu,N_\nu)}(b_{\mu\nu}),$$

with nucleon positions generated event by event and propagated on straight-line trajectories through the opposing nucleus (Bierlich et al., 2018). Angantyr is explicitly inspired by the wounded-nucleon model and the old Fritiof model. In the wounded-nucleon picture, soft production scales with wounded projectile and target nucleons through

$$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$

while the Fritiof-inspired component supplies a mechanism for longitudinal excitation and string-like particle production (Bierlich et al., 2018).

A distinctive feature of Angantyr is its treatment of projectile and target fluctuations. Diffractive excitation is interpreted in the Good–Walker picture as a consequence of fluctuations in the nucleon’s partonic substructure, with

$$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$

so diffraction is identified with the variance of the interaction amplitude (Bierlich et al., 2018). The model includes fluctuations in both projectile and target nucleons, which are represented through fluctuating effective radii drawn from a Gamma distribution and kept frozen during passage through the opposite nucleus (Bierlich et al., 2018). A plausible implication is that Angantyr’s fluctuation structure is not reducible to purely geometric participant counting; it also embeds event-by-event fluctuations in the underlying nucleon state.

3. Sub-collision classes and PYTHIA machinery

Each nucleon–nucleon encounter in Angantyr is classified as elastic, diffractive, or absorptive, and the full heavy-ion final state is obtained by stacking the corresponding sub-events (Bierlich et al., 2018). Primary absorptive collisions are generated as ordinary PYTHIA minimum-bias events, while additional non-diffractive interactions of already wounded nucleons are treated as secondary non-diffractive collisions modeled through a diffractive-like prescription (Lönnblad et al., 2023). This primary/secondary distinction is one of the model’s essential algorithmic devices for extrapolating pp-like event generation to nuclear collisions (Lönnblad et al., 2023).

Within each sub-collision, Angantyr uses standard PYTHIA machinery: hard and soft interactions, initial- and final-state radiation, multi-parton interactions, parton showers, fragmentation, and decays (Singh et al., 2021). Final hadrons are produced via Lund string fragmentation, and the resulting sub-events are merged into one nuclear event (Bhowmick et al., 2024). The standard PYTHIA infrared regularization of partonic scatterings,

$$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$

is retained as part of the MPI framework that Angantyr inherits from PYTHIA8 (Bierlich et al., 2018).

The model’s treatment of diffractive excitation is not peripheral bookkeeping. It is tied to fluctuations in nucleon substructure and to the generation of secondary wounded-nucleon contributions (Bierlich et al., 2018). In later work, Angantyr’s heavy-ion event construction is summarized as a stack of multiple PYTHIA-like nucleon–nucleon sub-collisions determined by a Glauber model with Good–Walker fluctuations, where one interaction is treated as primary and further interactions are handled as secondary non-diffractive events (Lönnblad et al., 2023). This suggests that Angantyr’s predictive power for multiplicity and rapidity systematics depends strongly on how these secondary excitations are modeled rather than on hydrodynamic response.

4. MPI, color reconnection, and locality

Two essential ingredients in Angantyr phenomenology are multi-parton interactions and color reconnection. MPI are repeatedly identified as central to multiplicity distributions and underlying-event activity, while CR reduces string length and can generate flow-like patterns even in a model without hydrodynamics (Singh et al., 2021). In Pb–Pb studies, multiplicity distributions and the trend of $\langle p_T\rangle$ with multiplicity are described best when MPI and CR are both active, whereas turning MPI off strongly suppresses particle production; if MPI is off, turning CR on or off makes no difference (Singh et al., 2021).

This MPI–CR dependence also appears in light-nuclei studies. In Au+Au collisions, the light-nuclei yield ratio $N_tN_p/N_d^2$ is affected by CR only when MPI is present; if MPI is turned off, CR has no visible effect on the ratio (Zuman et al., 2023). A closely related analysis including three-nucleon correlations reaches the same conclusion and states it explicitly: color reconnection depends entirely on MPI; if MPI is turned off, CR has no effect (Zhang et al., 24 Apr 2025). This establishes a model-internal constraint: CR is not an autonomous mechanism in Angantyr, but a reorganization of the color topology generated by multiple partonic scatterings.

Originally, Angantyr effectively restricted CR to partons within individual nucleon–nucleon sub-collisions. A later extension introduced a spatially constrained QCD-based color reconnection model, allowing reconnections across different sub-collisions only if dipoles are sufficiently close in transverse space (Lönnblad et al., 2023). The new parameter,

$\texttt{ColourReconnection:dipoleMaxDist},$

was tuned to

$\delta b_c = 0.5\ \mathrm{fm},$

so that CR becomes local in impact parameter rather than either fully intra-subcollision or unrealistically all-to-all (Lönnblad et al., 2023). The same study reports a pp retune with $\texttt{pT0Ref}=2.37$, $\texttt{m0}=1.05$, $$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$0, and $$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$1 fm, followed by Angantyr-specific adjustments for pA and AA via $$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$2 (Lönnblad et al., 2023).

A common misconception is that color reconnection in Angantyr is intrinsically a heavy-ion collective mechanism. The literature instead treats it as a hadronization-level QCD effect that can mimic some collective-looking trends, such as baryon enhancement or a bump in $$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$3 around intermediate $$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$4, without implying a thermalized medium (Singh et al., 2021). Later p–Pb and d–Au studies reinforce this point by showing that CR can generate flow-like peaks or baryon enhancement while leaving other medium-sensitive observables, such as high-$$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$5 suppression, absent (Ortiz et al., 2024).

5. Phenomenological domains and typical observables

Angantyr has been used in a wide range of phenomenological contexts, typically as a non-collective reference model.

Domain	Representative observable(s)	Role of Angantyr
Heavy-ion fluctuations	$$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$6, net-proton cumulants, $$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$7	Hadronic or non-collective baseline
Small-system collectivity tests	$$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$8, $$\frac{dN_{ch}}{d\eta} = w_p F(\eta) + w_t F(-\eta),$$9, $$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$0, particle ratios	Null hypothesis for no collective effects
Nuclear-structure studies	$$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$1, $$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$2, $$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$3	Propagation of initial geometry without hydrodynamics
Air-shower modeling	longitudinal profiles, muon distributions	High-energy hadronic interaction model in CORSIKA 8

In fluctuation studies, Angantyr is used to quantify what can be explained by geometry, hadronic production, and acceptance effects alone. For charged-particle multiplicity fluctuations in Au–Au and Pb–Pb, the scaled variance

$$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$4

is found to be systematically below the expectations of a simple participant superposition model, with weak beam-energy dependence and only mild centrality dependence (Bhowmick et al., 2024). In net-proton studies at top RHIC and LHC energies, Angantyr provides a baseline for cumulants and their ratios in a framework where a thermalized medium is not assumed, while separate afterburner studies show that radial flow and weak decays can substantially modify these cumulants relative to the pure Angantyr baseline (Behera et al., 2019).

In light-nuclei production, Angantyr has been used to study neutron density fluctuation, neutron–proton correlation, and three-nucleon correlation effects through the yield ratio

$$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$5

The ratio is not a direct fluctuation measure unless the neutron–proton correlation term is negligible; in the model, that correlation is generally not negligible (Zuman et al., 2023). Angantyr predicts that the ratio is nearly unchanged by rapidity coverage and centrality, rises only weakly with beam energy, and cannot reproduce the non-monotonic STAR energy dependence with a peak around $$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$6–$$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$7 GeV (Zuman et al., 2023).

In small-system and light-ion studies, Angantyr frequently functions as a control model for the absence of collective expansion. In O–O collisions at $$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$8 TeV, Angantyr serves as a baseline for no collective effects in comparisons to SMASH and a hydrodynamic hybrid model; apparent nonzero $$\frac{d\sigma_D}{d^2b} = \langle T^2\rangle - \langle T\rangle^2,$$9 and $$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$0 trends are interpreted as dominated by non-flow, while 4-particle cumulants remain mostly close to zero (Constantin et al., 6 Sep 2025). In O–O, p–O, and Ne–Ne structural studies, Angantyr has also been used to propagate initial-state $$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$1-cluster or elongated nuclear configurations into final-state multiplicity, $$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$2, and elliptic-flow-like observables without invoking hydrodynamics (Sharma et al., 26 Mar 2025).

Beyond collider heavy-ion phenomenology, Pythia 8/Angantyr has been embedded in CORSIKA 8 as the high-energy hadronic interaction model for air-shower simulations. A combined tuning to LEP, LHC, and NA22 data adjusted the parameters MultipartonInteractions:pT0Ref, StringZ:aLund, and StringPT:sigma, with the study concluding that collider and fixed-target data prefer different parameter values, especially for pT0Ref (Windau et al., 15 Aug 2025). This demonstrates that Angantyr has also become relevant outside heavy-ion phenomenology, in contexts where hadron–nucleus-like multiple scattering is essential.

6. Empirical performance, limitations, and extensions

Angantyr’s empirical performance is strongest for inclusive baselines and weakest for observables dominated by dense-medium dynamics. The original model paper states that it gives a good description of general final-state properties such as multiplicity and transverse-momentum distributions in pA and AA collisions, and that many observables are reproduced at the level of roughly 5–10% without tuning to heavy-ion data (Bierlich et al., 2018). Later studies confirm that Angantyr often reproduces minimum-bias multiplicity and pseudorapidity distributions reasonably well, including in d–Au and p–Pb, while failing more visibly in the most central events or in observables that are known to be medium sensitive (Nayak et al., 29 Mar 2025).

Several recurring limitations are explicit in the literature. Angantyr does not include hydrodynamic flow, a thermalized QGP medium, jet quenching, critical fluctuations near the QCD critical point, or, in the baseline setups emphasized by multiple comparison papers, collective behavior such as string shoving and ropes (Constantin et al., 6 Sep 2025). These omissions have direct phenomenological consequences. In Pb–Pb angular correlations, PYTHIA 8.235/Angantyr does not reproduce the ALICE near-side jet-peak widths well, especially in $$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$3, and performs worse than AMPT (Szigeti et al., 2019). In identified-particle balance functions in Pb–Pb, the Monash 2013 tune describes peripheral collisions reasonably well but does not quantitatively reproduce central data, leading the authors to suggest that a dedicated heavy-ion tuning of Angantyr may be needed (Gupta et al., 21 Apr 2026).

The model also has documented fluctuation mismatches. In p+Pb collisions at zero impact parameter, a Bayesian reconstruction of multiplicity fluctuations and rapidity correlations from ATLAS data finds that Angantyr overpredicts the relative variances and covariance of central multiplicity observables, which is interpreted as overly large proton-size fluctuations in the model (Pepin et al., 2022). In jet-background studies, the width of random-cone fluctuations in Angantyr exceeds gamma-based analytic expectations by approximately 13% unless leading jets are removed, indicating that its background is not equivalent to a random soft bath and is sensitive to the detailed single-particle $$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$4 spectrum (Hughes et al., 2020).

A major extension path is to couple Angantyr to later-stage dynamics rather than to alter its QGP-free core. The Angantyr+UrQMD framework adds hadronic rescattering after the PYTHIA event generation, enabled by a hadron vertex model that supplies space-time production points to UrQMD (Silva et al., 2020). In Pb–Pb at 2.76 TeV, this hadronic cascade leads to substantial suppression of mid- to high-$$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$5 yields, away-side jet suppression, and modifications of $$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$6 even without any partonic energy loss (Silva et al., 2020). This does not convert Angantyr into a hydrodynamic model, but it demonstrates that the non-QGP baseline can be systematically extended to include a realistic hadronic phase.

7. Interpretive significance

The principal significance of Angantyr lies in its role as a falsifiable baseline. Because it extrapolates PYTHIA’s pp dynamics to nuclear collisions while omitting QGP-medium formation, agreement with Angantyr indicates that a given observable may be explainable through geometry, fluctuating nucleon substructure, multiple scattering, Lund-string hadronization, MPI, CR, resonance decays, and acceptance effects alone (Bhowmick et al., 2024). Disagreement, by contrast, can isolate the sector of heavy-ion phenomenology that requires collective expansion, rescattering, critical dynamics, or medium-induced energy loss.

This role is especially clear in studies that contrast Angantyr with models containing explicit collectivity. In O–O collisions, the hybrid model produces negative and sizable 4-particle cumulants, larger $$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$7 and $$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$8 in central collisions, and strong intermediate-$$\frac{d\sigma_{2\rightarrow 2}}{dp_\perp^2} \propto \frac{\alpha_s^2(p_\perp^2)}{p_\perp^4} \rightarrow \frac{\alpha_s^2(p_\perp^2+p_{\perp 0}^2)}{(p_\perp^2+p_{\perp 0}^2)^2},$$9 enhancement in $\langle p_T\rangle$0, whereas these signatures are absent in Angantyr (Constantin et al., 6 Sep 2025). In Au+Au light-nuclei observables, Angantyr underestimates STAR data and cannot reproduce the non-monotonic peak near 20–30 GeV, reinforcing the interpretation that the observed structure may be connected to physics beyond standard hadronic transport and string-based modeling (Zhang et al., 24 Apr 2025).

At the same time, Angantyr also shows that some collective-looking signals do not uniquely imply a QGP. Spatially constrained CR can alter multiplicity systematics and baryon production across pp, pA, and AA (Lönnblad et al., 2023). In central d–Au, SC CR can mimic baryon enhancement without producing high-$\langle p_T\rangle$1 suppression (Nayak et al., 29 Mar 2025). In Pb–Pb, MPI+CR can reproduce a rising $\langle p_T\rangle$2 with multiplicity and baryon/meson-ratio bumps usually associated with radial flow (Singh et al., 2021). The appropriate conclusion is therefore not that Angantyr invalidates medium interpretations, but that it sharpens them by quantifying which effects survive in a QGP-free construction.

In this sense, Angantyr occupies a specific and durable place in contemporary nuclear-collision phenomenology: it is a PYTHIA-based, Glauber-driven, fluctuation-aware generator of complete hadronic final states for pA and AA systems, and its scientific utility derives precisely from what it excludes as much as from what it includes (Bierlich et al., 2018).