DIPSY: QCD & Disc Instability Frameworks

• DIPSY is a dual-use framework, with its QCD model simulating dipole cascades using NLL BFKL evolution, dipole swings, and rope hadronization to reproduce key observables in high-energy collisions.
• The disc instability model of DIPSY simulates gravitational fragmentation and companion formation in protoplanetary discs through viscous evolution, clump dynamics, and N-body integration.
• A third variant employs dual IP-adapters with a diffusion backbone to generate few-shot synthetic images, showcasing DIPSY’s versatility across particle physics, astrophysics, and machine learning.

DIPSY is a designation shared by two unrelated models, both prominent in academic literature: (1) the Lund Dipole Cascade Model for QCD event generation in high energy collisions, and (2) Disc Instability Population SYnthesis, a global simulation framework for the population synthesis of stellar and substellar companions formed by disc fragmentation. This article presents a comprehensive, technical summary of both DIPSY frameworks as grounded in primary literature.

1. DIPSY: Lund Dipole Cascade Model for High-Energy QCD Collisions

1.1. Theoretical Foundations and Core Formalism

The DIPSY event generator implements the QCD dipole picture in transverse coordinate space to describe event-by-event partonic structure and final states in electron, proton, and nuclear collisions at high energies (Gustafson, 2012, Gustafson, 2012, Flensburg et al., 2011). It is built on Mueller’s BFKL evolution, supplemented by non-leading logarithmic (NLL) corrections (energy-momentum conservation, running coupling, kinematic constraints), dynamical unitarization, and explicit treatment of color saturation.

The foundational splitting process is described by the leading-logarithmic (LL) BFKL kernel:

$$\frac{d\mathcal{P}}{dY\,d^2z} = \frac{\bar{\alpha}_s}{2\pi} \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2(\mathbf{z}-\mathbf{y})^2}$$

where $(\mathbf{x}, \mathbf{y})$ are the endpoints of a color dipole and $\bar{\alpha}_s = \alpha_s N_c/\pi$. The evolution of the dipole-number density $N(\mathbf{x},\mathbf{y};Y)$ in rapidity is governed by the Balitsky–Kovchegov–Mueller equation at large $N_c$:

$$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$

The non-linear term incorporates gluon saturation effects at high density.

To restore (approximate) boost-invariance, the "dipole swing" mechanism is included: two dipoles of the same color may recouple (swap endpoints), suppressing the formation of large dipoles and mimicking pomeron loops (Flensburg et al., 2011, Gustafson, 2012).

Confinement is introduced by an effective gluon mass, which suppresses emissions at transverse scales larger than $1/m_g$.

1.2. Monte Carlo Implementation and Algorithmic Workflow

DIPSY event generation proceeds through several stages (Flensburg et al., 2011, Gustafson, 2012):

1. Initialization: Each hadron or nucleus is modeled by an ensemble of color dipoles; e.g., the proton is an equilateral triangle of three valence quarks.
2. Dipole Cascade Evolution: Dipoles split according to the (NLO-corrected) BFKL kernel, with energy-momentum, $p_+$/$p_-$, and kinematic ordering. Running of $\alpha_s$ is included at each vertex.
3. Saturation/Unitarity: Within the cascade, the dipole swing is stochastically applied. In the collision, dipole–dipole pairs interact with probability

$(\mathbf{x}, \mathbf{y})$0

where $(\mathbf{x}, \mathbf{y})$1 at short distances.

1. Hard Process and Hadronization: Color-connected partonic final states are passed to the ARIADNE shower for time-like radiation, then hadronized with the Lund string model in PYTHIA.

Exclusive final states, including non-diffractive and diffractive topologies, are constructed via a backbone-gluon selection and color topology tracing, following the Good–Walker formalism for diffraction (Flensburg et al., 2012).

1.3. Physical Observables and Applications

DIPSY provides predictions and initial-state configurations for a broad suite of observables across e$(\mathbf{x}, \mathbf{y})$2e$(\mathbf{x}, \mathbf{y})$3, $(\mathbf{x}, \mathbf{y})$4, $(\mathbf{x}, \mathbf{y})$5, and $(\mathbf{x}, \mathbf{y})$6 collisions (Gustafson, 2012, Flensburg et al., 2011, Gustafson et al., 2015, Flensburg, 2011):

• Total, elastic, and diffractive cross sections (via Good–Walker):

$(\mathbf{x}, \mathbf{y})$7

with $(\mathbf{x}, \mathbf{y})$8 the eikonal amplitude at impact parameter $(\mathbf{x}, \mathbf{y})$9.

• Charged-particle multiplicities, $\bar{\alpha}_s = \alpha_s N_c/\pi$0, $\bar{\alpha}_s = \alpha_s N_c/\pi$1 spectra: minimum-bias agreement within $\bar{\alpha}_s = \alpha_s N_c/\pi$220% of LHC and RHIC data, without retuning parameters (Gustafson, 2012, Flensburg et al., 2011).
• Event-by-event transverse geometry: computation of initial eccentricities $\bar{\alpha}_s = \alpha_s N_c/\pi$3 for small and large systems, used for hydrodynamic and flow studies (Flensburg, 2011).
• Double parton scattering, jet structure, and underlying event modeling, with fluctuations and correlations emergent from dipole geometry.

1.4. Multiplicity-Driven Collective Phenomena and Flow

DIPSY has been used to estimate initial-state geometries and the potential for collectivity in high-multiplicity $\bar{\alpha}_s = \alpha_s N_c/\pi$4 and small systems (Avsar et al., 2010, Avsar et al., 2011). The participant eccentricity is defined from the spatial moments of produced gluons:

$\bar{\alpha}_s = \alpha_s N_c/\pi$5

Two- and four-particle cumulant eccentricities are given by:

$\bar{\alpha}_s = \alpha_s N_c/\pi$6

These geometric measures, via an empirical hydrodynamic scaling, yield $\bar{\alpha}_s = \alpha_s N_c/\pi$7 estimates up to 4–6% in the highest-multiplicity $\bar{\alpha}_s = \alpha_s N_c/\pi$8 collisions, comparable to heavy-ion results at RHIC and LHC. The separation of flow and nonflow contributions exploits cumulants and rapidity-gap correlations.

1.5. Rope Hadronization and Strangeness Enhancement

At high multiplicity, DIPSY implements rope hadronization where overlapping strings recombine into higher SU(3) multiplets, increasing the local string tension via Casimir scaling (Bierlich, 2017, Bierlich et al., 2014, Bierlich et al., 2015). The effective string tension at a breakup vertex is

$\bar{\alpha}_s = \alpha_s N_c/\pi$9

for $N(\mathbf{x},\mathbf{y};Y)$0 parallel and $N(\mathbf{x},\mathbf{y};Y)$1 antiparallel overlapping strings. The result is enhancement in strange- and multi-strange hadron yields versus non-strange hadrons, consistent with observed $N(\mathbf{x},\mathbf{y};Y)$2, $N(\mathbf{x},\mathbf{y};Y)$3, and $N(\mathbf{x},\mathbf{y};Y)$4 ratios as functions of event multiplicity at the LHC, without invocation of QGP formation.

Rope fragmentation is algorithmically inserted in the string-building phase prior to PYTHIA hadronization and is parameter-lean. The main uncertainty arises from the geometric overlap threshold (Bierlich, 2017, Bierlich et al., 2014).

1.6. Nuclear and Photon-Nucleus Collisions

DIPSY extends naturally to $N(\mathbf{x},\mathbf{y};Y)$5 and $N(\mathbf{x},\mathbf{y};Y)$6 by superposing independent dipole cascades for each nucleon (nuclear geometry via Woods–Saxon profiles, hard-core repulsion) and performing multi-dipole interactions including inter-nucleon color interference ("swing" between nucleons) (Gustafson et al., 2015). It quantitatively reproduces LHC $N(\mathbf{x},\mathbf{y};Y)$7Pb inelastic cross sections and captures deviations from Glauber scaling due to sub-nucleonic fluctuations and color coherence. Saturation and shadowing effects are predictive for future electron–ion collider physics.

2. DIPSY: Disc Instability Population SYnthesis in Star and Companion Formation

2.1. Model Architecture and Physical Principles

DIPSY (Disc Instability Population SYnthesis) is a global, end-to-end framework for simulating the formation and subsequent population of stellar and substellar companions via gravitational instability and fragmentation in protoplanetary discs (Schib et al., 2 Oct 2025, Schib et al., 2 Oct 2025).

The core is a 1D, axisymmetric, vertically integrated viscous disk model:

$N(\mathbf{x},\mathbf{y};Y)$8

where $N(\mathbf{x},\mathbf{y};Y)$9 is gas surface density; viscosity $N_c$0 is set by a local maximum of gravitational (GI) and background (typically MRI-driven) contributions, and $N_c$1 encodes infall, photoevaporation, clump accretion, and mass loss from tidally disrupted fragments. Thermal balance in each annulus is solved including heating and radiative cooling (opacity tables), as well as external irradiation.

Disc self-gravity and the Toomre parameter

$N_c$2

are monitored. Fragmentation occurs where $N_c$3 and the local cooling time $N_c$4, forming clumps with initial mass $N_c$5 given by the most-unstable scale.

2.2. Clump Insertion and Evolution

When fragmentation is satisfied:

• The initial fragment mass $N_c$6 is computed, e.g.

$N_c$7

• The clump is removed from the gas grid and evolved as a 1D precomputed contraction track, including H$N_c$8 dissociation, and subject to local irradiation.
• Gas accretion is modeled using Bondi–Hill rates, capped at $N_c$9yr$$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$0.
• Orbital migration is solved using torque densities that capture both Type I and Type II torques, and dynamically merge with dynamical friction when eccentricity and inclination are significant.
• N-body integration (Mercury6) tracks mutual clump scattering, mergers (perfectly inelastic), ejections, and accretion by the host star.

2.3. Population Synthesis Simulations and Statistics

Sampling 100 logarithmic host-star mass bins from 0.05–5 $$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$1, with $$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$2 systems, initial conditions are based on hydrodynamic simulation statistics and observations (disk size, stellar/disk masses, infall rates). Disc evolution includes photoevaporation (FUV/EUV) at rates $$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$3/yr. Simulation continues through 100 Myr.

Key baseline population outcomes (Schib et al., 2 Oct 2025):

• Only $$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$410% of discs fragment; $$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$550% of fragmenting discs retain a companion at 100 Myr.
• Among surviving companions: $$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$675% are brown dwarfs (13–73 $$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$7); $$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$815% low-mass stars, $$\frac{\partial N(\mathbf{x},\mathbf{y};Y)}{\partial Y} = \bar\alpha_s \int d^2z\, \frac{(\mathbf{x}-\mathbf{y})^2}{(\mathbf{x}-\mathbf{z})^2\,(\mathbf{z}-\mathbf{y})^2} \left[N(\mathbf{x},\mathbf{z};Y) + N(\mathbf{z},\mathbf{y};Y) - N(\mathbf{x},\mathbf{y};Y) - N(\mathbf{x},\mathbf{z};Y) N(\mathbf{z},\mathbf{y};Y) \right]$$910% planetary-mass ($1/m_g$0).
• Virtually all planetary-mass objects form beyond 100 AU; inside 100 AU the population is negligible.
• The mean companion mass is $1/m_g$130 $1/m_g$2, with only a weak increase with host-star mass.
• Multiple systems are rare ($1/m_g$3); free-floating objects (ejected clumps) are abundant.

2.4. Physical Uncertainties and Sensitivity Analyses

Model variants probe the effects of accretion-rate capping, multi-fragmentation per event, zero initial eccentricity, expanded infall radii, revised photoevaporation rates, and alternate initial mass formulae (Schib et al., 2 Oct 2025, Schib et al., 2 Oct 2025).

Principal uncertainties include:

• Gas accretion rate onto fragments: unlimited rates can produce stellar-mass companions, violating the disc-centrism of the model.
• Treatment of fragment–fragment collisions: assumed perfectly inelastic; realistic outcomes may include disruptions or erosion.
• Effects of MHD, winds, and grain/pebble accretion are omitted but are expected to modify both fragmentation and survival fractions.
• Magnetospheric truncation of inner disk not explicitly modeled; thus, population of close-in objects is an upper limit.

The robust qualitative result is the prevalence of a gravito-turbulent phase in essentially all massive discs, but true fragmentation—and especially the survival of planetary-mass companions at small $1/m_g$4—is rare. This synthesis tightly constrains predictions for direct imaging and astrometric companion surveys.

2.5. Comparison with Observations and Future Directions

The DIPSY framework connects observed brown dwarf and distant substellar/planetary-mass companions directly to disc fragmentation, predicting that the population of such wide-separation objects must be set predominantly by dynamical survival rather than fragmentation per se. Close-in planetary-mass companions are generally not explained by classical GI at low radii. Future improvements will require integrating detailed MHD effects, heavy element accretion physics, and higher dimensional hydrodynamic modeling.

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Reference Table: Major DIPSY Applications and Features

DIPSY Variant/Domain	Principal Capabilities	Key Paper(s)
Lund Dipole Cascade (QCD)	Event-by-event dipole evolution, saturation, all-flavour hadronization, diffraction, flow geometry, rope fragmentation	(Gustafson, 2012, Flensburg et al., 2011, Bierlich, 2017, Bierlich et al., 2014, Avsar et al., 2010)
Small-system collectivity	Initial-state geometry, $1/m_g$5, flow/nonflow separation	(Avsar et al., 2010, Avsar et al., 2011, Flensburg, 2011)
Rope Hadronization (QCD)	Overlapping color flux, strangeness enhancement, baryon/meson excess	(Bierlich et al., 2014, Bierlich, 2017, Bierlich et al., 2015)
$1/m_g$6, $1/m_g$7, $1/m_g$8 collisions	Nuclear geometry, shadowing, sub-nucleonic fluctuations, cross sections	(Gustafson et al., 2015, Gustafson, 2012)
Disc Instability Population SYnthesis (DI)	Global disc instability, clump evolution, N-body, synthetic populations	(Schib et al., 2 Oct 2025, Schib et al., 2 Oct 2025)

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3. DIPSY in Few-Shot Synthetic Data Generation (Vision; Unrelated to High-Energy Physics)

A recently introduced framework also referred to as DIPSY (“Dual IP-Adapter Synthesizer”) is a training-free approach for generating synthetic images for few-shot learning, combining text and image prompts in a diffusion backbone with a dual IP-Adapter setup (Boudier et al., 26 Sep 2025). It employs:

• Extended classifier-free guidance, independently weighting text prompts, positive image examples, and negative (contrastive) image examples.
• Class similarity-based sampling for effective contrastive guidance.
• Lightweight CLIP-based fine-tuning on combined real and synthetic data.

This DIPSY is entirely distinct from the QCD and disc instability DIPSY codes.

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4. Conclusion

"DIPSY" denotes leading computational models in both collider physics and star/planet formation. In QCD, it provides a unique event-level realization of dipole cascade evolution, collective geometry, and non-perturbative hadronization, with extensive experimental validation across system sizes and collision energies. In disc instability studies, it implements a global, physically coupled synthesis of fragmentation, migration, and N-body dynamics to yield statistical predictions for companion populations. In both domains, DIPSY frameworks are characterized by a strong grounding in physical first principles and detailed stochastic modeling, serving as widely used benchmarks and sources of theoretical predictions across multiple research areas.

(Avsar et al., 2010, Avsar et al., 2011, Flensburg et al., 2011, Gustafson, 2012, Gustafson, 2012, Flensburg et al., 2012, Bierlich et al., 2014, Gustafson et al., 2015, Flensburg, 2011, Bierlich, 2017, Bierlich et al., 2015, Schib et al., 2 Oct 2025, Schib et al., 2 Oct 2025, Boudier et al., 26 Sep 2025)