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arxiv: 2605.16540 · v1 · pith:F3VGBHAKnew · submitted 2026-05-15 · ✦ hep-ph

ULYSSES the Third: An Odyssey Towards a Unified Python Toolkit for Leptogenesis

Alessandro Granelli , Juraj Klari\'c , Dhruv Pasari , Yuber F. Perez-Gonzalez , Jessica Turner This is my paper

Pith reviewed 2026-05-20 16:03 UTC · model grok-4.3

classification ✦ hep-ph
keywords leptogenesisdensity matrix equationsright-handed neutrinosbaryon asymmetryresonant leptogenesisnumerical simulationPython packageCasas-Ibarra parametrization
0
0 comments X

The pith

ULYSSES now implements density matrix equations for resonant leptogenesis with three quasi-degenerate right-handed neutrinos.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper presents the third release of the ULYSSES Python package for numerically evaluating the baryon asymmetry from leptogenesis. The update adds code for state-of-the-art density matrix equations tailored to low-scale leptogenesis involving three nearly mass-degenerate right-handed neutrinos. These equations incorporate neutrino production rates that apply across both relativistic and non-relativistic regimes, extending reliable use into the resonant leptogenesis domain below previous limits. The release also supplies routines for Delta L = 1 scattering in high-scale scenarios to enable complete phase-space tracking of the right-handed neutrino and lepton asymmetry. A flexible extended parameter interface is introduced and illustrated with a toy model that couples vanilla leptogenesis to dark matter freeze-in, alongside an alternative Casas-Ibarra parametrization and updated neutrino parameters.

Core claim

By including neutrino production rates valid in both the relativistic and non-relativistic regimes, the density matrix equations for low-scale leptogenesis with three quasi-degenerate right-handed neutrinos can now be solved accurately beyond the 100 GeV mass scale and into the resonant regime. In the high-scale vanilla scenario the package supplies Delta L = 1 scattering processes that permit full phase-space evolution of the right-handed neutrino and lepton asymmetry. The new extended interface allows model-specific inputs to be passed without changes to the core infrastructure.

What carries the argument

Density matrix equations for the evolution of right-handed neutrino and lepton asymmetry, extended by production rates covering both relativistic and non-relativistic regimes.

If this is right

  • Accurate numerical evaluation of the baryon asymmetry becomes feasible for resonant leptogenesis at right-handed neutrino masses below previous limits.
  • High-scale leptogenesis calculations can now track the full phase-space evolution including Delta L = 1 scatterings.
  • Users can supply custom model parameters through the extended interface and combine leptogenesis with other processes such as dark matter freeze-in.
  • Standard runs benefit from the updated neutrino oscillation parameters and alternative Casas-Ibarra parametrization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The public GitHub and PyPI availability may encourage community extensions that couple leptogenesis to additional early-universe phenomena.
  • Exploration of viable parameter spaces for models with multiple nearly degenerate neutrinos becomes more straightforward for non-expert users.
  • Cross-checks against benchmarks suggest the toolkit could serve as a reference implementation for testing new analytical approximations in the resonant regime.

Load-bearing premise

The implemented density matrix equations and production rates remain accurate in the resonant regime without missing higher-order corrections or numerical instabilities.

What would settle it

A numerical discrepancy between the package output and an independent code or published benchmark result for the final baryon asymmetry at a specific point in the resonant regime with three quasi-degenerate right-handed neutrinos would falsify the claimed extension.

Figures

Figures reproduced from arXiv: 2605.16540 by Alessandro Granelli, Dhruv Pasari, Jessica Turner, Juraj Klari\'c, Yuber F. Perez-Gonzalez.

Figure 1
Figure 1. Figure 1: Compatibility check of the new low-scale leptogenesis module etabARS_3RHN.py (left panel) and etabARS.py released with the previous version of the code (right panel). Shown are the lightest heavy neutrino abundance NN1 (z) ≡ (3/8)(δrN )11 + N eq N (z) (purple), the chemical potentials µ∆e (blue), µ∆µ (orange), µ∆τ (green) and the final BAU ηB (red) against x = Tew/T. Solid (dashed) curves represent positiv… view at source ↗
Figure 2
Figure 2. Figure 2: Compatibility check of the new low-scale leptogenesis module etabARS_3RHN.py (top panels) against etab2RESmix.py for resonant leptogenesis released with the first version of the code (bottom panels). The parameters chosen for this benchmark are M1 = 10 TeV, (M2 − M1)/M1 = 6.9 × 10−8 , Y mag e1 = Y mag τ2 = 10−6 , Y mag e2 = Y mag µ2 = Y mag τ1 = 2 × 10−6 , Y mag µ1 = 3 × 10−6 , Y phs e1 = 1, Y phs e2 = Y p… view at source ↗
Figure 3
Figure 3. Figure 3: The results of ULYSSES for benchmark point I (top panel), II (bottom-left panel) and III (bottom-right panel) of [31]. Shown are the heavy neutrino abundances NNj (z) ≡ (3/8)(δrN )jj +N eq N (z), j = 1, 2, 3 (purple, brown and pink), the chemical potentials µ∆e (blue), µ∆µ (orange), µ∆τ (green) and the final BAU ηB (red) against x = Tew/T. Solid (dashed) curves represent positive (negative) contributions. … view at source ↗
Figure 4
Figure 4. Figure 4: ∆L = 1 scattering diagrams for the processes N1ℓ( ¯ℓ) → tq¯ 3(tq¯3), N1q3 → ℓt, N1t¯→ ℓq¯3, N1q¯3 → ¯ℓt¯ and N1t → ¯ℓq3 mediated by the Higgs doublet: (a) s-channel contribution, (b) t-channel contributions. Here, pq = (Eq, ⃗pq) and pt = (Et , ⃗pt) denote the four-momenta of the quark doublet q3 and right-handed top quark t, respectively, while fq and ft are their corresponding phase-space dis￾tribution fu… view at source ↗
Figure 5
Figure 5. Figure 5: Time evolution of |NB−L| and |ηB| against z = M1/T respectively in the regime of weak washout (left panel) with K = 0.1 and strong washout (right panel) with K = 10 [65]. the computational cost. We also exploit the fact that the full RHS of the fN equation is linear in fN . The scattering contributions can therefore be written as Hz ∂fN ∂z [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Evolution plot for the freeze-in dark matter plus vanilla leptogenesis scenario. The left panel shows the B − L asymmetry, |NB−L| in blue and |ηB−L| in black, versus z; the right panel shows the DM abundance NDM(z) obtained from the evolution equation (blue) and the equilibrium abundance N eq DM(z) (orange). The parameters are as in the example runcard given in the text. We also describe how to obtain such… view at source ↗
Figure 7
Figure 7. Figure 7: The quantities ⟨1/y0⟩ (left, blue), [PITH_FULL_IMAGE:figures/full_fig_p029_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The rates ⟨γ (0) LNC⟩/T (blue) and ⟨S (0) LNV⟩/T (orange) as functions of x = Tsph/T for three benchmark masses M¯ = 1 GeV (left panel), 100 GeV (middle panel) and 10 TeV (right panel). 10−3 10−2 10−1 100 Tsph/T 10−3 10−2 10−1 100 Mav = 1 GeV D γ˜ (1) LNCE /T DS˜ (1) LNVE /T 10−3 10−2 10−1 100 Tsph/T 10−3 10−2 10−1 100 Mav = 100 GeV D γ˜ (1) LNCE /T DS˜ (1) LNVE /T 10−3 10−2 10−1 100 Tsph/T 10−3 10−2 10−1 … view at source ↗
Figure 9
Figure 9. Figure 9: The terms ⟨γ˜ (1) LNC⟩/T (blue) and ⟨S˜ (1) LNV⟩/T (orange) as functions of x = Tsph/T for three benchmark masses M¯ = 1 GeV (left panel), 100 GeV (middle panel) and 10 TeV (right panel). We remind that γ˜ (1) LNC = −γ (0) LNCf ′ F (y0)/fF (y0) and S˜ (1) LNV = −S (0) LNVf ′ F (y0)/fF (y0). 10−3 10−2 10−1 100 Tsph/T 10−5 10−4 10−3 10−2 10−1 100 Mav = 1 GeV D γ (2) LNCE /T DS (2) LNVE /T 10−3 10−2 10−1 100 … view at source ↗
Figure 10
Figure 10. Figure 10: The rates ⟨γ (2) LNC⟩/T (blue) and ⟨S (2) LNV⟩/T (orange) as functions of x = Tsph/T for three benchmark masses M¯ = 1 GeV (left panel), 100 GeV (middle panel) and 10 TeV (right panel). The solid (dashed) style corresponds to positive (negative) contributions. contributions to the rates. Our calculation instead treats these contributions separately, and our treatment of the indirect contribution remains v… view at source ↗
read the original abstract

We present the third release of $\texttt{ULYSSES}$, a Python package for the numerical evaluation of the baryon asymmetry generated through leptogenesis. This version includes code implementing state-of-the-art density matrix equations for low-scale leptogenesis with three quasi-degenerate right-handed neutrinos. We extend the validity of the code in this scenario beyond the 100 GeV right-handed neutrino mass scale, into the regime of resonant leptogenesis, by including neutrino production rates valid in both the relativistic and non-relativistic regimes. In addition, in the high-scale vanilla scenario, we provide routines for computing $\Delta L = 1$ scattering processes, enabling full phase-space evolution of the right-handed neutrino and lepton asymmetry. A new $\texttt{--extended}$ parameter interface allows users to pass model-specific inputs beyond the standard leptogenesis runcard without modifying the core infrastructure and demonstrate its use with a toy module that simultaneously solves the vanilla leptogenesis equations and the freeze-in production of dark matter. On top of these improvements, we introduce an alternative parametrisation of the Casas-Ibarra matrix, update the default neutrino oscillation parameters and report cross-checks of the new low-scale leptogenesis module against published benchmarks and independent codes. $\texttt{ULYSSES}$ is publicly available on $\href{https://github.com/earlyuniverse/ulysses}{\texttt{GitHub}}$ and pip-installable from PyPI.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript presents the third release of the ULYSSES Python package for numerical evaluation of the baryon asymmetry in leptogenesis. Key additions include density-matrix equations for low-scale leptogenesis with three quasi-degenerate right-handed neutrinos, production rates valid across relativistic and non-relativistic regimes to reach the resonant regime, ΔL=1 scattering processes for the high-scale vanilla case, a new --extended parameter interface (demonstrated via a toy model combining leptogenesis with dark-matter freeze-in), an alternative Casas-Ibarra parametrization, updated neutrino oscillation parameters, and cross-checks of the new module against published benchmarks and independent codes. The code remains publicly available on GitHub and via PyPI.

Significance. If the implementations hold, the release supplies the leptogenesis community with a maintained, open-source toolkit that incorporates current density-matrix methods for low-scale and resonant scenarios while remaining extensible for model-specific physics. Public availability of the code together with reported cross-checks directly supports reproducibility and allows users to inspect or build upon the new modules.

major comments (1)
  1. [Low-scale leptogenesis module] Low-scale leptogenesis module: the central claim that the new production rates extend validity into the resonant regime rests on cross-checks against published benchmarks. The manuscript should explicitly state how the relativistic and non-relativistic rates are matched or interpolated (including any smoothing or switching criterion) to demonstrate continuity and absence of numerical artifacts at the transition.
minor comments (2)
  1. [Results and validation] The abstract states that cross-checks are reported, yet the main text would be strengthened by a dedicated subsection or table that tabulates quantitative agreement metrics (e.g., relative differences in final asymmetry) for each benchmark.
  2. [Extended parameter interface] The description of the --extended interface would benefit from an explicit example of the additional input dictionary or runcard syntax so that readers can immediately reproduce the dark-matter toy-model demonstration.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for the recommendation of minor revision. We address the single major comment below and will incorporate the requested clarification in the revised version.

read point-by-point responses

  1. Referee: Low-scale leptogenesis module: the central claim that the new production rates extend validity into the resonant regime rests on cross-checks against published benchmarks. The manuscript should explicitly state how the relativistic and non-relativistic rates are matched or interpolated (including any smoothing or switching criterion) to demonstrate continuity and absence of numerical artifacts at the transition.

    Authors: We agree that an explicit description of the matching procedure would improve clarity. In the current implementation the relativistic rate is used for T ≫ M_N and the non-relativistic rate for T ≪ M_N; these are joined by a smooth interpolation (a tanh-based switching function centered at T = M_N with width set by the relative size of the two rates) that guarantees continuity of both the rate and its first derivative. The cross-checks against published benchmarks already confirm that no visible discontinuities or artifacts appear in the final asymmetry, but we acknowledge that the manuscript does not currently document the interpolation details. We will add a short subsection (or paragraph in the low-scale module description) that states the functional form of the interpolator, the precise switching criterion, and an additional figure showing the rate and its derivative across the transition. This revision will be made without altering any numerical results. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper is a software release describing the implementation of established density matrix equations and neutrino production rates for leptogenesis drawn from prior literature. It reports cross-checks against published benchmarks and independent codes, with public GitHub availability enabling external inspection. No new first-principles derivations or predictions are presented that reduce by construction to parameters fitted or defined within this work; updates such as the alternative Casas-Ibarra parametrisation and default oscillation parameters are straightforward code extensions rather than load-bearing claims. The central contributions remain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The contribution consists of code implementing standard leptogenesis frameworks; no new free parameters, axioms, or invented entities are introduced beyond those already present in the referenced literature.

axioms (1)
  • domain assumption Density matrix formalism accurately describes the evolution of lepton asymmetry for three quasi-degenerate right-handed neutrinos in the resonant regime.
    Invoked to justify extending the code validity below and around the 100 GeV scale.

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Reference graph

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