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arxiv: 2605.21419 · v1 · pith:ZVN4E2BTnew · submitted 2026-05-20 · ✦ hep-ph · astro-ph.CO· gr-qc· hep-th

Cosmological Collider Signatures from Right-Handed Neutrino Loop

Jingtao You , Linghao Song , Chengcheng Han , Hong-Jian He , Xingang Chen , Zhong-Zhi Xianyu This is my paper

Pith reviewed 2026-05-21 03:36 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COgr-qchep-th
keywords cosmological colliderright-handed neutrinosprimordial non-Gaussianityinflationseesaw mechanismchemical potentialfermion loopsMajorana neutrinos
0
0 comments X

The pith

An effective chemical potential from right-handed neutrinos can make their heavy loop effects visible in primordial non-Gaussianities.

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

This paper examines how right-handed neutrinos from the seesaw mechanism for neutrino masses can generate cosmological collider signatures through loops during inflation. The authors introduce a dimension-five operator coupling the inflaton to these neutrinos that respects shift symmetry and produces an effective chemical potential in the slow-roll background. This chemical potential reduces the strong exponential suppression that normally hides heavy particle effects and strengthens the oscillatory patterns in the three-point correlation function of the inflaton, especially from the dominant helicity state. If these patterns appear in cosmic microwave background data, they would offer a new route to probe the high-energy physics responsible for tiny neutrino masses.

Core claim

We study cosmological collider signatures generated by right-handed neutrino loops in the setup of inflation combined with neutrino seesaw mechanism. We formulate the inflaton interaction with the right-handed neutrino through a unique dimension-5 operator respecting shift symmetry, which induces an effective chemical potential in the slow-roll background, leading to helicity-dependent right-handed-neutrino production and enhancing the CC signatures. Using the Schwinger-Keldysh formalism, we derive seed integrals for fermion propagators of the right-handed Majorana neutrino and compute the factorized nonlocal contributions to the three-point inflaton correlator generated by the right-handed-

What carries the argument

The triangle loop of right-handed Majorana neutrinos whose production is modulated by the chemical potential from the shift-symmetric dimension-5 inflaton-neutrino operator, evaluated with Schwinger-Keldysh seed integrals to yield nonlocal terms in the inflaton bispectrum.

If this is right

  • The oscillatory non-Gaussianity from the neutrino loop becomes less suppressed and potentially detectable in future cosmological surveys.
  • Heavy right-handed neutrinos can leave imprints on primordial density correlations without requiring direct production at colliders.
  • The framework enables systematic calculation of other fermion loop contributions to cosmological collider observables.
  • Signals from the dominant helicity mode can be distinguished by their amplified strength and specific oscillation pattern.

Where Pith is reading between the lines

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

  • The frequency of the oscillations could encode the mass scale of the right-handed neutrinos, offering a direct cosmological handle on seesaw parameters.
  • Similar chemical-potential effects might arise in other inflationary models with heavy fermions, broadening the reach of collider-style searches in the sky.
  • Non-detection of these signatures would constrain the allowed strength of the inflaton-neutrino coupling at inflationary energies.
  • This loop mechanism could be combined with other early-universe processes to test consistency between neutrino mass generation and inflation.

Load-bearing premise

The inflaton interacts with the right-handed neutrino through a unique dimension-5 operator that respects shift symmetry and thereby induces an effective chemical potential in the slow-roll background.

What would settle it

A search in the primordial bispectrum for the specific oscillatory frequency and amplitude pattern predicted for the dominant helicity mode, with the reduced Boltzmann suppression from the chemical potential, would confirm or exclude the loop contribution if the signal is detected or absent at the expected level.

read the original abstract

We study cosmological collider (CC) signatures generated by right-handed neutrino loops in the setup of inflation combined with neutrino seesaw mechanism. We formulate the inflaton interaction with the right-handed neutrino through a unique dimension-5 operator respecting shift symmetry, which induces an effective chemical potential in the slow-roll background, leading to helicity-dependent right-handed-neutrino production and enhancing the CC signatures. The right-handed neutrino is described by two-component Weyl spinor with Majorana mass term. Using the Schwinger-Keldysh (SK) formalism, we derive a set of seed integrals for fermion propagators of the right-handed Majorana neutrino. With these we compute the factorized nonlocal contributions to the three-point inflaton correlator generated by the right-handed-neutrino triangle loop. We show that the chemical potential can substantially soften the heavy-mass Boltzmann suppression and amplify the oscillatory non-Gaussianity signatures associated with the dominant helicity mode. These provide a systematic framework for analyzing the fermion loop signatures in the cosmological collider physics and demonstrate that the heavy right-handed neutrinos associated with seesaw mechanism may leave observable imprints in the primordial non-Gaussianities.

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

2 major / 2 minor

Summary. The manuscript studies cosmological collider signatures from right-handed neutrino loops in an inflationary setup combined with the neutrino seesaw mechanism. A unique dimension-5 operator respecting shift symmetry is introduced to induce an effective chemical potential in the slow-roll background, leading to helicity-dependent production. Using the Schwinger-Keldysh formalism, seed integrals for the Majorana fermion propagators are derived and used to compute the factorized nonlocal contributions to the three-point inflaton correlator from the triangle loop. The central claim is that the chemical potential substantially softens the heavy-mass Boltzmann suppression and amplifies the oscillatory non-Gaussianity signatures for the dominant helicity mode.

Significance. If the technical claims hold, the work supplies a systematic framework for fermion-loop contributions in cosmological collider physics and indicates that heavy right-handed neutrinos could produce observable imprints in primordial non-Gaussianities. The derivation of SK seed integrals for fermions and the explicit treatment of the seesaw-compatible operator constitute reproducible strengths that could be extended to other fermionic species.

major comments (2)
  1. [Setup and abstract] The headline result that the chemical potential softens the e^{-m/H} (or e^{-π m/H}) suppression for m/H ≫ 1 is load-bearing for the amplification claim, yet the abstract and setup provide no explicit regime bounds such as μ/H ≳ m/H or the precise modification to the two-component Weyl propagator dispersion. Without this, it remains unclear whether the dominant-helicity production rate stays parametrically unsuppressed.
  2. [Seed integrals and correlator computation] In the computation of the triangle-loop contribution to the three-point function, the factorized nonlocal terms rely on the helicity-dependent seed integrals; the manuscript must demonstrate that the chemical-potential shift does not merely produce a subdominant correction to the mode functions, which would render the claimed enhancement of oscillatory non-Gaussianity parametrically smaller.
minor comments (2)
  1. [Introduction and model setup] A short paragraph justifying why the chosen dimension-5 operator is the unique shift-symmetric interaction compatible with the seesaw mechanism would improve readability for readers unfamiliar with the model-building details.
  2. [Notation and propagators] Notation for the effective chemical potential μ and the Majorana mass should be introduced once and used consistently; occasional redefinition risks confusion in the propagator expressions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address the two major comments point by point below. We have revised the manuscript to incorporate clarifications on the regime of validity and to strengthen the demonstration that the enhancement is parametric.

read point-by-point responses

  1. Referee: [Setup and abstract] The headline result that the chemical potential softens the e^{-m/H} (or e^{-π m/H}) suppression for m/H ≫ 1 is load-bearing for the amplification claim, yet the abstract and setup provide no explicit regime bounds such as μ/H ≳ m/H or the precise modification to the two-component Weyl propagator dispersion. Without this, it remains unclear whether the dominant-helicity production rate stays parametrically unsuppressed.

    Authors: We agree that explicit regime bounds are necessary to support the central claim. In the manuscript the dimension-5 operator generates an effective chemical potential μ that enters the Weyl-fermion mode equation, shifting the dispersion for one helicity to approximately |k| − μ. This leads to unsuppressed production when μ/H ≳ m/H, replacing the standard Boltzmann factor e^{-π m/H} by a milder suppression. To address the referee’s concern we have added the explicit condition μ/H ≳ m/H together with the modified dispersion relation to both the abstract and the setup section (Section II). revision: yes

  2. Referee: [Seed integrals and correlator computation] In the computation of the triangle-loop contribution to the three-point function, the factorized nonlocal terms rely on the helicity-dependent seed integrals; the manuscript must demonstrate that the chemical-potential shift does not merely produce a subdominant correction to the mode functions, which would render the claimed enhancement of oscillatory non-Gaussianity parametrically smaller.

    Authors: We thank the referee for this important observation. The chemical potential is included at the level of the free fermion mode functions before constructing the Schwinger-Keldysh propagators; the resulting Bogoliubov coefficients for the dominant helicity are therefore modified at leading order. The seed integrals are then evaluated with these shifted modes, and the factorized nonlocal contributions to the three-point function inherit the parametric enhancement. In the revised manuscript we have added an explicit comparison (new paragraph in Section IV) showing that the correction remains leading for the dominant helicity and is not parametrically suppressed relative to the zero-chemical-potential case. revision: yes

Circularity Check

0 steps flagged

Derivation from dimension-5 operator through SK seed integrals to loop correlator is self-contained

full rationale

The paper begins from the explicitly stated dimension-5 operator that respects shift symmetry and induces an effective chemical potential in the slow-roll background. It then formulates the right-handed neutrino as a two-component Weyl spinor with Majorana mass, derives seed integrals for the fermion propagators via the Schwinger-Keldysh formalism, and computes the factorized nonlocal contributions to the three-point inflaton correlator from the triangle loop. The claimed softening of Boltzmann suppression and amplification of oscillatory non-Gaussianity for the dominant helicity mode follow directly from these derived integrals rather than reducing to the inputs by construction. No parameters are fitted to data and relabeled as predictions, no load-bearing uniqueness theorem is imported solely via self-citation, and the central results remain independent of any renaming or ansatz smuggling. The computation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 3 axioms · 0 invented entities

The central claim rests on standard quantum field theory techniques in de Sitter space together with a specific model choice for the inflaton-neutrino interaction. No new particles are postulated beyond the right-handed neutrinos already required by the seesaw mechanism.

free parameters (2)
  • effective chemical potential
    Induced by the dimension-5 operator in the slow-roll background; its magnitude depends on the operator coefficient and inflaton velocity.
  • Majorana mass of right-handed neutrino
    Input parameter from the seesaw mechanism that controls the heavy-mass regime and Boltzmann suppression.
axioms (3)
  • domain assumption The inflaton interaction with the right-handed neutrino proceeds through a unique dimension-5 operator respecting shift symmetry.
    This choice is stated as the setup that induces the effective chemical potential.
  • domain assumption Slow-roll approximation holds during inflation and defines a constant background for the chemical potential.
    Invoked to obtain the helicity-dependent production rate.
  • standard math Schwinger-Keldysh formalism correctly computes the in-in correlators for fermions in de Sitter space.
    Standard tool for cosmological perturbation calculations during inflation.

pith-pipeline@v0.9.0 · 5753 in / 1720 out tokens · 84216 ms · 2026-05-21T03:36:58.323423+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
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    Relation between the paper passage and the cited Recognition theorem.

    We formulate the inflaton interaction with the right-handed neutrino through a unique dimension-5 operator respecting shift symmetry, which induces an effective chemical potential... leading to helicity-dependent right-handed-neutrino production and enhancing the CC signatures.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Using the Schwinger-Keldysh (SK) formalism, we derive a set of seed integrals for fermion propagators... compute the factorized nonlocal contributions to the three-point inflaton correlator generated by the right-handed-neutrino triangle loop.

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Reference graph

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