REVIEW
Heavy sterile neutrinos: Bounds from big-bang nucleosynthesis and SN 1987A
High Energy Physics - Phenomenology · Submitted 14 Aug 2000 · 19 references
Pith's verdict: The BBN curves for 10-140 MeV are genuinely computed and will be the reference for that window; the SN 1987A band borrowed from their earlier paper is the part that doesn't survive scrutiny at the high-mass end.
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Referee report
The paper
The paper claims
Heavy sterile neutrinos mixed with the known flavours are largely ruled out by big-bang nucleosynthesis and by the neutrino burst of SN 1987A, for masses between 10 and 140 MeV.
The reading
What carries the argument
The engine is a set of Boltzmann equations in scaled variables $x = m_0 a(t)$ and $y = p a(t)$, one for the sterile occupation number with a production term driven by the matter-suppressed mixing angle $sin 2θ_M$ and one for the departure of each active flavour from equilibrium, coupled to an energy-conservation equation $x dρ/dx = -3(ρ+p)$ that tracks how the electromagnetic plasma is heated by decay products. The decay terms are written channel by channel, with the $ν_2 → ν_1 ℓ^+ℓ^-$ rate set by the lifetime $τ_{ν_s} = 1.0 s (M_s/10 MeV)^5 sin^2 2θ$ (0.7 s for the $ν_e$ channel). The resulting photon temperatures and distorted $ν_e$ spectra are passed to a modified Kawano nucleosynthesis code at $η_{10} = 5$, and the helium shift is converted to an effective extra-neutrino number through $ΔY = 0.013 ΔN$. The supernova bound is not a simulation but an energy-loss/energy-transfer argument: a sterile state that escapes the core too freely accelerates cooling, and one that decays or scatters inside the core still transports energy outward, so both extremes are excluded while an intermediate window remains.
Extended reading notes
Core claim
For Dirac sterile neutrinos of mass $10 < M_s < 140$ MeV mixed with a single active flavour, the authors find that big-bang nucleosynthesis forbids mixing angles below a mass-dependent curve: a sterile neutrino produced abundantly through mixing in the early universe either survives long enough to add energy density at the nucleosynthesis epoch or decays into $e^+e^-$ and neutrinos that reshape the neutron-proton ratio, and either way the primordial helium yield moves outside the tolerated range. The curves are given both for an optimistic tolerance of $ΔN = 0.2$ and a conservative $ΔN = 1.0$ extra light neutrino species, and are fitted by $(sin^2θ)_{min} = s_1 M_s^{α} + s_2$ with the coefficients tabulated. Equivalently, a maximum lifetime $τ_{max}$ is derived as a function of mass. Superimposed on the same plane, the SN 1987A energy-loss and energy-transfer argument excludes roughly $3×10^{-8} < sin^2(2θ) < 0.1$ for masses below about 100 MeV. A separate production-efficiency estimate, $(δm^2/MeV^2) sin^2 2θ < 2.3×10^{-7}$, marks the region where sterile states were never abundant and the nucleosynthesis bound therefore does not apply. Above $M_s = 135$ MeV the two-body decay $ν_2 → π^0 + ν_a$ takes over, and the authors give an order-of-magnitude exclusion band for that regime rather than a numerical one.
Load-bearing premise
The exclusion curves assume that the distortion a heavy sterile neutrino imprints on primordial helium can be traded for a tolerated number of extra light neutrino species, $ΔN$ between 0.2 and 1.0, and — for the $M_s > 140$ MeV tail, as the authors themselves acknowledge — that the dominant pion decay channel can be handled by an instantaneous-decay estimate rather than by the numerical code, with the cancellation window near 0.2 s left to future non-equilibrium calculations.
Editorial extensions
If this is right
- Any heavy sterile neutrino with mass between 10 and 140 MeV and mixing below the tabulated $(sin^2θ)_{min}$ curve is excluded if it was ever in equilibrium in the early plasma, independent of any laboratory measurement.
- The same particle is excluded for mixing angles between roughly $3×10^{-8}$ and $0.1$ in $sin^2(2θ)$ by the duration of the SN 1987A neutrino burst, up to masses near 100 MeV.
- A sterile state that mixes more weakly than $(δm^2/MeV^2) sin^2 2θ < 2.3×10^{-7}$ was never abundant, so the nucleosynthesis constraint on it disappears and only direct experiment can reach it.
- For masses above 135 MeV the pion channel $ν_2 → π^0 + ν_a$ dominates and shortens the lifetime so sharply that lifetimes above roughly 0.1 s are excluded except near a narrow cancellation window around 0.2 s.
- Majorana rather than Dirac heavy neutrinos would halve the cosmological number density and weaken all of these bounds, but only mildly.
- The NOMAD limit on $ν_τ$–sterile mixing covers part of the same plane, so the cosmological and astrophysical bounds and the accelerator bound can be read as one combined exclusion map.
Reading between the lines
- Because the exclusion curves are driven by the helium yield, a future measurement that tightens the primordial helium or deuterium abundance — and hence pushes the tolerated $ΔN$ well below 0.2 — would extend the excluded band downward in mixing angle without any new particle physics.
- The two constraints are complementary in a way the figure makes visible: supernova physics bites at larger mixing angles where the sterile state is strongly coupled, nucleosynthesis bites at smaller mixing angles where it is long-lived, so the surviving window is a diagonal strip that a next-generation calculation would have to close from both ends.
- The acknowledged gap above 140 MeV is the natural place for a follow-up: a full kinetic treatment of the pion channel, including the non-equilibrium $ν_e$ it injects into neutron-proton reactions, could turn the order-of-magnitude band of Eq. (25) into a bound comparable in status to the lower-mass curves.
- The same machinery would apply almost unchanged to any new light singlet that mixes with one active flavour and decays visibly in the early plasma, so the paper's real export is a method for converting a mixing angle into a helium-abundance shift.
Original abstract
Cosmological and astrophysical effects of heavy (10 - 200 MeV) sterile Dirac neutrinos, mixed with the active ones, are considered. The bounds on mass and mixing angle from both supernovae and big-bang nucleosynthesis are presented.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Cosmological and astrophysical effects of heavy (10 - 200 MeV) sterile Dirac neutrinos, mixed with the active ones, are considered. The bounds on mass and mixing angle from both supernovae and big-bang nucleosynthesis are presented.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Cosmological and astrophysical effects of heavy (10 - 200 MeV) sterile Dirac neutrinos, mixed with the active ones, are considered. | contribution 0.88 | 0.60 | 0.06 | asserted 0.74 |
| s1 | The bounds on mass and mixing angle from both supernovae and big-bang nucleosynthesis are presented. | result 0.62 | 0.81 | 0.65 | asserted 0.98 |
What was examined, and what was not
- arXiv listing abstract v2
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- P abstract
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Figures
Figures reproduced from arXiv:hep-ph/0008138 by the authors.
References
How later papers used it
75 later papers cite it
2 later papers by other authors are listed below: 2 used its data or values.
Uses its data or values 2 of 6 papers with this label
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Applied the bounds in this paper to make the conservative analysis.
Direct Search for Right-handed Neutrinos and Neutrinoless Double Beta Decay (2013) · 0.81 · paraphrased: the licence does not allow quoting
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Took a conservative bound for the mixing with ν_μ, τ and referred to this paper for the detail.
Mixing of Active and Sterile Neutrinos (2011) · 0.81 · paraphrased: the licence does not allow quoting
How the literature uses it
74 arXiv papers cite this in 154 sentences
Papers citing it · 105 sentences without a confident label
Contests it 3 papers
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Our conclusion differs from that of [ref] , where it was argued that in the case of normal hierarchy there is an open region of parameter space compatible with both direct experimental searches and BBN bounds of [ref] .
Experimental bounds on sterile neutrino mixing angles · Discussion · contest 0.76
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These results, however, contradicted Ref. [ref] (see also [ref] ), which studied the same setup with HNLs with masses below the pion mass and found that $N_eff$ may only increase.
How new physics affects primordial neutrinos decoupling: Direct Simulation Monte Carlo approach · Injection of 70 MeV neutrinos · contest 0.81
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Hence, the neutrino life-time used in Ref. [ref] to get BBN limits should be multiplied by $2/(1-M_π^2/M_N^2)$, and corresponding limit on neutrino mixing angle should be divided by this factor.
How to find neutral leptons of the nuMSM? · Sterile neutrino decays · contest 0.84
Builds on it 2 papers
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Hence, our work extends previous studies, see, e.g., [ref] , and offers a flexible public tool to be used by the community.
Dynamics of metastable Standard Model particles from long-lived particle decays in the MeV primordial plasma · Introduction and summary · 0.93
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Our analysis can be applied to other particles decaying into photons, such as heavy neutral leptons [ref] .
Multimessenger Constraints on Radiatively Decaying Axions from GW170817 · Introduction · 0.89
Uses its method or tool 2 papers
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In terms of these variables, we can write the equations of motion (EoMs) for the heavy sterile neutrinos distribution function $f_ν_s$ as [ref]
Massive sterile neutrinos in the early universe: From thermal decoupling to cosmological constraints · Equations of motion · 0.90
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Semikoz for sharing with us the original version of the code, used in [ref] and J. Racle for writing an initial version of the BBN code as a part of his Master's project [ref] at EPFL.
Restrictions on the lifetime of sterile neutrinos from primordial nucleosynthesis · Acknowledgments · 1.00
Uses its data or values 6 papers
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In Fig. [ref] we display the red/blue bands in the sterile neutrino mass and mixing $(m_s, sin^2 θ)$ parameter space in which $ΔN_eff$ can be between 0.2 and 1 obtained in the analysis of Ref. [ref] (see Fig. 1 of Ref. [ref] ).
Possible Hints of Sterile Neutrinos in Recent Measurements of the Hubble Parameter · Introduction · 0.97
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Here we apply the bounds in Ref. [ref] to make the conservative analysis.
Direct Search for Right-handed Neutrinos and Neutrinoless Double Beta Decay · Constraints from direct search and cosmology · 0.81
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The maximum allowed lifetime $τ_BBN$ is given by [equation] where $t_1 = 128.7$, $t_2 = 0.04179$, and $β= - 1.828$ [ref] .
Mixing of Active and Sterile Neutrinos · Search for light sterile neutrinos · 0.97
Compares with it 5 papers
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These two works drew different conclusions about : [ref] reported $Δ> 0$ for the whole studied mass range, whereas [ref] presented in their Fig. 3 that $Δ< 0$ for masses $60 MeV≲<m_π$ and lifetimes $τ_N ≪1 s$.
When FIMPs Decay into Neutrinos: The $N_\mathrm{eff}$ Story · Introduction · 0.88
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Compared to the Refs. [ref] this paper accounts for the neutrino flavour oscillations in the plasma and employs more accurate strategy of solving Boltzmann equations, which results in the revision of the bounds of [ref] (see Section [ref] for detailed comparison).
Restrictions on the lifetime of sterile neutrinos from primordial nucleosynthesis · Introduction · 0.80
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Additionally, we make a direct comparison with the previous works [ref] and the more recent analysis presented in [ref] .
An Extended Analysis of Heavy Neutral Leptons during Big Bang Nucleosynthesis · Introduction · 1.00
Cites it as background 13 papers
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The effect of these sterile neutrinos on BBN has been studied in detail for sterile neutrino masses below the pion mass, i.e. $m_s < 135$ MeV (e.g. see Ref. [ref] and references therein).
Possible Hints of Sterile Neutrinos in Recent Measurements of the Hubble Parameter · Introduction · 0.99
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More recently, BBN has been used to place bounds on heavier and more strongly coupled sterile neutrinos which can be produced via thermal processes in the early universe plasma [ref] .
Sterile neutrino production at small mixing in the early universe · Introduction · 0.89
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Sterile neutrinos may also play the role of the dark matter, e.g., [ref] and affect a host of interesting cosmological and astrophysical processes, including the production of baryon [ref] and lepton [ref] asymmetries, Big Bang Nucleosynthesis [ref] , the evolution of the matter power spectrum [ref] , reionization [ref] , neutrino oscillations [ref] , pulsar kicks [ref] , and supernovae [ref] .
Constraining Sterile Neutrino Warm Dark Matter with Chandra Observations of the Andromeda Galaxy · Introduction · 0.95
Discussion
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