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Bounds on neutrino masses from baryogenesis in thermal and non-thermal scenarios

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Narendra Sahu

High Energy Physics - Phenomenology · Submitted 22 Feb 2006 · 123 references

Pith's verdict: A careful compilation of the author's prior leptogenesis bounds; the thermal part is solid, the cosmic-string dominance claim rests on an unverified O(1) neutrino-per-loop assumption.

T0 · AI review

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arXiv IDhep-ph/0602201 (version 1)
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CitationNarendra Sahu. "Bounds on neutrino masses from baryogenesis in thermal and non-thermal scenarios." arXiv:hep-ph/0602201 (2006). https://pith.science/paper/IBYG2MD5
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The paper

The paper claims

The thesis argues that thermal leptogenesis requires the lightest right-handed neutrino to satisfy $M_1 \geq 10^8$ GeV, and that for $B-L$ symmetry-breaking scales above about $10^{11}$ GeV, decaying $B-L$ cosmic strings can dominate the…

The reading

The thesis tries to convert the observed baryon asymmetry of the Universe into constraints on the neutrino sector. In the thermal leptogenesis route, it argues that the CP-violating decays of the lightest right-handed Majorana neutrino $N_1$ must satisfy $M_1 \geq 10^8$ GeV (about $10^9$ GeV in type-I seesaw models), independent of whether type-I or type-II seesaw terms dominate the light neutrino mass matrix. In the non-thermal route, it argues that $B-L$ cosmic strings formed at a phase transition above about $10^{11}$ GeV can release $N_1$ particles from collapsing loops and generate the asymmetry more efficiently than thermal leptogenesis, with slowly shrinking "slow death" loops dominating over self-intersecting "quick death" loops. If true, the thermal path puts right-handed neutrinos beyond the reach of near-future accelerators, while the string path opens a lower-scale, non-thermal window and sharpens the role of topological defects in baryogenesis.

What carries the argument

The load-bearing objects are the CP-asymmetry parameter $\epsilon_1$ and the loop-injection rate of heavy neutrinos. The thermal bound follows from the upper bound $|\epsilon_1| \le 3 M_1 m_3/(16\pi v^2)$ combined with the sphaleron conversion factor $B = (p/(p-1))L$; this is what turns neutrino oscillation data into a floor on $M_1$. The non-thermal bound follows from the slow-death injection rate $(dY_N/dZ)_{\rm SD} = 1.57\times10^{-17}\, N_N f_{SD}\, (M_1/\eta_{B-L})^2 (M_1/{\rm GeV}) / Z^4$ (with $N_N$ the number of right-handed neutrinos released per terminal loop), whose $Z^{-4}$ growth dominates over the quick-death rate $\propto Z^{-2}$ at early times and keeps building the $B-L$ asymmetry long after thermal sources freeze out.

Extended reading notes

Core claim

Within a normal hierarchy $M_1 \ll M_2 < M_3$, the final lepton asymmetry is set by the CP-violating decays of $N_1$, and the model-independent upper bound on the CP asymmetry $|\epsilon_1| \le 3 M_1 m_3/(16\pi v^2)$, with $m_3 \simeq \sqrt{\Delta m^2_{\rm atm}} \simeq 0.05$ eV, converts the observed baryon density into a lower bound $M_1 \geq 0.84 \times 10^9$ GeV in type-I seesaw models and $M_1 \geq 0.84 \times 10^8$ GeV in type-II seesaw models. In a Left-Right symmetric model with spontaneous CP violation, the type-II phase choice reproduces the $10^8$ GeV floor while the type-I phase choice bounds the heavy neutrino hierarchy by $M_2/M_1 \leq 17$ and $M_3/M_1 \leq 289$. For the non-thermal part, $B-L$ cosmic strings trap right-handed neutrino zero modes; loops in the scaling regime later release $N_1$'s. The analytical estimate with one $N_1$ per terminal loop and slow-death parameters $x=0.5$, $\Gamma=100$, $K=1$, $f_{SD}=1$ yields $\eta_{B-L} \gtrsim 1.7\times 10^{11}$ GeV for the string contribution to meet the observed baryon asymmetry, with $M_1 \lesssim 2.4\times 10^{12}\,(\eta_{B-L}/10^{13}\,{\rm GeV})^{1/2}$ GeV; numerical Boltzmann solutions show the string-induced asymmetry dominates the thermal one for $\eta_{B-L} > 10^{11}$ GeV.

Load-bearing premise

The string-sector bounds rest on the assumption that each disappearing string loop releases $\mathcal{O}(1)$ heavy right-handed neutrino $N_1$ (the parameter $N_N$), and that loop formation and shrinkage follow the scaling solution with $x\approx 0.5$, $\Gamma\approx100$, $K=1$ and $f_{SD}=1$; if $N_N$ is much smaller or the loop-production rate differs, the $\eta_{B-L}>10^{11}$ GeV threshold and the claimed dominance over thermal leptogenesis do not follow.

Editorial extensions

If this is right

  • If thermal leptogenesis is the source, $M_1 \geq 10^8$–$10^9$ GeV means the lightest right-handed neutrino is out of reach of foreseeable colliders; low-energy neutrino data alone will not pin down the seesaw scale.
  • If $B-L$ cosmic strings are the source, $\eta_{B-L} > 10^{11}$ GeV becomes a discovery window for string-scale physics: slow-death loops can produce the full baryon asymmetry even when the thermal $N_1$ abundance cannot.
  • The string mechanism implies an upper bound on the CP-violating phase in $N_1$ decays for a given $\eta_{B-L}$: at $\eta_{B-L}=10^{13}$ GeV the required suppression is $\delta \sim 10^{-7}$–$10^{-6}$ for representative parameters.
  • The $M_2/M_1 \le 17$, $M_3/M_1 \le 289$ hierarchy constraints from spontaneous CP violation give a concrete consistency test for Left-Right and SO(10) model building.
  • For $\tilde m_1 \lesssim 10^{-5}$ eV the string contribution becomes negligible except at large $\eta_{B-L}$, so measurements of the effective neutrino mass parameter control which mechanism can operate.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The parameter $N_N$ — the number of $N_1$ particles released per terminal loop — is left free. A first-principles computation of zero-mode occupation from the string winding number and loop energy budget would turn the $\eta_{B-L} > 10^{11}$ GeV threshold into a sharp, falsifiable prediction.
  • The late-time injection of $N_1$ from string loops is a distinctive cosmological fingerprint: the asymmetry keeps growing until $Z\sim 600$ rather than freezing out at $Z\sim 10$. Diffuse high-energy neutrino or gamma-ray signals from those late decays could distinguish string leptogenesis from a purely thermal history.
  • If a TeV-scale right-handed neutrino with charged-lepton-like Dirac couplings were confirmed while baryogenesis remained unexplained, both mechanisms discussed here would be excluded (thermal needs $M_1\ge10^8$ GeV, strings need $\eta_{B-L}>10^{11}$ GeV for $f_1\le1$); that would point to a different non-thermal source.
  • The qualitative conclusion that slow-death strings dominate quick-death strings for baryon asymmetry may extend to other gauged U(1) breaking scales and to supersymmetric SO(10) chains, where the same loop decay could source the asymmetry without a high reheating temperature.
Original abstract

Baryogenesis via leptogenesis is an attractive scenario that links the physics of right handed neutrino sector with the low energy neutrino data. In the light of current neutrino oscillation data we studied the bound on the mass scale ($M_1$) of lightest right handed neutrino ($N_1$) as well as their mass hierarchy ($M_2/M_1$ and $M_3/M_1$) from the leptogenesis constraint which we discussed in two different parts of the thesis. In part-I, we studied the canonical leptogenesis in a {\it thermal} scenario and hence the bound on $M_1$. It is shown that the mass scale of $N_1$ must satisfy the constraint $M_1\geq 10^8$ GeV in order to produce the adequate lepton asymmetry. We then led to propose a model where this bound can be relaxed to TeV scale. In part-II, we studied the formation and evolution of topological defects which are non-thermal objects and are expected to be formed during the early Universe phase transitions. In particular, we considered $B-L$ cosmic strings and their effect on leptogenesis and hence the bound on the mass scale of $N_1$. It is shown that for the $B-L$ symmetry breaking scale $\eta_{B-L}>10^{11}$GeV, in certain parameter space, the cosmic strings make a more dominant contribution than thermal leptogenesis.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,483 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.14 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.71 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Baryogenesis via leptogenesis is an attractive scenario that links the physics of right handed neutrino sector with the low energy neutrino data. In the light of current neutrino oscillation data we studied the bound on the mass scale ($M_1$) of lightest right handed neutrino ($N_1$) as well as their mass hierarchy ($M_2/M_1$ and $M_3/M_1$) from the leptogenesis constraint which we discussed in two different parts of the thesis. In part-I, we studied the canonical leptogenesis in a {\it thermal} scenario and hence the bound on $M_1$. It is shown that the mass scale of $N_1$ must satisfy the constraint $M_1\geq 10^8$ GeV in order to produce the adequate lepton asymmetry. We then led to propose a model where this bound can be relaxed to TeV scale. In part-II, we studied the formation and evolution of topological defects which are non-thermal objects and are expected to be formed during the early Universe phase transitions. In particular, we considered $B-L$ cosmic strings and their effect on leptogenesis and hence the bound on the mass scale of $N_1$. It is shown that for the $B-L$ symmetry breaking scale $\eta_{B-L}>10^{11}$GeV, in certain parameter space, the cosmic strings make a more dominant contribution than thermal leptogenesis.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Baryogenesis via leptogenesis is an attractive scenario that links the physics of right handed neutrino sector with the low energy neutrino data. background 1.00 0.06 0.04 asserted 0.85
s1 In the light of current neutrino oscillation data we studied the bound on the mass scale ($M_1$) of lightest right handed neutrino ($N_1$) as well as their mass hierarchy ($M_2/M_1$ and $M_3/M_1$) from the leptogenesis constraint which we discussed in two different parts of the thesis. contribution 0.99 0.90 0.14 asserted 0.85
s2 In part-I, we studied the canonical leptogenesis in a {\it thermal} scenario and hence the bound on $M_1$. contribution 0.90 0.90 0.04 asserted 0.96
s3 It is shown that the mass scale of $N_1$ must satisfy the constraint $M_1\geq 10^8$ GeV in order to produce the adequate lepton asymmetry. result 1.00 0.82 0.29 asserted 1.00
s4 We then led to propose a model where this bound can be relaxed to TeV scale. contribution 0.83 0.82 0.15 asserted 0.42
s5 In part-II, we studied the formation and evolution of topological defects which are non-thermal objects and are expected to be formed during the early Universe phase transitions. contribution 0.97 0.83 0.03 hedged possibility 0.50
s6 In particular, we considered $B-L$ cosmic strings and their effect on leptogenesis and hence the bound on the mass scale of $N_1$. contribution 0.97 0.80 0.09 asserted 0.70
s7 It is shown that for the $B-L$ symmetry breaking scale $\eta_{B-L}>10^{11}$GeV, in certain parameter space, the cosmic strings make a more dominant contribution than thermal leptogenesis. result 1.00 0.87 0.19 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.85.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 2. 2: ∆L = 1 lepton number violating scatterings mediated by Standard Model Higgs through s or t-channel. Γ N1 φ,t = m2 t 64π 3v 4 M2 1 m˜ 1 K2(Z) Z ∞ 1 dx√ xK1(Z √ x)  x − 1 x + 1 x ln  x − 1 + y ′ y ′  (2.30) Γ N1 φ,s = m2 t 128π 3v 4 M2 1 m˜ 1 K2(Z) Z ∞ 1 dx√ xK1(Z √ x)  x − 1 x 2 . (2.31) Here we have used y ′ = (m2 φ /M2 1 ) and the dimensionless quantity x = s ′/M2 1 , with s ′ being the square of center of mass energy. Note that in the above scattering rates we have neglected the corrections due to second and third generat
Figure 3. 1: One loop radiative correction through the virtual triplet
Figure 4. 3: The allowed values of M1 against the final required asymmetry is shown for η raw = 2.0 × 10−9 The windowing effect emerges clearly as we consider the cases of large raw asymmetries. This is shown in fig. 4.4. It is seen that as the raw asymmetry increases the allowed regions become progressively narrower and lie in the range (1010 − 1015)GeV . Thus a given raw lepton asymmetry determines a corresponding small range of the heavy Majorana neutrino masses for which we can obtain the final asymmetry of the required order α×10−10. Again smaller is the effective neutrino mass ˜m1 larger…
Figure 6. 1: Schematic configuration of isospin vectors after the ru
Figure 7. 1: A non-zero winding in the phase ensures a cosmic string wit

Showing 5 of the paper's 7 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0602201 by the authors.

References

Discussion

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