arxiv: 2604.14983 · v1 · submitted 2026-04-16 · ✦ hep-ph · hep-th

Recognition: unknown

Phenomenology of Vanishing Effective Majorana Mass with a Sterile Neutrino under Cosmological and JUNO Constraints

Rushi Chambyal , Tapender , Labh Singh , Surender Verma

Authors on Pith no claims yet

Pith reviewed 2026-05-10 10:47 UTC · model grok-4.3

classification ✦ hep-ph hep-th

keywords sterile neutrinoeffective Majorana massneutrinoless double beta decaycosmological mass sumJUNO solar parameters3+1 neutrino modelactive-sterile interferenceCP phases

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The pith

A sterile neutrino can drive the effective Majorana mass exactly to zero through active-sterile interference, but only within parameter regions tightly limited by the sum of neutrino masses from cosmology, and those regions stay largely un-

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

The paper examines how an eV-scale sterile neutrino added to three active neutrinos produces a vanishing effective Majorana mass |M_ee| for neutrinoless double beta decay via destructive interference. Latest cosmological upper limits on the total neutrino mass sum restrict the sterile mixing angle θ14 and the lightest active neutrino mass to narrow ranges that still allow the cancellation. JUNO's refined precision on the solar parameters θ12 and Δm21² imposes no additional tightening on the sterile parameters because the extra CP phases in the 3+1 mixing matrix generate new cancellations that wash out the constraint from θ12.

Core claim

In the 3+1 framework an eV sterile neutrino can cancel the active-neutrino contribution to the effective Majorana mass |M_ee| exactly to zero. When the latest Planck and DESI+CMB bounds on the neutrino mass sum are imposed, the allowed values of the sterile mixing angle θ14 and the lightest active neutrino mass are restricted. Adding JUNO's precise solar oscillation data does not further limit the sterile parameters, since additional CP-violating phases permit fresh cancellations that keep |M_ee| at zero.

What carries the argument

Vanishing of the effective Majorana mass |M_ee| through destructive interference between the three active neutrinos and the sterile neutrino, enabled by the additional CP phases present in the 3+1 mixing matrix.

If this is right

The sterile mixing angle θ14 must lie below a cosmology-derived upper limit to keep the mass sum small enough for exact cancellation.
The lightest active neutrino mass is bounded from above and below in the vanishing-|M_ee| region.
Sterile-neutrino parameters remain insensitive to JUNO's improved solar-angle precision because extra phases restore the cancellation.
Other observables such as oscillation probabilities in the allowed parameter space receive definite predictions once the phases are fixed for zero |M_ee|.

Where Pith is reading between the lines

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

Future tighter cosmological limits on the mass sum would directly shrink or eliminate the window for exact active-sterile cancellation.
Searches for sterile neutrinos in short-baseline oscillation experiments would need to incorporate the specific phase choices required by zero |M_ee|.
If the cancellation mechanism holds, a next-generation 0νββ experiment could still report a null result even when the absolute neutrino mass scale is non-zero.

Load-bearing premise

That the CP-violating phases can be chosen so the sterile and active contributions to |M_ee| cancel exactly while the model still satisfies oscillation data and the cosmological sum-of-masses bound.

What would settle it

A cosmological measurement of the neutrino mass sum that lies outside the narrow window permitting exact cancellation to |M_ee|=0, or a positive observation of neutrinoless double beta decay that yields a non-zero |M_ee| in the region where the phases are required to produce zero.

Figures

Figures reproduced from arXiv: 2604.14983 by Labh Singh, Rushi Chambyal, Surender Verma, Tapender.

**Figure 2.** Figure 2: The Correlation plots for IH of neutrino mass. The vertical dashed (red color) in [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: Correlation between sin2 θ12 and the phase γ for normal hierarchy (NH) and inverted hierarchy (IH). The vertical dashed lines represent the SNO+ and JUNO 3σ constraint on sin2 θ12. We, also, explored the implications of the latest measurement of solar mixing angle θ12 by JUNO. The representative correlations are shown in Fig. (3). Due to lack of a correlation of parameters of the model with θ12 JUNO’s high… view at source ↗

read the original abstract

In the present work we investigate the phenomenological implications of a vanishing effective Majorana neutrino mass within a $3+1$ neutrino framework adding a eV-scale sterile neutrino beside three active neutrino states in light of latest cosmology driven bounds on sum of neutrino masses ($\sum_{i}m_i$). We explore the parameter space where the destructive interference between active and sterile states leads to vanishing amplitude, $M_{ee}$, of neutrinoless double beta ($0\nu\beta\beta$) decay. The allowed parameter space has been identified and predictions have been obtained taking into account the latest Planck and DESI+CMB bound on $\sum_{i}m_i$. We find that these bounds restrict the sterile mixing angle $\theta_{14}$ and the lightest active neutrino mass. Furthermore, we incorporate the refined precision data from JUNO experiment regarding solar oscillation parameters ($\theta_{12}, \Delta m_{21}^2$). We find that the sterile neutrino parameters like $\theta_{14}$ may not be sensitive to the JUNO precision measurements as the constraint imposed by precise $\theta_{12}$ is washed out by new cancellations driven through additional CP violating phases leading to vanishing $|M_{ee}|$.

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.

Desk Editor's Note private letter to a colleague

The vanishing M_ee with eV sterile neutrino clashes with cosmological mass sum bounds, and the paper doesn't resolve it.

read the letter

The main takeaway is that this paper applies the vanishing |M_ee| mechanism in a 3+1 model to the newest Planck/DESI cosmology bounds and JUNO solar data, but the results run into an inconsistency with the total neutrino mass sum that isn't resolved. They explore the parameter space where active-sterile interference cancels the effective Majorana mass, then apply the sum m_i limit to restrict θ14 and the lightest active mass. They also check the impact of JUNO's precision on θ12 and Δm21², concluding that extra CP phases wash out any additional constraints on the sterile mixing. This is new in the sense of using the updated datasets on an established scenario. The point about JUNO insensitivity is a solid observation that follows from the extra degrees of freedom in the 3+1 setup with phases. The soft spot is substantial. With m4 around 1 eV, the sum m1 + m2 + m3 + m4 is at least 1 eV, far above the 0.12 eV bound they cite. The mixing angle θ14 affects only the 0νββ rate through the sterile term, not the cosmological mass sum. Achieving the cancellation needed for vanishing M_ee typically requires θ14 large enough that the sterile neutrino would be produced thermally, worsening the sum problem. The paper gives no indication of any suppression factor for the relic density or other fix. This makes the claimed restrictions on θ14 and m1 hard to reconcile with the cosmology input. The reliance on precise phase cancellations for the vanishing condition also means the JUNO result is somewhat built-in rather than a new prediction. This work would mainly interest neutrino phenomenologists focused on 0νββ and sterile neutrinos. Someone following those specific bounds might get value from the updated numbers, but the unresolved tension with the mass sum limits its usefulness. I do not think it deserves peer review in this form.

Referee Report

1 major / 0 minor

Summary. The manuscript investigates the phenomenology of vanishing effective Majorana mass |M_ee| for neutrinoless double beta decay in a 3+1 neutrino framework with an eV-scale sterile neutrino. It explores the parameter space where destructive interference between active and sterile contributions produces |M_ee|=0, subject to Planck+DESI cosmological bounds on the sum of neutrino masses ∑m_i and incorporating JUNO precision data on solar parameters θ12 and Δm21². The authors conclude that these bounds restrict the sterile mixing angle θ14 and lightest active mass m1, but that sterile parameters remain insensitive to JUNO refinements because additional CP-violating phases permit further cancellations that preserve the vanishing |M_ee| condition.

Significance. If the central results hold, the work would illustrate how phase freedom in extended neutrino models can decouple 0νββ constraints from cosmological and oscillation bounds, potentially identifying viable regions for eV-scale steriles that are robust to JUNO data. It contributes to ongoing discussions on sterile neutrino phenomenology at the intersection of multiple experimental probes.

major comments (1)

[Abstract (and associated cosmological constraints discussion)] The claim in the abstract that cosmological bounds on ∑m_i restrict θ14 while permitting vanishing |M_ee| via active-sterile destructive interference is internally inconsistent with the 3+1 framework. In this setup the mass sum is strictly m1+m2+m3+m4 with m4~1 eV contributing fully, exceeding the quoted Planck+DESI bound (~0.12 eV) irrespective of mixing angles. The mixing angle θ14 enters only the 0νββ amplitude (as a term ~θ14² m4 e^{iφ}) and does not suppress the cosmological contribution. No mechanism (such as mixing-dependent relic density suppression) is provided to reconcile these requirements, rendering the reported allowed parameter space unphysical.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for raising this important point about the consistency of the cosmological constraints in the 3+1 framework. We provide our response below.

read point-by-point responses

Referee: The claim in the abstract that cosmological bounds on ∑m_i restrict θ14 while permitting vanishing |M_ee| via active-sterile destructive interference is internally inconsistent with the 3+1 framework. In this setup the mass sum is strictly m1+m2+m3+m4 with m4~1 eV contributing fully, exceeding the quoted Planck+DESI bound (~0.12 eV) irrespective of mixing angles. The mixing angle θ14 enters only the 0νββ amplitude (as a term ~θ14² m4 e^{iφ}) and does not suppress the cosmological contribution. No mechanism (such as mixing-dependent relic density suppression) is provided to reconcile these requirements, rendering the reported allowed parameter space unphysical.

Authors: We thank the referee for highlighting this crucial consistency issue. We agree that a fully thermalized eV-scale sterile neutrino would contribute m4 ≈ 1 eV to the mass sum, exceeding the Planck+DESI limit, and that θ14 does not directly suppress this sum. In our analysis the bound on θ14 arises indirectly because the vanishing |M_ee| condition (via active-sterile cancellation) must be satisfied simultaneously with the cosmological limit applied to the active-neutrino masses m1+m2+m3. However, the manuscript does not explicitly discuss how small θ14 can suppress the sterile relic density through incomplete thermalization. We will revise the abstract and the cosmological-constraints section to state this assumption clearly, add references to the sterile-neutrino production literature, and note that the reported parameter space is viable only under such suppression. This resolves the internal inconsistency. revision: yes

Circularity Check

0 steps flagged

No circularity; parameter-space exploration under external constraints is self-contained

full rationale

The paper explicitly investigates the phenomenological implications of the condition that |M_ee| vanishes via active-sterile destructive interference in the 3+1 framework. It then applies independent external inputs (Planck+DESI sum-of-masses bounds and JUNO solar-parameter precision) to restrict the allowed region within that condition. The observation that θ14 becomes insensitive to JUNO data is presented as a direct consequence of the additional CP phases needed to enforce vanishing |M_ee|, not as a fitted parameter renamed as a prediction or as a result derived from self-citation. No equations reduce to their own inputs by construction, no uniqueness theorems are imported from the authors' prior work, and no ansatz is smuggled via citation. The derivation chain remains independent of its own outputs.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard 3+1 neutrino mixing framework, the assumption that |M_ee| can be set to zero by phase choice, and the validity of the latest cosmological sum-of-masses upper limits as hard constraints.

free parameters (3)

sterile mixing angle θ14
Fitted or scanned to achieve vanishing |M_ee| while satisfying cosmological bounds.
lightest active neutrino mass m1
Restricted by the requirement that sum of masses respects Planck/DESI+CMB limits under the cancellation condition.
additional CP violating phases
Introduced to produce new cancellations that wash out JUNO constraints.

axioms (2)

domain assumption Neutrino mixing is described by the standard 3+1 PMNS matrix with one sterile state.
Invoked throughout the parameter-space exploration in the 3+1 framework.
domain assumption Cosmological upper bounds on ∑mi can be directly applied to the active+sterile mass sum.
Used to restrict θ14 and m1.

pith-pipeline@v0.9.0 · 5520 in / 1596 out tokens · 27337 ms · 2026-05-10T10:47:11.241741+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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hep-ph 2026-04 unverdicted novelty 3.0

JUNO data strongly disfavors Dirac neutrino texture zero pattern C, leaving only patterns A1 and A2 compatible with current oscillation observables.

Reference graph

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