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REVIEW 3 major objections 3 minor 73 references

Right-handed weak currents in neutrinoless $\beta \beta $ decays and ton scale $\beta\beta$ detectors

T0 review · 3 major / 3 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Ton-scale neutrinoless double beta decay detectors can isolate right-handed weak currents by comparing ground- and excited-state transitions, reaching $\langle\lambda\rangle\approx5\times10^{-8}$ and…

desk verdict A useful 0νββ RHC sensitivity paper with a nice compact relation and a real experimental target, but the abstract's 'exclusively explored' claim sails past the paper's own NME caveat. read the letter →

arxiv 2501.03454 v2 pith:72KAAOOF submitted 2025-01-07 hep-ph nucl-exnucl-th

H. Ejiri , T. Fukuyama , T. Sato This is my paper · ORCID
classification hep-phnucl-exnucl-th
keywords neutrinolessdoublebetadecayright-handedweakcurrentsleft-rightsymmetricmodelton-scaledetectorsexcited-statenuclearmatrixelementsMajorananeutrinograndunifiedtheories
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Neutrinoless double $\beta$ decay, in which a nucleus emits two electrons and no antineutrinos, is the most sensitive practical probe of lepton-number violation. This paper argues that the next generation of ton-scale detectors can use it not only to hunt for neutrino mass but also to search for right-handed weak currents, extensions of the Standard Model in which the weak force is symmetric between left and right. The crucial move is to measure two decay branches: the usual transition to the nuclear ground state and the transition to an excited $2^+$ state, the latter tagged by its gamma ray. The ground-state branch is especially sensitive to the coupling $\langle\eta\rangle$, while the excited-state branch responds essentially only to $\langle\lambda\rangle$, so comparing them separates the two currents and gives the ratio $\langle\lambda\rangle/\langle\eta\rangle\approx\tan\beta$, a parameter of grand unified theories. If the argument holds, ton-scale detectors now being built to find the neutrino mass could instead discover new physics in the inverted neutrino mass hierarchy, down to $\langle\lambda\rangle\approx5\times10^{-8}$ and $\langle\eta\rangle\approx1.5\times10^{-10}$.

What carries the argument

The load-bearing identity is $\langle\lambda\rangle/\langle\eta\rangle\approx\tan\beta$, which ties the ratio of the two right-handed-current couplings to the ratio of Higgs vacuum expectation values in the left-right symmetric model. The measurement mechanism is the $\beta\beta$–$\gamma$ coincidence: the $0^+\to0^+$ decay deposits only the two-electron energy in one detector cell, while the $0^+\to2^+$ decay additionally emits a $\gamma$ ray that deposits energy in neighbouring cells of a multi-cell bolometer. That separation makes the ground-state channel $\eta$-sensitive and the excited-state channel $\lambda$-only. The rate formulas carry the argument through phase-space factors and nuclear matrix elements, including the rank-2 tensor decomposition $[H\otimes L]^{(0)}$ of the $2^+$ amplitude and the $s_{1/2},p_{3/2}$ electron partial waves, which is how the paper estimates the $\Delta$-isobar contribution.

What would settle it

Run a ton-scale segmented detector on a nucleus such as $^{130}$Te or $^{76}$Ge, record the $\beta\beta$–$\gamma$ coincidence rate for the $0^+\to2^+$ transition, and compare it with the $0^+\to0^+$ ground-state rate. If the excited-state rate falls below the level expected for $\langle\lambda\rangle\approx5\times10^{-8}$ while the ground-state rate is consistent with that coupling, the claim that the $\lambda$ region is exclusively explored by the excited-state channel is contradicted. A model-side test would be an ab initio calculation of the $2^+$ right-handed-current nuclear matrix element: if it agrees with the interacting-boson-model value rather than the QRPA value, the claimed reach shifts to $\langle\lambda\rangle_{\min}\approx5\times10^{-7}$.

Watch

Extended reading notes

Core claim

The paper claims that the right-handed-current couplings $\langle\lambda\rangle$ and $\langle\eta\rangle$ of the left-right symmetric model are separately measurable with a segmented ton-scale detector. It shows that the ground-state $0^+\to0^+$ decay is dominated by the $\langle\eta\rangle$ term through a phase-space-enhanced recoil/magnetization contribution, whereas the excited-state $0^+\to2^+$ decay receives essentially only the $\langle\lambda\rangle$ term. Since the excited state is tagged by its $\gamma$ ray, a $\beta\beta$–$\gamma$ coincidence measurement separates the two channels and yields $\langle\lambda\rangle/\langle\eta\rangle\approx\tan\beta$, which is bounded to $1\le\tan\beta\le60$ in supersymmetric grand unified theories and to $1\le\tan\beta\le165$ in non-supersymmetric ones. With quasiparticle-random-phase-approximation (QRPA) and shell-model nuclear matrix elements and the quenched axial coupling $g_A^{\rm eff}/g_A\approx0.55$, the paper finds that ton-scale detectors can explore $\langle\lambda\rangle\approx5\times10^{-8}$ and $\langle\eta\rangle\approx1.5\times10^{-10}$, and that the $\Delta$-isobar contribution to the $2^+$ matrix element is about 20% of the two-nucleon mechanism.

Load-bearing premise

The reach numbers assume the quasiparticle-random-phase-approximation and shell-model nuclear matrix elements for the right-handed currents are accurate to within a factor of a few; the paper itself notes that interacting-boson-model matrix elements for the $2^+$ transition are about ten times smaller, which would raise $\langle\lambda\rangle_{\min}$ from $0.5\times10^{-7}$ to about $5\times10^{-7}$ and could erase the claimed exclusive sensitivity at $\langle\lambda\rangle\approx5\times10^{-8}$.

Editorial extensions

If this is right

  • If the neutrino mass ordering is normal and the mass term is invisible, ton-scale detectors can still discover right-handed currents in the $\langle\lambda\rangle\approx5\times10^{-8}$ or $\langle\eta\rangle\approx1.5\times10^{-10}$ regions instead of returning a null result.
  • A signal in the excited $2^+$ window with no ground-state signal would imply $\langle\lambda\rangle/\langle\eta\rangle\gtrsim300$, disfavouring supersymmetric GUTs and favouring non-supersymmetric models.
  • Measuring both channels determines $\tan\beta$, the ratio of Higgs vacuum expectation values, and distinguishes the SUSY ($\tan\beta\le60$) from the non-SUSY ($\tan\beta\le165$) parameter region.
  • Because $\langle\lambda\rangle$ is a single nucleus-independent coupling, observing the $2^+$ decay in several isotopes would test the nuclear matrix elements by checking that the extracted $\langle\lambda\rangle$ agrees across nuclei.
  • If the interacting-boson-model matrix elements are correct rather than the QRPA ones, the excited-state sensitivity falls to $\langle\lambda\rangle_{\min}\approx5\times10^{-7}$ and the claimed exclusive reach is lost.

Reading between the lines

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

  • The same $\beta\beta$–$\gamma$ tagging should also suppress the two-neutrino background and solar-neutrino background for the ground-state channel, so the method's benefit is not limited to the right-handed-current search.
  • A future measurement of $\langle\lambda\rangle$ and $\langle\eta\rangle$ could be combined with direct lower limits on the right-handed $W_R$ mass and the $W_L$–$W_R$ mixing angle to translate the two couplings into constraints on the left-right symmetry-breaking scale, a step the paper does not carry out numerically.
  • The predicted $\eta$-enhancement pattern implies a model-independent cross-check: the ratio of ground-state to excited-state rates should vary systematically with nuclear mass number; a violation of that pattern would signal missing nuclear-structure physics rather than a new current.
  • Tracking detectors that measure the two-electron energy and angular correlation would provide an independent check of the $\lambda/\eta$ separation extracted from the ground-versus-excited ratio.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper studies neutrinoless double beta decay (0νββ) mediated by right-handed weak currents (RHCs) in the left-right symmetric model, for both 0+→0+ and 0+→2+ transitions. It derives the transition amplitude, gives explicit RHC nuclear matrix elements (NMEs), estimates the Δ-isobar contribution to the 2+ NME, and uses phase-space factors and QRPA/shell-model NMEs to estimate the sensitivity of future ton-scale ββ−γ coincidence detectors to the effective couplings <λ> and <η>. The paper claims that <λ>≈5×10^-8 and <η>≈1.5×10^-10 can be exclusively explored by combining ground- and excited-state measurements, and that the ratio <λ>/<η>≈tanβ constrains SUSY and non-SUSY GUT scenarios.

Significance. If the sensitivity claim were robust, the paper would provide a concrete experimental route to discover or constrain right-handed currents beyond the light-neutrino-mass mechanism, with a direct tie to the left-right symmetry breaking scale and tanβ. The paper also contains useful explicit formulas for the 0+→2+ RHC operator, a clear discussion of the η-enhancement in the ground-state channel, and a quantitative (if model-dependent) estimate of the Δ-isobar contribution. The paper is honest about NME uncertainties in places, but the central 'exclusively explored' claim is not supported by the spread of NMEs that the paper itself reports.

major comments (3)
  1. [Abstract and Sec. IV (paragraph after item E)] The abstract's central claim that <λ>≈5×10^-8 and <η>≈1.5×10^-10 are 'exclusively explored' is not robust to the NME model spread acknowledged in the same paper. In Sec. IV the authors state that the IBM NMEs for the 2+ RHCs are an order of magnitude smaller than the QRPA ones, which raises <λ_min> for the excited-state transition from about 0.5×10^-7 to about 5×10^-7 and can remove any signal in the 2+ window for <λ>≈10^-7. Because the claimed reach and the 'exclusively' statement rely directly on the QRPA 2+ NMEs, the abstract and the concluding item C need to be qualified with this model dependence, or the claim must be restricted to the QRPA values.
  2. [Sec. III.C and Sec. IV, g_A values] There is an internal inconsistency in the effective axial-vector coupling used for the two NME estimates. In Sec. III.C the Δ-isobar contribution is quoted as about 20% 'using quenched g_A^eff ≈ 0.7 [48]', while Sec. IV states that g_A^eff/g_A ≈ 0.55 following Refs. [48,56], and the concluding remarks (item 3) use g_A^eff ≈ 0.55g_A. The 20% estimate in Eq. (56) and the surrounding text should be recomputed or clarified with a single consistent value, since the difference affects the NME at the level claimed.
  3. [Sec. IV, Eq. (11) and item E] The claim that the excited-state channel 'exclusively' isolates <λ> needs to account for the interference terms in Eq. (11). The paper's reach estimates use the diagonal terms Γ_k^(J)=C_kk^(J)(<k>)^2 only, and the last paragraph of Sec. IV correctly notes that C_λη(<λ><η>) plays a role in the ground-state transition. However, the ratio R(0/2) advocated in item E is derived from diagonal rates alone; if both λ and η are nonzero, the ground-state rate includes the interference term and the extraction of <λ>/<η> from R(0/2) is not as direct as stated. The authors should state the conditions under which the interference terms are negligible, or include them in the sensitivity estimates.
minor comments (3)
  1. [Throughout] There are several typographical errors, including '¿From' in Sec. II and 'RCH' instead of 'RHC' in the last sentence of Sec. I. These should be corrected.
  2. [Fig. 4 and Fig. 5] The figures would be easier to interpret if the exact numerical values used for Γ_λ^(0), Γ_λ^(2), Γ_η^(0), and Γ_η^(2) were stated in the captions or in a table, since the text refers to values 'around 10, 1, 10^6, and 5' that are not all visible in the figures.
  3. [Sec. IV, Eq. (58)] The notation 'd' is used both for the detector sensitivity in Eq. (58) and for the final-state angular momentum in the text around Eqs. (50)-(56); using different symbols would avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the RHC reach estimates are arithmetic combinations of external NMEs, standard phase-space factors, and background-sensitivity scalings; self-citations are non-load-bearing.

full rationale

The paper's central derivation chain is self-contained. The transition rate formula (Eq. 11) is standard, and the RHC nuclear matrix elements are taken from external QRPA/shell-model calculations ([43,47,57,58]) and IBM ([61]) rather than fitted to the claimed sensitivity. The minimum RHC values follow from the cited sensitivity formula (Eq. 58, Ref. [16]) and the published NME/phase-space rates shown in Fig. 3; no parameter is tuned to make <lambda>≈5e-8 or <eta>≈1.5e-10 come out. The ratio <lambda>/<eta>≈tan(beta) is a model relation derived from L-R symmetric gauge-boson masses (Eqs. 16,17,27), not an input. Self-citations appear ([16] for the sensitivity formula, [27] for L-R model notation, [48,56] for the quenched axial coupling g_eff^A/g_A≈0.55), but each is backed by independent published analyses or external data (single beta-decay rates, summed spin-isospin strength), so they do not load-bear the target result. The strongest caveat is the model dependence of the 2+ NMEs: the paper itself states in Sec. IV that 'the recent IBM NMEs [61] for the 2+ RHCs are smaller by an order of magnitude than the QRPA ones' and that this would raise <lambda_min> to about 5e-7, erasing the excited-state window near <lambda>≈5e-8. This is a robustness/uncertainty limitation of the reach claim, not a circularity: the prediction is not equivalent to its inputs by construction; it is merely sensitive to the choice of input NMEs.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claims rest on the L-R symmetric model, standard nuclear approximations, and quoted NME and detector inputs. The only fitted-type parameter is the axial quenching g_A^eff; tanβ and detector parameters are model or input choices. No new particles, forces, or conserved quantities are introduced.

free parameters (4)
  • Effective axial-vector coupling g_A^eff/g_A = 0.55 (Sec. V) or 0.7 (Sec. III C)
    Used to quench the RHC NMEs; cited from beta-decay analyses [48,56], but the text is internally inconsistent about the value.
  • tanβ (Higgs vev ratio) = 1-60 (SUSY GUT), 1-165 (non-SUSY GUT)
    Controls the <λ>/<η>≈tanβ relation; the range is an input from renormalizability of Yukawa couplings [42], not from DBD data.
  • RHC NMEs for 0+ and 2+ transitions = QRPA, shell model, and IBM values; spread up to 10x
    The reach estimates C_kk scale with squared NMEs, and the paper's own caveat about IBM NMEs shows the central result depends on these model inputs.
  • Detector parameters for typical ton-scale experiment = N=1 t, B=1/(t y), T=5 y, ε=0.7, γ-coincidence B'/B≈0.01
    These assumed numbers set the sensitivity d and hence λ_min and η_min; they are illustrative, not measured.
assumptions (6)
  • domain assumption The exchanged neutrino energy ω dominates the energy denominator, so the closure approximation applies in Eq. (29).
    Used to reduce the 0νββ amplitude to a product of nuclear and lepton operators in Sec. III A; standard but an approximation.
  • domain assumption Nuclear currents are described by impulse approximation V0=Στ_i^+ δ(r_i-x), A=Σg_A τ_i^+ σ_i δ(r_i-x).
    Assumed in Sec. III B before deriving effective operators; ignores meson-exchange corrections beyond the Δ mechanism.
  • domain assumption The minimal L-R symmetric model with κ≫κ', Y≫Y', and g_L=g_R holds, so the relation <λ>/<η>≈tanβ follows from Eq. (27).
    The central ratio prediction depends on this model choice; deviations such as a different Higgs sector or g_L≠g_R would change the relation.
  • domain assumption The radial-overlap A-dependence is weak, so the Δ-mechanism ratio r computed for 76Ge applies to other nuclei.
    Used to convert the ratio from Ref. [46] into a general 20% estimate in Sec. III C.
  • domain assumption The 0νββ mass term does not contribute significantly to the 0+→2+ transition.
    Invoked in Sec. I and used to make the 2+ channel a clean λ probe; based on Ref. [62].
  • ad hoc to paper For the IH mass region, the <m>-induced ground-state rate and the C_mλ, C_mη interference terms are negligible compared with the diagonal RHC rates.
    Eq. (11) contains these terms, but Sec. IV uses only Γ_k=C_kk<k>^2; for IH, <m>/m_e≈6×10^{-8}, the same order as <λ>≈5×10^{-8}, so this assumption is not demonstrated.

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Pith. "Pith review of Right-handed weak currents in neutrinoless $\beta \beta $ decays and ton scale $\beta\beta$ detectors." pith.science (2026). https://pith.science/paper/72KAAOOF

@misc{pith2026250103454,
  author       = {Pith},
  title        = {Pith review of: Right-handed weak currents in neutrinoless $\beta \beta $ decays and ton scale $\beta\beta$ detectors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/72KAAOOF}},
  note         = {Machine review of arXiv:2501.03454}
}
abstract

Right handed weak-currents (RHCs) in the left-right (L-R) symmetric model for neutrinoless double beta decays (DBDs) of both the $0^+~\to~0^+$ and $0^+~\to~2^+$ transitions are discussed from both theoretical and experimental view points. $<\lambda>$ and $<\eta>$-terms are related by $<\lambda>/<\eta> \approx \tan\beta$, which is constrained in the regions of $1-60$ for SUSY grand unified theories (GUTs) and of $1-165$ for non-SUSY GUTs. The enhancement mechanisms of the $<\eta>$ term over the $<\lambda>$ term in the $0^+$ transition are shown, and the $\Delta$ isobar contribution to the NME for the transition to the 2$^+$ state is found to be of the order of $20\%$ of the NME with the quenched weak coupling. The new and interesting RHC regions of $<\lambda>\approx 5\times10^{-8}$ and $<\eta>\approx 1.5\times 10^{-10}$ are shown to be exclusively explored by measuring both the $\beta\beta $ and $\gamma$ rays associated with the ground and excited DBDs by means of the ton-scale DBD detectors for the IH (inverted hierarchy) $\nu$-masses. The actual RHCs to be studied depend on the RHC NMEs.

Figures

Figures reproduced from arXiv: 2501.03454 by the authors.

Figure 1
Figure 1. FIG. 1. Semileptonic interaction of hadron. Left panel shows electron and neutrino production processes of nucleon and [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Diagrams of neutrino exchange within baryon. Left panel shows 0 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. RHC rates (Γ [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The RHC rate Γ [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Pink circle : the region around minimum RHCs of [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

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