{"id":"62496b79-ee06-40ca-b086-1ec2a9a021b1","arxiv_id":"2501.03454","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"In the left-right symmetric model, 0νββ decay experiments with ββ-γ coincidence could probe right-handed current couplings λ≈5×10^{-8} and η≈1.5×10^{-10}.","lead":"This paper investigates how future ton-scale detectors can search for right-handed weak currents in neutrinoless double beta decay, a rare process that could reveal new physics beyond the Standard Model. It predicts a ratio between two current parameters and shows that measuring both ground and excited state decays could reach tiny new-physics values.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Abstract's 'exclusively explored' 5e-8 lambda region depends on QRPA 2+ NMEs that the paper itself notes are an order of magnitude larger than IBM values, which would move lambda_min to ~5e-7 and erase the claimed sensitivity.","rationale":"The most load-bearing concern is the sensitivity of the claimed reach into <lambda> ~ 5e-8 to the choice of nuclear matrix elements for the 0+ -> 2+ transition. The reader and this stress-test converge on the same point: the paper's own Sec. IV discloses that IBM NMEs are an order of magnitude smaller than the QRPA values used in Figs. 3-5, which would raise the excited-state <lambda_min> to ~5e-7. Because the ground-state channel cannot separate lambda from eta without the excited state, the abstract's 'exclusively explored' claim is conditional on the QRPA NMEs being accurate to within a factor of a few. The paper deserves credit for explicitly noting the IBM caveat in the body, but the abstract does not carry it, and the abstract is the central claim under review. Thus the appropriate verdict is CONDITIONAL, consistent with the reader's assessment. A separate numerical inconsistency between Eq. (58) (Gamma_min = 0.24 for A=100, d=1) and the text (Gamma_min = 2.4) is worth checking but would affect <lambda_min> only by a factor ~3, not the order of magnitude produced by the NME spread.","tokens_in":16503,"tokens_out":10011,"duration_ms":78894,"concrete_test":"Recompute the excited-state <lambda_min> in Fig. 4 using the IBM NMEs of Ref. [61] for the 0+ -> 2+ transition, keeping the phase-space factors and detector parameters fixed. If <lambda_min> shifts from ~0.5e-7 to >= 5e-7, the abstract's stated region <lambda> ~ 5e-8 is not 'exclusively explored' and the claim must be revised to carry the NME-model caveat.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that <lambda> ~ 5e-8 and <eta> ~ 1.5e-10 are exclusively explored by ground- and excited-state beta-beta-gamma measurements rests entirely on the 0+ -> 2+ RHC nuclear matrix elements. In Sec. IV the paper derives <lambda_min> ~ 0.5e-7 for the excited-state channel using QRPA NMEs [43,47], and the abstract promotes this as an accessible region. However, the same section concedes that the IBM NMEs [61] for the 2+ RHCs are smaller by an order of magnitude, which would raise the excited-state <lambda_min> to ~5e-7. With IBM NMEs the 2+ window would show no signal for <lambda> ~ 1e-7, let alone ~5e-8, and the ground-state channel alone cannot distinguish lambda from eta because the diagonal rates and the C_lambda-eta interference term are both present. The abstract's unqualified 'exclusively explored' statement is therefore not robust to the model spread in NMEs. A secondary inconsistency, geff_A ~ 0.7 in the Sec. III.C Delta-isobar estimate versus geff_A/gA ~ 0.55 used for the main NMEs in Sec. IV, affects the 2+ NME at the ~20% level and is not the primary issue.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":16894,"tokens_out":2282,"duration_ms":23716,"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":[{"comment":"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.","section":"Abstract and Sec. IV (paragraph after item E)"},{"comment":"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.","section":"Sec. III.C and Sec. IV, g_A values"},{"comment":"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.","section":"Sec. IV, Eq. (11) and item E"}],"minor_comments":[{"comment":"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.","section":"Throughout"},{"comment":"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.","section":"Fig. 4 and Fig. 5"},{"comment":"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.","section":"Sec. IV, Eq. (58)"}],"recommendation":"major_revision","confidential_remarks":"The paper's central discovery claim is more fragile than the abstract suggests, but the underlying formalism and the NME-dependence caveat are present in the body. The recommended revision is to bring the abstract and conclusions in line with the model spread, to fix the g_A inconsistency, and to clarify the treatment of interference terms. This is fixable within the scope of the manuscript. The paper would be more suitable for a specialist journal in nuclear/particle physics after those changes."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Hi [Name],\n\nThis paper is worth a look if you work on 0νββ phenomenology or ton-scale detector projections. The new pieces are the compact relation <λ>/<η>≈tanβ (with the GUT bounds 1-60/165), a fresh estimate that the Δ-isobar contribution to the 2+ RHC NME is around 20% of the 2N-mechanism, and a set of reach plots for ground- and excited-state transitions with ββ-γ coincidence. The formalism is standard, well referenced, and the derivation of the ratio is straightforward from the L-R model assumptions. The paper also gives a clear statement of why the 0+→0+ channel is η-enhanced and the 0+→2+ channel selects λ, which is the physical basis for using the rate ratio R(0/2) to separate the two currents. That part is solid.\n\nThe soft spot is in the headline claim. The abstract says regions <λ>≈5×10^{-8} and <η>≈1.5×10^{-10} are 'exclusively explored' by ton-scale detectors. That number follows from QRPA 2+ NMEs. In Sec. IV the paper itself notes that the IBM 2+ RHC NMEs are an order of magnitude smaller, which moves λ_min to ≈5×10^{-7} for the excited-state window. With IBM NMEs there is no 2+ signal at 10^{-7}, let alone 5×10^{-8}. The ground-state channel alone cannot cleanly separate λ and η because both diagonal terms and the interference term contribute. So the abstract overstates the robustness of the reach. The fix is easy: qualify the sentence with 'for QRPA NMEs' and move the IBM caveat into the abstract or the introduction. It is not a fatal flaw because the paper is otherwise honest about the model dependence, but it is exactly the sentence people will quote.\n\nThere is also a small internal inconsistency: Sec. III.C uses g_A^eff≈0.7 for the Δ-isobar ratio while Sec. IV uses g_A^eff/g_A≈0.55 for the main NMEs. It affects the 2+ NME at the ~20% level and is worth cleaning up, but it is not load-bearing.\n\nThe citation pattern is fine. The self-citations are to standard NME and phase-space calculations, not to anything that pre-inserts the result. The paper deserves a serious referee. It is a legitimate sensitivity projection with a new relation, and the field needs the excited-state channel to be discussed quantitatively. Just make sure the referee asks the authors to tone down the abstract and show the reach as a band over the NME spread.\n\nBest.","headline":"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.","tokens_in":17396,"tokens_out":2232,"would_cite":true,"duration_ms":19090,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["neutrinoless double beta decay","right-handed weak currents","left-right symmetric model","ton-scale detectors","excited-state double beta decay","nuclear matrix elements","Majorana neutrino","grand unified theories"],"falsifier":"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 $\\langle\\lambda\\rangle_{\\min}\\approx5\\times10^{-7}$.","tokens_in":16320,"feed_emoji":"🔬","tokens_out":14040,"duration_ms":115167,"temperature":0.7,"pith_summary":"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 $\\langle\\eta\\rangle\\approx1.5\\times10^{-10}$.","feed_headline":"Ton-scale ββ detectors could reach λ ≈ 5×10^-8","feed_subtitle":"Separating the 0+ ground-state and 2+ excited-state decays isolates the η and λ right-handed currents.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the standard 0νββ transition-rate formula with the <m>, <λ>, and <η> terms that the paper starts from.","marker":"[1]"},{"why":"Gives the detector-sensitivity formula Γmin and documents the model spread of nuclear matrix elements.","marker":"[16]"},{"why":"Provides the left-right symmetric model notation and the <η>-mechanism analysis used for the λ/η relation.","marker":"[27]"},{"why":"Provides the transition-amplitude formalism and QRPA matrix elements for the ground-state rates.","marker":"[43]"},{"why":"Supplies the 0+→2+ NMEs for 76Ge used to estimate the Δ-mechanism at about 20% of the two-nucleon mechanism.","marker":"[46]"},{"why":"Provides the QRPA matrix elements for the excited 2+ transition in the left-right symmetric model.","marker":"[47]"},{"why":"Supplies the quenched axial coupling gAeff/gA≈0.55 used to set the nuclear matrix element scale.","marker":"[48]"},{"why":"Provides the shell-model NMEs used for the ground-state transition rates.","marker":"[58]"},{"why":"Gives the interacting-boson-model NMEs for the 2+ transition, an order of magnitude smaller than QRPA, which the paper cites as the main caveat.","marker":"[61]"}],"fun_headline_variants":["Ton-scale ββ detectors isolate λ and η right-handed currents","Excited-state γ-ray tags reveal λ vs η in neutrinoless ββ","λ≈5e-8 and η≈1.5e-10: ton-scale ββ reach","ββ decay: ground and excited states separate right-handed currents"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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 $\\langle\\lambda\\rangle\\approx5\\times10^{-8}$.","fun_headline_variants_meta":{"raw":{"variants":["Ton-scale ββ detectors isolate λ and η right-handed currents","Excited-state γ-ray tags reveal λ vs η in neutrinoless ββ","λ≈5e-8 and η≈1.5e-10: ton-scale ββ reach","ββ decay: ground and excited states separate right-handed currents"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000981,"raw_usage":{"total_tokens":4256,"prompt_tokens":1132,"completion_tokens":3124,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":748,"completion_tokens_details":{"reasoning_tokens":3039}},"tokens_in":748,"tokens_out":3124,"duration_ms":21414,"temperature":1.0,"reasoning_tokens":3039,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:53:30.033950+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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 $\\langle\\lambda\\rangle_{\\min}\\approx5\\times10^{-7}$.","supporting_citations":[{"cited_title":"[43] where a superscript i (a subscript j) etc","cited_arxiv_id":null,"evidence_quote":"Supplies the standard 0νββ transition-rate formula with the <m>, <λ>, and <η> terms that the paper starts from."},{"cited_title":"Vergados, H","cited_arxiv_id":null,"evidence_quote":"Gives the detector-sensitivity formula Γmin and documents the model spread of nuclear matrix elements."},{"cited_title":"Ejiri, J","cited_arxiv_id":null,"evidence_quote":"Provides the left-right symmetric model notation and the <η>-mechanism analysis used for the λ/η relation."},{"cited_title":"(28) Here the four momentum of the exchanged neutrino is kµ = ( ω, k), r = x − y and ei is energy of electron, ω =p k2 + m2ν","cited_arxiv_id":null,"evidence_quote":"Provides the transition-amplitude formalism and QRPA matrix elements for the ground-state rates."},{"cited_title":"Engel and J","cited_arxiv_id":null,"evidence_quote":"Supplies the 0+→2+ NMEs for 76Ge used to estimate the Δ-mechanism at about 20% of the two-nucleon mechanism."},{"cited_title":"Pantis, A","cited_arxiv_id":null,"evidence_quote":"Provides the QRPA matrix elements for the excited 2+ transition in the left-right symmetric model."},{"cited_title":"Pantis, F.Simkovic, J.D","cited_arxiv_id":null,"evidence_quote":"Supplies the quenched axial coupling gAeff/gA≈0.55 used to set the nuclear matrix element scale."},{"cited_title":"Fang and A","cited_arxiv_id":null,"evidence_quote":"Provides the shell-model NMEs used for the ground-state transition rates."},{"cited_title":"Agostini, G","cited_arxiv_id":null,"evidence_quote":"Gives the interacting-boson-model NMEs for the 2+ transition, an order of magnitude smaller than QRPA, which the paper cites as the main caveat."}],"review_version":1}