{"id":"af3a03fc-9447-47b3-8b4d-411537086c17","arxiv_id":"2508.04274","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"No evidence for extra-dimensional neutrino towers appears in three experiments, leading to conditional bounds on the compactification radius for ADD+ and Dark Dimension models.","lead":"Using neutrino data from MINOS, KamLAND, and Daya Bay, this paper searches for signs of extra dimensions with massive bulk sterile neutrinos. It finds no signal and places new limits on the extra dimension's size, though the limits depend strongly on assumed model parameters.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Strong positive-cR bounds rely on λi values that may leave the perturbative regime; the paper never checks this.","rationale":"I read the analysis as a careful, reproducible study: the code is public, the pipeline is validated against published results, and the paper is transparent that a fully free ci-λi fit yields no exclusions. The central claim is explicitly conditional, which is good. The reader's weakest_assumption focuses on the n=0 KK mode and mlightest. I do not see the n=0 omission as the main issue: Eq. (2.11) contains the vY0 entry, and the n=0 sterile mode has no bulk mass, so no diagonal entry is expected. Treating mlightest as a scanned parameter is also natural because the model does not predict the absolute neutrino mass. The more load-bearing concern is the exponential growth of λi with positive c_iR and the absence of any perturbativity check. The strongest bounds in the paper are produced precisely where λi is forced to be exponentially large, and the paper gives no evidence that such λi values are within the regime of validity of the 5D effective theory. A simple calculation from Eq. (2.9) shows that λi crosses 4π already at modest c_iR for ADD+, and at c_iR ~ 5 for DD. This is a concrete, checkable concern that does not require new data. I therefore agree with the conditional verdict but for a different reason than the reader's stated weakest assumption.","tokens_in":9298,"tokens_out":34386,"duration_ms":431889,"concrete_test":"At each point along the 90% and 99% CL contours in Figures 3 and 4 (for both ADD+ and DD), compute the profiled best-fit λi—or, equivalently, the λi required to reproduce the fitted light neutrino masses via Eq. (2.9). Mark all contour segments where max_i λi > 4π (and, as a stricter check, where max_i λi > 1). If the regions where R is most strongly constrained lie predominantly in the λi > 4π segments, the headline claim should be revised to state that the strong bounds hold only in a non-perturbative regime, or those bounds should be removed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 5 states that positive c_iR yield much stronger constraints because the λi needed to reproduce the SM mass splittings grow exponentially with c_iR, as seen from Eq. (2.9). This is the central mechanism behind the headline bounds. But Eq. (2.9) shows Y0 = λi (Mf/MPl) sqrt(2π c_i R/(e^{2π c_i R}-1)); for large positive c_iR this is exponentially suppressed, so the required λi grows as (m_light/v)(MPl/Mf) e^{π c_i R}/sqrt(2π c_i R). For ADD+ (Mf=10 TeV), even c_iR=1 and mlightest=0.001 eV already gives λi ~ 13, above 4π; for larger c_iR or mlightest it becomes orders of magnitude larger. For DD, the same happens at c_iR ≳ 5. The paper never imposes a perturbativity or unitarity bound on λi, and it never reports the fitted λi values. If the exclusion contours for positive c_iR are located where λi > 4π, those bounds are predictions of a strongly coupled regime and should not be presented as robust constraints from a perturbative EFT. This does not invalidate the small-λ or negative-cR regions, but it directly affects the strongest statement made in the abstract and Section 5.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper performs a frequentist profile-likelihood analysis of neutrino oscillation data from MINOS/MINOS+, KamLAND, and Daya Bay to constrain a class of extra-dimensional models with one large compactified dimension and bulk Dirac masses for right-handed neutrinos (ADD+ and Dark Dimension scenarios). The model predicts a tower of sterile KK modes that mix with active neutrinos. The authors validate their pipeline against published SM results and against the reference oscillograms of Carena et al., then scan the compactification radius R, the lightest neutrino mass, and either the bulk-mass parameters c_i or Yukawa couplings λ_i, obtaining 90% and 99% exclusion limits on R. They find no BSM signal. Positive c_iR produce strong bounds because matching the observed solar and atmospheric splittings forces exponentially large λ_i; negative c_iR or small λ_i leave the radius weakly constrained.","tokens_in":9691,"tokens_out":9762,"duration_ms":118499,"significance":"If the derivation and statistical procedure are sound, the paper is a useful phenomenological map of allowed (R, c_i, λ_i) space for two well-motivated higher-dimensional neutrino-mass frameworks. Its strengths include an open-source analysis pipeline, validation against published SM results and against the reference oscillograms of Carena et al., and a clear separation of the ADD+ and DD interpretations of Mf. The paper also identifies which regions of parameter space remain open for future experiments. However, the strongest exclusion statements are weakened by two unaddressed issues: the fitted Yukawa couplings in the positive-c_iR region may be non-perturbative, and the effective mass matrix omits the n=0 KK mode while scanning mlightest as an external parameter. The scope of the datasets also falls short of the 'global' label used in the abstract.","major_comments":[{"comment":"The paper's strongest claim — that large positive c_iR lead to strong bounds on R — rests on the statement that the λ_i required to reproduce Δm^2_21 and Δm^2_31 grow exponentially with c_iR (Sec. 5, Fig. 3). This follows from Eq. (2.9): Y0 = λ_i (Mf/MPl) sqrt(2π c_iR/(e^{2π c_iR}-1)). For positive c_iR, the zero-mode coupling is exponentially suppressed, so λ_i must scale roughly as (m_light/v)(MPl/Mf) e^{π c_iR}. For ADD+ with Mf=10 TeV and mlightest=10^-3 eV, even c_iR=1 already implies λ_i ~ O(10), above the 4π perturbativity limit; for larger c_iR or larger mlightest, λ_i becomes orders of magnitude larger. The paper never reports the fitted λ_i values and never imposes a perturbativity or unitarity bound. Consequently, the strong positive-c_iR exclusion contours may be predictions of a strongly coupled regime and should not be presented as robust EFT constraints. The small-λ and ne","section":"Sec. 5, Eq. (2.9)"},{"comment":"The mass matrix in Eq. (2.11) as written has no diagonal entry for the n=0 KK mode: the sterile diagonal starts at m1, m2, ..., and the first row contains vY0 with no corresponding mass row. Since Eq. (2.9) for Y0 plays a key role in the exponential-growth argument, the treatment of the zero mode is not a detail. In addition, mlightest is scanned as an external profiled parameter (Sec. 4), whereas the model itself predicts the light mass from the same λ_i and c_i. If the zero-mode contribution is non-negligible, or if mlightest is not freely adjustable independently of the Yukawa couplings, the oscillation probabilities and therefore the R exclusions could shift. The authors should state the basis used in Eq. (2.11), justify the omission (or correction) of the n=0 state, and discuss the status of mlightest as an external versus derived parameter.","section":"Eq. (2.11), Sec. 4"},{"comment":"The manuscript repeatedly calls the analysis 'global' (abstract, Sec. 4), but the datasets are MINOS/MINOS+, KamLAND, and Daya Bay only. These probes cover νμ and ν̄e disappearance channels relevant for θ23, θ13, θ12, Δm^2_31, Δm^2_21, but they do not include atmospheric neutrino data (Super-K, IceCube/DeepCore) or accelerator appearance data (T2K, NOvA), which are pertinent to sterile-KK mixing and have been used in previous LED analyses such as Ref. [27]. The comparison of the c=0 benchmark with [27] is therefore not an apples-to-apples validation of 'global' coverage. Either expand the dataset or adjust the 'global' terminology to 'combined analysis of MINOS/MINOS+, KamLAND, and Daya Bay'.","section":"Abstract, Sec. 4"}],"minor_comments":[{"comment":"Notation is inconsistent between 'cR' (Fig. 3 caption) and 'ciR' in the text. Also, 'For mlightest ≳ 0.1, eV' contains a misplaced comma; it should read '0.1 eV'.","section":"Sec. 5"},{"comment":"In Eq. (4.2), specify that LSM and LBSM are the profile likelihoods maximized over the common nuisance parameters, and state the number of degrees of freedom used for the Δχ²-to-CL conversion. This is important for reproducibility.","section":"Sec. 4"},{"comment":"The 'NKK = 10' truncation is mentioned in the Figure 1 caption; it would be helpful to state in Sec. 4 how many KK modes are used in the final fit and whether the results are stable when the truncation is increased.","section":"Sec. 3"},{"comment":"The statement that the fully general fit (both c_i and λ_i free) always accommodates the data implies that the bounds in Figs. 3 and 4 are conditional on fixing one of these parameter sets. This caveat should be made more prominent in the abstract and conclusions.","section":"Sec. 4"},{"comment":"The arXiv number and submission date appear inside the text body after the abstract; this should be removed in the journal version. The code repository link should include a version/commit for reproducibility.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"To the editor: The manuscript is a competently executed phenomenological fit, and the code release is a strength. My main reservation is that the headline constraints for positive c_iR are likely located in a non-perturbative regime of λ_i; the authors should either impose a perturbativity bound and restrict the claimed limits, or report the fitted λ_i values and demonstrate that they remain small. The zero-mode/lightest-mass treatment in Eq. (2.11) also needs clarification or correction. These issues are fixable in revision; I do not see an irreparable flaw."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThis is a competent and useful constraints paper, but it has one load-bearing soft spot: the strongest bounds, the ones in the abstract and Section 5 for positive cR, come from Yukawa couplings that have left perturbation theory, and the paper never checks or reports this.\n\nWhat is actually new: the extension of LED neutrino analyses to nonzero bulk Dirac masses with both signs, and the first oscillation-based mapping of these constraints onto the Dark Dimension parameter space. The numerical work is solid. The pipeline is validated against published SM results and against Carena et al. oscillograms. The profile-likelihood statistics are standard and transparent. The authors honestly report that the fully free fit (varying both ci and λi) excludes nothing, so the constraints are conditional by construction. That is stated clearly.\n\nThe central problem is the perturbativity of the positive-cR region. The authors themselves note that matching the SM mass splittings forces λi to grow exponentially with cR (Eq. 2.9). The stress-test estimate is correct: for ADD+ with Mf ~ 10 TeV, even cR = 1 and mlightest = 0.001 eV requires λi > 4π, and the numbers get orders of magnitude worse for larger cR or mlightest. The paper then quotes strong upper bounds on R in exactly that region without imposing a unitarity or perturbativity condition and without reporting the fitted λi values. Those contours may be interesting as a statement about the model class, but they are not robust EFT constraints. The negative-cR and small-λ regions are unaffected, so the paper still has value, but the abstract and conclusion need rewording.\n\nSecondary issues: calling three experiments a \"global\" fit overstates the scope, since solar and atmospheric data are missing and can matter for sterile mixing. The mass matrix in Eq. (2.11) silently starts the KK tower at n = 1 and treats mlightest as an external scan parameter; both choices deserve explicit justification. And the fully-free fit's no-exclusion result means every headline contour is conditional on fixing either ci or λi, which the reader must constantly keep in mind.\n\nBottom line: this deserves a serious referee. The analysis is honest, the validation is real, and the new parameter regions are worth mapping. But the authors need to either impose a perturbativity bound, report the fitted λi values, or explicitly label the positive-cR contours as strong-coupling predictions. With that fixed, I would cite it.","headline":"A genuinely useful constraints paper, but the headline positive-cR bounds are sitting in a strong-coupling regime the authors never check.","tokens_in":10154,"tokens_out":2661,"would_cite":true,"duration_ms":34234,"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":"No signatures of extra-dimensional sterile neutrinos appear in a joint fit to MINOS/MINOS+, KamLAND, and Daya Bay; the resulting upper bound on the compactification radius R depends sharply on bulk mass and Yukawa assumptions.","keywords":["large extra dimensions","sterile neutrinos","Kaluza–Klein tower","bulk Dirac mass","neutrino oscillations","dark dimension","compactification radius","exclusion limits"],"falsifier":"Take the same three datasets and rerun the profile likelihood with the n=0 Kaluza\\textendash Klein state included (mass $c_i$ and coupling $Y_i^0$) at benchmark points such as $c_iR=1$, $m_{\\rm lightest}=10^{-3}$ eV; if the 90% upper limit on $R$ moves by more than the width of the plotted contour, the omission in Eq. (2.11) is shaping the result.","tokens_in":9230,"feed_emoji":"🌌","tokens_out":10978,"duration_ms":131390,"temperature":0.7,"pith_summary":"This paper asks whether a single large extra dimension containing right-handed neutrinos with bulk Dirac masses can survive contact with neutrino oscillation data. It jointly fits MINOS/MINOS+, KamLAND, and Daya Bay and finds no deviation from three-flavor mixing, so the data place upper limits on the compactification radius R. The limits depend strongly on two model parameters: the dimensionless bulk mass $c_iR$ and the brane Yukawa coupling $\\lambda_i$. Positive $c_iR$ or $\\lambda_i \\gtrsim 10^{-3}$ force large active\\textendash sterile mixing and push the excluded region out toward the gravity bound, while negative $c_iR$ or $\\lambda_i \\lesssim 10^{-4}$ leave R essentially unconstrained by oscillations. Because the same framework covers ADD-like extra dimensions and the ``dark dimension'' candidate motivated by the cosmological constant, the bounds matter for both.","feed_headline":"No extra-dimensional neutrinos found in three experiments","feed_subtitle":"Joint fit turns the null into radius bounds: strongest when bulk masses are positive or Yukawas are sizable.","key_machinery":"The engine of the calculation is a generation-diagonal mass matrix (Eq. 2.11) that couples one active neutrino to a tower of Kaluza\\textendash Klein sterile states with masses $m_{i,n}=\\sqrt{(n/R)^2+c_i^2}$ and brane couplings $Y_i^n = \\lambda_i (M_f/M_{\\rm Pl}) \\sqrt{2n^2/(n^2+c_i^2R^2)}$; the zero-mode coupling $Y_i^0$ carries the exponential $c_iR$ dependence that drives the strongest bounds. The analysis machinery is a profile likelihood over these masses and couplings with three binned datasets, using $\\Delta\\chi^2 = -2\\log(L_{\\rm BSM}/L_{\\rm SM})$ and Wilks' theorem to convert the test statistic into exclusion contours.","core_discovery":"The paper's central claim is that current long- and short-baseline oscillation data contain no trace of the Kaluza\\textendash Klein sterile-neutrino tower predicted by these models, and that the null result translates into a quantitative map of allowed compactification radii. In the ADD+ scenario and in the Dark Dimension scenario, the same 5D mass matrix (Eq. 2.11) with bulk masses $c_i$ couples one active neutrino per generation to KK modes of mass $\\sqrt{(n/R)^2+c_i^2}$. To reproduce the observed solar and atmospheric splittings, positive $c_iR$ requires dimensionless Yukawa couplings $\\lambda_i$ that grow exponentially with $c_iR$, so the active neutrino is necessarily strongly mixed wit","pith_inferences":["Not stated in the paper but implied by the fully general fit: any model that scans both $c_iR$ and $\\lambda_i$ can evade every plotted oscillation bound.","Not stated in the paper: the exponential growth of the required Yukawa coupling with positive $c_iR$ carries a naturalness cost\\textemdash a positive-bulk-mass dark dimension would need finely tuned fundamental couplings to remain invisible.","A natural next step the paper does not take: fold in short-baseline appearance data, the channel that originally motivated bulk masses, to probe the negative-$c_iR$ region that disappearance data cannot constrain.","A robustness check the paper does not perform: recompute the contours with the $n=0$ Kaluza\\textendash Klein mode in the mass matrix; if the limits shift appreciably, the truncation in Eq. (2.11) is the operative assumption."],"forward_implications":["For positive bulk masses, the excluded compactification radii reach the short-range-gravity frontier, so the dark dimension's $0.1\\textendash 10\\,\\mu$m window is only open for negative $c_iR$ or small $\\lambda_i$.","The $cR=0$ ADD benchmark reproduces the published bounds from [27], so the same pipeline can be extended to updated neutrino datasets.","In the Dark Dimension scenario, $\\lambda_i \\gtrsim 10^{-3}$ yields bounds at least as strong as standard ADD, while $\\lambda_i \\lesssim 10^{-4}$ leaves only the gravity limit ($R \\lesssim 30\\,\\mu$m).","Normal and inverted mass orderings give different exclusions below $m_{\\rm lightest} \\sim 0.1$ eV; above that scale the ordering distinction disappears.","With both $c_i$ and $\\lambda_i$ free, the model reproduces all three datasets, meaning the plotted contours are bounds on conditional parameter space, not on the model as a whole."],"supporting_citations":[{"why":"Defines the large-extra-dimension scale relation $M_f$ that both ADD+ and the paper's analysis rely on.","marker":"[1]"},{"why":"Establishes volume-suppressed neutrino masses from bulk right-handed neutrinos, the starting point of the model.","marker":"[11]"},{"why":"Introduces the active-sterile KK mixing formalism for probing extra dimensions with neutrinos.","marker":"[15]"},{"why":"Adds bulk Dirac masses to the LED framework and supplies the Figure 4 oscillograms the paper reproduces.","marker":"[21]"},{"why":"Provides the previously published LED neutrino bounds that the $cR=0$ benchmark is checked against.","marker":"[27]"},{"why":"Supplies the MINOS/MINOS+ two-detector dataset used in the joint likelihood.","marker":"[35]"},{"why":"Supplies the KamLAND reactor dataset that anchors the solar parameters $\\theta_{12}$, $\\Delta m^2_{21}$.","marker":"[36]"},{"why":"Supplies the Daya Bay dataset that pins down $\\theta_{13}$ and $\\Delta m^2_{31}$.","marker":"[37]"},{"why":"Gives the KATRIN upper bound on the effective electron-neutrino mass used as an external constraint on $m_{\\rm lightest}$.","marker":"[38]"},{"why":"Gives the torsion-balance bound $R \\lesssim 30\\,\\mu$m that marks the edge of the viable compactification radius.","marker":"[39]"}],"fun_headline_variants":["Neutrino null result squeezes extra-dimension radius bounds","No extra dimensions seen in neutrino oscillation data","Null neutrino search bounds extra-dimension radius","Neutrino oscillations show no extra-dimension signal"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The bounds are computed from a mass matrix that omits the n=0 Kaluza\\textendash Klein mode, the lightest state of the bulk neutrino tower, and treats the lightest neutrino mass as an external input scanned in the fit; if that state mixes with the active neutrinos, or if the lightest mass is set by the model rather than chosen by hand, the excluded radii could shift.","fun_headline_variants_meta":{"raw":{"variants":["Neutrino null result squeezes extra-dimension radius bounds","No extra dimensions seen in neutrino oscillation data","Null neutrino search bounds extra-dimension radius","Neutrino oscillations show no extra-dimension signal"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0009,"raw_usage":{"total_tokens":3663,"prompt_tokens":646,"completion_tokens":3017,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":390,"completion_tokens_details":{"reasoning_tokens":2956}},"tokens_in":390,"tokens_out":3017,"duration_ms":28290,"temperature":1.0,"reasoning_tokens":2956,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T00:43:55.887119+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the same three datasets and rerun the profile likelihood with the n=0 Kaluza\\textendash Klein state included (mass $c_i$ and coupling $Y_i^0$) at benchmark points such as $c_iR=1$, $m_{\\rm lightest}=10^{-3}$ eV; if the 90% upper limit on $R$ moves by more than the width of the plotted contour, the omission in Eq. (2.11) is shaping the result.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes volume-suppressed neutrino masses from bulk right-handed neutrinos, the starting point of the model."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the active-sterile KK mixing formalism for probing extra dimensions with neutrinos."},{"cited_title":"Machado, Pedro A","cited_arxiv_id":null,"evidence_quote":"Adds bulk Dirac masses to the LED framework and supplies the Figure 4 oscillograms the paper reproduces."},{"cited_title":"Large extra dimensions and neutrino experiments","cited_arxiv_id":null,"evidence_quote":"Provides the previously published LED neutrino bounds that the $cR=0$ benchmark is checked against."},{"cited_title":"Search for sterile neutrinos in minos and minos+ using a two-detector fit.Physical review letters, 122(9):091803, 2019","cited_arxiv_id":null,"evidence_quote":"Supplies the MINOS/MINOS+ two-detector dataset used in the joint likelihood."},{"cited_title":"Constraints on θ 13 from a three-flavor oscillation analysis of reactor antineutrinos at kamland","cited_arxiv_id":null,"evidence_quote":"Supplies the KamLAND reactor dataset that anchors the solar parameters $\\theta_{12}$, $\\Delta m^2_{21}$."},{"cited_title":"Precision measurement of reactor antineutrino oscillation at kilometer-scale baselines by daya bay","cited_arxiv_id":null,"evidence_quote":"Supplies the Daya Bay dataset that pins down $\\theta_{13}$ and $\\Delta m^2_{31}$."},{"cited_title":"Direct neutrino-mass measurement based on 259 days of katrin data","cited_arxiv_id":null,"evidence_quote":"Gives the KATRIN upper bound on the effective electron-neutrino mass used as an external constraint on $m_{\\rm lightest}$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the torsion-balance bound $R \\lesssim 30\\,\\mu$m that marks the edge of the viable compactification radius."}],"review_version":1}