{"id":"0fb3e34d-49a1-486b-95ac-678dd8d9b506","arxiv_id":"2607.22163","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A combined ESSnuSB+T2HK sensitivity analysis resolves most LIV-induced θ23 octant degeneracies and keeps δCP near −90°, with residual degeneracies for |a_eτ| and a_ee at the 360 km combination.","lead":"This paper simulates whether combining two planned neutrino observatories, ESSnuSB in Europe and T2HK in Japan, could detect a subtle kind of spacetime-symmetry breaking called Lorentz invariance violation (LIV). It finds the combination removes most, but not all, fake 'wrong-octant' solutions for the neutrino mixing angle θ23, giving a matter-independent route to constrain Planck-scale LIV.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Single-parameter-at-a-time fits leave open the possibility that simultaneous LIV coefficients restore θ23/δCP degeneracies.","rationale":"The reader's weakest assumption matches the most load-bearing concern I can identify. Section 3 says 'these LIV coefficients are marginalized over relevant ranges,' which is ambiguous, but Section 4.2's description of Figs. 4 and 5—scanning one a_αβ and marginalizing only the corresponding phase—indicates that the fits do not treat the full six-dimensional LIV parameter space as free. Consequently, the headline claim that ESSnuSB+T2HK 'resolves the degeneracies for most LIV parameters' is conditional on a single-parameter-at-a-time modeling choice. This is not an internal inconsistency: it is a standard sensitivity-study limitation. But it directly affects the central claim, because the physical LIV Hamiltonian of Eq. (2.8) generically contains all six coefficients. A simultaneous fit could easily recover wrong-octant solutions for parameters that look resolved in one-parameter projections. The paper explicitly acknowledges residual islands for |a_eτ| and a_ee (360 km), which reinforces the point that the conclusion is not universal even in the simplified fits. I also note the absence of released simulation files, but that is secondary to the modeling concern. Since the reader already returned CONDITIONAL, my stress test does not move the verdict; it sharpens the reason for the condition.","tokens_in":17115,"tokens_out":6687,"duration_ms":71305,"concrete_test":"Run a GLoBES simultaneous fit for both combined setups (ESSnuSB 360 km + T2HK and 540 km + T2HK) with all six LIV magnitudes (a_ee, a_μμ, a_ττ, |a_eμ|, |a_eτ|, |a_μτ|) and three phases φ_αβ free together with θ23 and δCP, using true values from Table 2 and all a=0. Project the 95% C.L. region onto each (θ23, a_αβ) plane and check whether wrong-octant θ23 intervals such as [42°, 44°] reappear for parameters other than |a_eτ|. As a stronger variant, repeat with the benchmark true values listed in Sec. 3 (a_ee=2.4, a_μμ=3.0, a_ττ=2.0, |a_eμ|=0.7, |a_eτ|=1.2, |a_μτ|=2.0 × 10^-23 GeV) and arbitrary phases, to test whether the degeneracy resolution survives when LIV is actually present.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4.2's allowed regions (Figs. 4 and 5, Tables 3 and 4) are generated by scanning one a_αβ at a time: for off-diagonal parameters only the corresponding phase φ_αβ is marginalized, and the text does not state that the remaining five a_αβ are simultaneously free. Eq. (3.1) marginalizes over generic p_test, but the figure descriptions—'the plotted plane is (θ23, aαβ)'—and the instruction that only the corresponding φ_αβ is marginalized strongly imply that each panel has only one LIV magnitude active. The central claim that the combination 'resolves the degeneracies for most LIV parameters' is therefore established only for one-LIV-parameter fits. If two or more LIV coefficients are present—the generic expectation for Planck-scale physics—the extra degrees of freedom can enlarge the allowed regions and recreate wrong-octant fake solutions for parameters that appear resolved in the single-parameter projections. The acknowledged residual island for |a_eτ| shows how an extra phase degree of freedom can prevent resolution; additional free LIV magnitudes could have the same effect for other parameters. No released GLoBES files are provided to check this internally.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents GLoBES-based sensitivity projections for the ESSnuSB (360 km and 540 km baselines) and T2HK (295 km) experiments to isotropic, CPT-violating LIV coefficients a_αβ in the SME. The authors study correlations between each a_αβ and θ23 or δCP, and show that while the individual ESSnuSB baselines (especially 540 km) suffer from wrong-octant degeneracies due to neutrino-antineutrino event asymmetry, combining either ESSnuSB baseline with T2HK removes most of these degeneracies. The central claim is that the ESSnuSB+T2HK synergy provides a matter-independent way to break LIV-induced degeneracies and constrain Planck-scale LIV, although residual lower-octant islands remain for |a_eτ| and for a_ee in the 360 km combination.","tokens_in":17445,"tokens_out":3338,"duration_ms":37919,"significance":"If the central claim is correct, the paper provides a useful quantitative projection: it shows that high-statistics first-oscillation-maximum data can substitute for strong matter effects in resolving LIV-induced degeneracies, and it maps which parameters remain difficult. The authors use the standard GLoBES machinery, state benchmark LIV magnitudes explicitly, and provide two-dimensional contours and tabulated allowed ranges. These are concrete, testable predictions. However, the significance is tempered by the fact that the fits vary one LIV parameter at a time, so the resolved-degeneracy claim has not been demonstrated for the generic multi-LIV scenario expected from Planck-scale physics.","major_comments":[{"comment":"The marginalization description never states whether the other five a_αβ coefficients are fixed to zero or floated in the fits. The text says only that δ_CP (Fig. 4) or θ23 (Fig. 5) is marginalized, and that for off-diagonal parameters the corresponding φ_αβ is marginalized; this strongly implies each panel has only one LIV magnitude active. If so, the central claim that the combination 'resolves the degeneracies for most LIV parameters' holds only for one-parameter-at-a-time LIV. Since generic Planck-scale LIV would have several non-zero a_αβ, the extra degrees of freedom can reopen the wrong-octant solutions. The authors should state this limitation explicitly or, preferably, perform a simultaneous multi-LIV fit or a representative two-parameter scan to show the degeneracy resolution is robust.","section":"§4.2 and §3"},{"comment":"The Fig. 2 caption reads \"a_eτ = 0.7×10^-23 GeV\", whereas Table 2 and the text state the benchmark magnitude is |a_eτ| = 1.2×10^-23 GeV. This is an inconsistency in the displayed LIV magnitude for the bi-event plots. Please verify which value was actually used in the simulation and correct the caption or the benchmark table; if the bi-event plots used 0.7, they do not correspond to the same benchmark as the χ² analysis.","section":"Fig. 2 caption and Table 2"},{"comment":"The abstract claims degeneracies are 'resolved for most LIV parameters,' but Table 3 shows that for a_ee the 360 km + T2HK combination still leaves a lower-octant interval [42.6,43.4]°, and for |a_eτ| both combinations leave a lower-octant island. The paper acknowledges these residuals, so this is not a contradiction, but the phrasing 'resolved for most' could be sharpened to state exactly which parameters remain degenerate; the current wording risks overstating the outcome for a_ee and |a_eτ|.","section":"§1/§5, central claim"}],"minor_comments":[{"comment":"Typo: 'HHowever' in the fourth paragraph of the Introduction.","section":"§1"},{"comment":"Axis labels like 'a /10 23[GeV]' and 'a /10 23[GeV]' are missing subscripts (a_ee, a_μμ, |a_eτ|, etc.) due to formatting; please fix for readability.","section":"Figs. 4 and 5"},{"comment":"The text says 'these LIV coefficients are marginalized over relevant ranges during the test hypothesis fitting' but does not specify whether the ranges are the same as the plotted ranges in Figs. 4–5. Clarifying this would help reproduction.","section":"§3"},{"comment":"No GLoBES input files or a link to such files are provided. Given that the paper's main quantitative claims rest on these simulations, releasing the simulation files would significantly increase reproducibility and trust in the results.","section":"Reproducibility"}],"recommendation":"major_revision","confidential_remarks":"The paper is a standard sensitivity projection and is likely publishable after revision. The main risk is that the single-parameter-at-a-time treatment is insufficient to support the 'resolved for most LIV parameters' claim in a generic multi-LIV scenario. I do not see a fatal technical flaw; the inconsistency in the Fig. 2 benchmark value is a clear but citable fix. The authors should be asked to clarify the marginalization and ideally add a multi-LIV check."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a solid, workmanlike sensitivity study. The genuinely new piece is swapping DUNE for T2HK as the complement to ESSnuSB, and the question it answers is useful: does resolving LIV-induced θ23/δCP degeneracies require DUNE's strong matter effects, or will high statistics at the first oscillation maximum do the job? The paper suggests the latter for most aαβ parameters. That is a planning-level result worth having.\n\nWhat it does well: the GLoBES setup is standard and internally consistent, the benchmark LIV magnitudes are taken from the authors' own earlier DUNE study rather than fitted to anything, and the paper is honest about the residuals that persist—|aeτ| leaves a lower-octant island in both combinations, and the 360 km + T2HK combo does not fully remove the aee octant degeneracy. Tables 3 and 4 give concrete allowed ranges, which is helpful.\n\nNow the soft spot. Section 4.2 scans one LIV parameter at a time. For off-diagonal parameters, only the corresponding phase φαβ is marginalized; the text never states that the other five aαβ magnitudes are simultaneously free. So the claim that degeneracies are „resolved for most LIV parameters\" is strictly established only for single-parameter fits. If several LIV coefficients are non-zero at once—the generic expectation for Planck-scale physics—the extra degrees of freedom could enlarge the allowed regions and bring back fake octants for parameters that look resolved in these projections. The authors should either state this as an explicit limitation or, better, run a fit with all aαβ active. This is the main thing a referee should ask for.\n\nA second, smaller issue: the paper does not release GLoBES files. For a purely simulation-based sensitivity study, that makes the numbers hard to check and limits the paper's value to the community. A minor factual glitch: Figure 2's caption quotes aeτ = 0.7×10−23 GeV, while the benchmark table later says |aeτ| = 1.2×10−23 GeV. Probably a typo, but it should be fixed.\n\nOverall: the central argument holds up for what it actually tests. It is not a field-changer, but it is a legitimate extension of the authors' program and a reasonable input for experimental design. I would send it to peer review with a request for a simultaneous-LIV fit and clearer statement of the single-parameter assumption. I would not cite it as a definitive resolution claim, but I would cite it as a useful complementarity study.","headline":"Competent GLoBES study with a real limitation: the degeneracy-resolution claim is only established for one-LIV-parameter-at-a-time fits, so the headline needs a simultaneous-fit check.","tokens_in":17934,"tokens_out":2224,"would_cite":true,"duration_ms":26090,"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":"The paper claims that combining ESSnuSB's 360 km and 540 km baselines with T2HK's high-statistics 295 km first-maximum data resolves LIV-induced θ23-octant and δCP degeneracies for most isotropic CPT-violating parameters a_αβ.","keywords":["Lorentz invariance violation","CPT violation","neutrino oscillations","long-baseline experiments","ESSnuSB","T2HK","parameter degeneracy","θ23 octant"],"falsifier":"Re-run the joint ESSnuSB (360 km and 540 km) + T2HK simulation with all six a_αβ coefficients and their phases left free in the test hypothesis, generating true data with, say, a_ee = 2.4×10⁻²³ GeV and |a_eτ| = 1.2×10⁻²³ GeV simultaneously; if the 95% allowed regions in the (θ23, a_αβ) and (δCP, a_αβ) planes then contain lower-octant solutions or δCP ≈ +90°, the central 'resolved for most parameters' claim fails for the simultaneous-LIV case.","tokens_in":16991,"feed_emoji":"⚛️","tokens_out":3564,"duration_ms":35215,"temperature":0.7,"pith_summary":"The paper tries to establish that the combination of two complementary long-baseline neutrino experiments—ESSnuSB, probing the second oscillation maximum, and T2HK, delivering high, balanced statistics at the first maximum—can break the parameter degeneracies that Lorentz-violating new physics introduces into standard neutrino oscillation measurements. Specifically, the joint analysis removes most wrong-octant fake solutions for the atmospheric mixing angle θ23 and keeps the CP phase δCP tightly pinned near its true value, even without relying on large matter effects. If correct, this provides a matter-independent route to constrain Planck-scale Lorentz invariance violation at upcoming facilities, with the notable caveat that degeneracies persist for a few parameters like |a_eτ| and, in one combination, a_ee.","feed_headline":"ESSnuSB + T2HK combination resolves most LIV parameter degeneracies","feed_subtitle":"High-statistics first-maximum data complement ESSnuSB's second-maximum CP probe of Planck-scale Lorentz violation.","key_machinery":"The central object is the isotropic, CPT-violating LIV Hamiltonian H_LIV = a_αβ, a Hermitian matrix of energy-independent coefficients that perturb the neutrino and antineutrino effective Hamiltonians with opposite sign and complex conjugation. The degeneracy-breaking mechanism is baseline complementarity: ESSnuSB's long baselines sample the second oscillation maximum, where intrinsic CP asymmetry is large, while T2HK's short, high-intensity baseline samples the first maximum with roughly balanced neutrino and antineutrino statistics. The χ² analysis marginalizes over standard oscillation parameters and, for off-diagonal LIV parameters, the new phase φ_αβ, scanning each a_αβ against θ23 and","core_discovery":"Using dedicated simulations of the ESSnuSB 360 km and 540 km baselines and the T2HK 295 km baseline, the authors show that a combined χ² analysis shrinks the allowed (θ23, a_αβ) and (δCP, a_αβ) regions so that the wrong-octant fake solutions produced by isotropic, CPT-violating LIV parameters mostly disappear. The 360 km ESSnuSB baseline alone already rules out the lower octant for a_ττ, |a_eμ|, and |a_μτ|, but leaves two-octant solutions for a_ee and |a_eτ|; T2HK alone also cannot resolve a_ee and |a_eτ|. Synergizing T2HK with either ESSnuSB baseline eliminates these fake octants for most parameters, and the 540 km ESSnuSB + T2HK combination even resolves the a_ee octant that the 360 km com","pith_inferences":["Because the fits appear to vary one LIV coefficient at a time, the claim that degeneracies are resolved 'for most LIV parameters' may not hold if several a_αβ coefficients are simultaneously non-zero; a multi-parameter fit could expand the allowed regions and reopen some octant degeneracies.","The persistent |a_eτ| island suggests that fully covering this parameter may require a third probe with a different energy-matter profile, such as atmospheric neutrinos or an additional baseline, rather than just combining these two beams.","Comparing with the authors' earlier ESSnuSB + DUNE study implies a trade-off: matter-enhanced configurations give stronger overall LIV magnitude constraints, while the matter-independent ESSnuSB + T2HK combination trades some constraining power for robustness against matter-model uncertainties.","A natural testable extension would be to generate fake data with non-zero a_ee and |a_eτ| together and run the global fit with all six LIV parameters free, checking whether the combined allowed regions expand beyond the single-parameter contours shown here."],"forward_implications":["A joint ESSnuSB + T2HK analysis removes wrong-octant θ23 fake solutions for most a_αβ parameters, with the 540 km + T2HK combination also breaking the a_ee octant degeneracy.","The combined setup keeps δCP confined to a tight interval around −90° for all parameters, eliminating the δCP = +90° solution that T2HK alone admits for |a_eτ|.","Resolving LIV-induced degeneracies does not require the strong matter effects of a long-baseline experiment like DUNE; precision at the first maximum plus second-maximum CP sensitivity suffices for most parameters.","Residual degeneracies persist for |a_eτ| (small lower-octant island in both combinations) and for a_ee in the 360 km + T2HK combination, so those parameters are only partially resolved.","The 360 km ESSnuSB baseline individually constrains LIV parameters more tightly than the 540 km baseline due to higher statistics, but adding T2HK brings the 540 km configuration to comparable combined performance."],"fun_headline_variants":["ESSnuSB and T2HK synergy breaks LIV degeneracies","Combining ESSnuSB and T2HK resolves most LIV octant fakes","Two-baseline combo clears LIV-induced parameter fakes","ESSnuSB+T2HK data kill most Lorentz-violation degeneracies"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The demonstration that degeneracies are resolved for most LIV parameters assumes each a_αβ coefficient is switched on one at a time; the text never states that all six coefficients are freed simultaneously in the fit, and if several are non-zero together the allowed regions could expand and the degeneracies could reappear (Section 3 marginalization description and Section 4.2 fitting procedure).","fun_headline_variants_meta":{"raw":{"variants":["ESSnuSB and T2HK synergy breaks LIV degeneracies","Combining ESSnuSB and T2HK resolves most LIV octant fakes","Two-baseline combo clears LIV-induced parameter fakes","ESSnuSB+T2HK data kill most Lorentz-violation degeneracies"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000871,"raw_usage":{"total_tokens":3656,"prompt_tokens":840,"completion_tokens":2816,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":584,"completion_tokens_details":{"reasoning_tokens":2740}},"tokens_in":584,"tokens_out":2816,"duration_ms":20295,"temperature":1.0,"reasoning_tokens":2740,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T05:35:17.673820+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the joint ESSnuSB (360 km and 540 km) + T2HK simulation with all six a_αβ coefficients and their phases left free in the test hypothesis, generating true data with, say, a_ee = 2.4×10⁻²³ GeV and |a_eτ| = 1.2×10⁻²³ GeV simultaneously; if the 95% allowed regions in the (θ23, a_αβ) and (δCP, a_αβ) planes then contain lower-octant solutions or δCP ≈ +90°, the central 'resolved for most parameters' claim fails for the simultaneous-LIV case.","supporting_citations":[],"review_version":1}