{"id":"596f69e3-2d2e-4262-8334-5b5709598e95","arxiv_id":"1908.07037","paper_version":2,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"A nonparametric statistical test on recoil energies from two different detector targets can determine the dark matter mass without assuming the galactic velocity distribution.","lead":"This paper develops a way to infer the dark matter particle's mass from two future direct detection experiments without assuming how dark matter moves in our galaxy. The method compares recoil-energy patterns in xenon and argon detectors, and could become a standard cross-check if a signal is detected.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Power-law halos break mass uniqueness: if eta(v) ∝ v^{-α}, the reweighted velocity distributions match for every assumed mass, so the CvM test cannot determine m_χ for such astrophysics.","rationale":"The reader's verdict accepted the paper with high confidence, identifying the form-factor/interaction assumption as the weakest point. Our concern is distinct and more load-bearing: it attacks the core uniqueness claim by exhibiting a family of physically reasonable halos for which the central equality holds at every tested mass, so the method has zero discriminating power. This is an internal mathematical property of the construction, not an external modeling uncertainty, and it survives even if all form factors are perfectly known. The paper acknowledges the need for a decreasing eta but does not flag that power-law eta functions, which are decreasing, destroy mass sensitivity. The method remains useful for Maxwellian-like halos and for the specific benchmark scenarios, but the 'completely independent of any astrophysical assumption' phrasing in Sec. VI is an overstatement. A revision that states this limitation, and ideally adds a diagnostic check for scale-invariance of the recovered eta, is necessary before the central claim is fully supported. Hence the verdict should be CONDITIONAL rather than unconditional ACCEPT.","tokens_in":12940,"tokens_out":8421,"duration_ms":83714,"concrete_test":"Generate Monte Carlo Xe/Ar data with the optimistic configuration, true m_χ=50 GeV, and a power-law halo with eta(v) ∝ v^{-3} (e.g., f(v) ∝ v^{-5} with a high escape cutoff). Apply the CvM test for tested masses from 10 to 200 GeV and plot the median p-value. If the concern is correct, the median p-value stays high (≳0.1) for all tested masses, i.e., the method returns no mass interval; a standard SHM run on the same event numbers should reproduce the paper's [21,190] GeV range. An even sharper check is analytic: substitute eta(v)=v^{-α} into the equality condition and verify the two weighted PDFs are proportional for all m, independent of the form factors.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central uniqueness claim in Sec. III is that the weighted distributions are equal only at the true mass. For an assumed mass m, the equality condition between the two reweighted samples reduces, after the common form-factor product F_1^2 F_2^2 cancels, to eta(r_1(m)√x) ∝ eta(r_2(m)√x), with r_D(m)=μ_AD(m)/μ_AD(m_true). For any power-law halo with eta(v) ∝ v^{-α}, this ratio is (r_1/r_2)^{-α}, a constant, so the two weighted CDFs are identical for every m. The test then yields high p-values for all masses, and no mass can be excluded. This is not a form-factor issue: it holds under the paper's own SI/Helm assumptions. The paper's suggested consistency check, that eta(v_m) be decreasing, does not remove the degeneracy, since power laws are decreasing. Thus the statement in Sec. VI that results are 'completely independent of any astrophysical assumption' is too strong; the method assumes the underlying halo is not scale-invariant over the probed velocity range.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a halo-independent method to determine the dark matter mass from two direct-detection signals in experiments with different target nuclei. Recoil energies are converted to squared minimum velocities using an assumed mass, and events in each experiment are reweighted by the other experiment's nuclear form factor, so that under the true mass the two weighted samples should share a common distribution proportional to the product of the two form factors times the halo integral. A Cramér-von Mises two-sample test is used to assign a p-value to each assumed mass. The method is demonstrated on xenon/argon benchmark configurations, with quoted 90% CL ranges such as [7,38] GeV for a true 20 GeV mass in the optimistic configuration, robustness checks against energy resolution and background, an extension to the ratio of neutron and proton couplings, and an extension to light mediators.","tokens_in":13184,"tokens_out":7898,"duration_ms":82115,"significance":"If the central uniqueness claim holds, this would be a valuable and practical complement to parametric halo fits: it avoids binning and does not require fitting the velocity distribution, and the authors provide explicit Monte Carlo verification of the null distribution of the weighted test statistic, robustness studies, and concrete sensitivity projections for realistic experiments. These are genuine strengths. However, the advertised claim of full astrophysical independence is stronger than what the mathematical construction actually delivers, because a simple family of halos breaks the uniqueness of the inferred mass. The paper's main conclusion is defensible only after an explicit non-scale-invariance assumption is added and the claims are correspondingly qualified.","major_comments":[{"comment":"The claimed uniqueness of the true mass is not valid for scale-invariant halos. For an assumed mass m, the equality of the two reweighted densities reduces, after the common form-factor product F_1^2(E_1(x)) F_2^2(E_2(x)) cancels, to eta(r_1(m) sqrt(x)) proportional to eta(r_2(m) sqrt(x)), where r_D(m) = mu_AD(m)/mu_AD(m_true). If eta(v) = C v^{-alpha}, then this ratio is (r_1/r_2)^{-alpha}, a constant, so after normalization the two weighted PDFs are identical for every m and the CvM p-value will be large for all masses; no mass can be excluded. This degeneracy occurs under the paper's own SI/Helm assumptions and is not a form-factor artefact. The consistency check suggested in Sec. VI, that eta(v_m) must be decreasing, does not remove the degeneracy because power laws are decreasing. The abstract and Sec. VI statements that the results are 'completely independent of any astrophysical assumption' are therefore too strong; the method requires an explicit non-scale-invariance assumption over the probed velocity range, or an additional characterization of the halos for which it is valid.","section":"Sec. III, Eqs. (5)-(8)"}],"minor_comments":[{"comment":"The prefactor (n_tilde_1 + n_tilde_2)^2 / (n_tilde_1 n_tilde_2) is written on the left-hand side of the defining equation, which is easy to misread as part of the statistic rather than as a separate normalization; the authors should define T_CvM explicitly and state the prefactor separately.","section":"Sec. III, Eq. (9)"},{"comment":"The Radon-Nikodym justification should refer to absolute continuity of the weighted measure with respect to the original measure, which follows from boundedness of the form factors, rather than to the weighted distribution being 'equal or smaller' than the original distribution pointwise.","section":"Footnote 1"},{"comment":"The quoted 90% CL ranges such as [7,38] GeV for a true 20 GeV mass are derived from the median p-value curve; the authors should state this explicitly, since the 68% and 95% bands in the figures show considerable realization-to-realization spread.","section":"Sec. III.A, Figs. 1-2"},{"comment":"The arbitrary reference recoil energy E_ref in Eq. (14) should be accompanied by a statement of whether the numerical results depend on its choice.","section":"Sec. V, Eq. (14)"}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid methods contribution and the Monte Carlo validation is a strength, but the power-law degeneracy directly undermines the strongest advertised claim of full astrophysical independence. I believe this can be fixed within the manuscript's scope by stating the required non-scale-invariance assumption, quantifying the affected halo family, and revising the abstract and conclusions accordingly. No concerns about novelty or citation practice; the paper builds appropriately on existing halo-independent methods."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the paper does something genuinely useful: it turns the old halo-independent observation into a binning-free two-sample test on weighted velocity distributions, and shows with Monte Carlo that it can pin down a DM mass in the 20-70 GeV window from two noble-liquid targets. Second, the central uniqueness claim is not as clean as stated. The stress-test is right: if the halo is a power law, eta(v) ~ v^{-alpha}, then for any assumed mass the two reweighted distributions are identical up to a constant, because the ratio r_D(m) just rescales the argument and normalization removes the constant. The CvM test then sees no difference at any mass. That contradicts the Sec. III claim that equality happens only at the true mass and the Sec. VI phrase 'completely independent of any astrophysical assumption.' The paper does mention that eta should be decreasing and that shape assumptions are minimal, but decreasing power laws pass that check, so the caveat is insufficient. This is not a fatal flaw for practical use--real halos are not exact power laws over the probed velocity range--but the paper should state the assumption explicitly: the method requires the halo not be scale-invariant over the relevant interval.\n\nWhat is good: the construction in Sec. III is clean. The Radon-Nikodym point justifies the weighting direction, the effective event numbers are a sensible correction, and the null-distribution check gives confidence that the p-values are calibrated. The robustness tests for energy resolution and background are honest and show the method survives at modest resolutions and backgrounds. The coupling-ratio section is also useful, with the sign degeneracy handled correctly. No code is released, which is a minor point but would help reproducibility.\n\nThe precision claims are honest: wide intervals, only lower bound for heavy masses, square-root exposure scaling. The paper is well-scoped for a methods paper.\n\nWho this is for: direct detection phenomenologists and experimental collaborations planning target combinations. It deserves a serious referee. I would send it to review, but the authors should be asked to fix the scale-invariance caveat and soften the 'completely independent' phrasing. With that, it is a solid contribution.","headline":"A genuinely useful nonparametric mass test with a real but fixable overclaim: power-law halos break the claimed astrophysics independence.","tokens_in":13660,"tokens_out":2816,"would_cite":true,"duration_ms":30108,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["95.35.+d"],"model":"deepseek-v4-flash","headline":"The dark matter mass can be extracted from two direct detection signals without assuming the galaxy's dark matter velocity distribution, using a distribution-free two-sample test in velocity-squared space.","keywords":["dark matter mass determination","direct detection","halo-independent method","nonparametric two-sample test","velocity distribution","spin-independent scattering","nuclear form factor","xenon and argon detectors"],"falsifier":"Generate mock event sets from spin-independent scattering with a known 50 GeV dark matter mass but add an extra recoil-energy dependence in the cross section that is not included in the assumed form factors, for example a $1/E_R$ factor; if the Cramér–von Mises test rejects the true mass at 90% confidence in a large fraction of realizations, the core equality fails and the method's interaction assumption is falsified.","tokens_in":12784,"feed_emoji":"🌌","tokens_out":6608,"duration_ms":62338,"temperature":0.7,"pith_summary":"This paper proposes a way to determine the dark matter mass from two direct detection experiments with different target nuclei while making no assumption about the local dark matter velocity distribution. The core idea is that converting measured nuclear recoil energies into dark matter velocities requires choosing a dark matter mass, and the two experiments' weighted event distributions in velocity-squared space are identical only when the chosen mass is the true one. The paper demonstrates this with a nonparametric two-sample hypothesis test that needs no binning and no parametrised halo model, and it works with about 20 events per experiment, with robust results around 100 or more. For realistic xenon and argon detectors, a true 50 GeV mass can be bracketed to roughly 21–190 GeV at 90% confidence, and the same data can then constrain the relative coupling to neutrons and protons. The price is an assumption about the interaction: elastic spin-independent scattering with known nuclear form factors.","feed_headline":"Dark matter mass recovered without knowing the halo","feed_subtitle":"A distribution-free two-sample test brackets a 50 GeV mass to 21–190 GeV at 90% confidence.","key_machinery":"The load-bearing object is the weighted empirical cumulative distribution in squared minimum velocity $v^2$. For detector $D$, each event's recoil energy is mapped to $v_m^2 = m_{A_D} E_R / (2 \\mu_{A_D}^2)$ for an assumed $m_\\chi$, and the event is weighted by the other detector's nuclear form factor $F^2_{D'}(E_R)$, relying on the fact that the halo integral $\\eta(v_m)$ is a detector-independent function of $v_m$. The product $h(v^2) = F_1^2(v^2) F_2^2(v^2) \\eta(v^2)$ is the common distribution both reweighted samples should follow, so the Cramér–von Mises statistic between the two empirical CDFs provides a $p$-value for each tested mass.","core_discovery":"The central claim is that the normalized weighted event distributions in $v^2$ space are equal for two experiments only when the correct dark matter mass $m_\\chi$ is used to convert recoil energies into velocities. For an assumed mass, each sample is reweighted with the other experiment's nuclear form factor, producing empirical cumulative distributions that ought to agree under the null hypothesis; disagreement, quantified by the Cramér–von Mises statistic, rejects that mass. Applied to Monte Carlo realizations of xenon and argon detectors, the paper finds median 90% confidence intervals of $[7,38]$ GeV for a true 20 GeV mass, $[21,190]$ GeV for a true 50 GeV mass, and a lower bound of at least 23 GeV for a true 100 GeV mass in the optimistic configuration. The method also detects inconsistency: if no mass yields a high $p$-value, at least one signal fails the assumed dark matter scattering hypothesis.","pith_inferences":["If the true interaction is not the assumed spin-independent elastic one, the equalizing reweighting is biased and the true mass could be rejected; treating the interaction model as a discrete hypothesis and comparing p-values across models would make the method self-diagnosing.","Because the method only uses relative event weights, the same two-sample construction could be applied to annually modulated event rates, where the time modulation provides another handle that the paper does not exploit.","The coupling-ratio degeneracy suggests a concrete extension: adding a third target with a very different proton-to-neutron ratio, such as a light nucleus alongside xenon and argon, should break the sign ambiguity shown in the paper.","After the mass is fixed, the data could be fed into a separate halo-reconstruction step, making the astrophysics-independent mass estimate a prior for mapping the full velocity distribution."],"forward_implications":["Two positive signals from different target nuclei can pin down the dark matter mass with no assumption about the local velocity distribution, removing the largest astrophysical nuisance in direct detection fits.","With a few hundred events, masses between roughly 20 and 70 GeV can be bracketed, while heavier masses yield only a lower bound—a kinematic limit that applies to any mass-measurement method from nuclear recoils.","Once the mass is known, the relative event rates in the two detectors constrain the ratio of dark matter couplings to neutrons and protons; a residual two-fold degeneracy requires a third target to resolve.","The test is robust to energy resolution below about 2 keV and to backgrounds below about 10% of the signal, and it can flag when one signal is not compatible with the assumed elastic spin-independent scattering hypothesis.","For a light mediator the same reweighting works with a modified effective form factor, and although the mediator mass itself is hard to determine, regions of the $(m_\\phi, m_\\chi)$ plane can be excluded halo-independently."],"supporting_citations":[{"why":"Introduces the halo-independent quantity $\\eta(v_m)$ extracted from recoil spectra, the foundation of the comparison.","marker":"[8]"},{"why":"Establishes the detector-independence of the velocity integral, allowing two targets to be compared without halo assumptions.","marker":"[9]"},{"why":"Defines the effective target mass number and the light-mediator form-factor parametrization used in the analysis.","marker":"[42]"},{"why":"Supplies the standard halo model parameters and Helm form factor used to generate mock xenon and argon data.","marker":"[11]"},{"why":"Provides the weighted two-sample test statistics and effective event-number definitions used for the Cramér–von Mises test.","marker":"[49]"},{"why":"Gives the asymptotic null distribution of the test statistic used to convert observed values into p-values.","marker":"[50]"}],"fun_headline_variants":["No-halo needed: dark matter mass from two detectors","Dark matter mass without the halo model, from two experiments","Astrophysics-free DM mass from two detection signals","Two detectors, zero halo: DM mass from nonparametric test","Dark matter mass from dual targets, no halo fit"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes the dark matter–nucleus interaction is known and factorizable—specifically elastic spin-independent scattering with known nuclear form factors—so unmodelled energy or momentum dependence in the cross section would break the equality of the reweighted distributions even at the true mass.","fun_headline_variants_meta":{"raw":{"variants":["No-halo needed: dark matter mass from two detectors","Dark matter mass without the halo model, from two experiments","Astrophysics-free DM mass from two detection signals","Two detectors, zero halo: DM mass from nonparametric test","Dark matter mass from dual targets, no halo fit"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000865,"raw_usage":{"total_tokens":3736,"prompt_tokens":918,"completion_tokens":2818,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":534,"completion_tokens_details":{"reasoning_tokens":2738}},"tokens_in":534,"tokens_out":2818,"duration_ms":21063,"temperature":1.0,"reasoning_tokens":2738,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:28:13.246349+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate mock event sets from spin-independent scattering with a known 50 GeV dark matter mass but add an extra recoil-energy dependence in the cross section that is not included in the assumed form factors, for example a $1/E_R$ factor; if the Cramér–von Mises test rejects the true mass at 90% confidence in a large fraction of realizations, the core equality fails and the method's interaction assumption is falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the weighted two-sample test statistics and effective event-number definitions used for the Cramér–von Mises test."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the asymptotic null distribution of the test statistic used to convert observed values into p-values."}],"review_version":1}