{"id":"6139fee8-f20d-4362-9663-1823c44924f7","arxiv_id":"1307.7802","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Direct detection limits from LUX 2013 require the extra Z' boson of the 3-3-1LHN model to be heavier than about 2 TeV.","lead":"A 331 extension of the Standard Model predicts a heavy neutral fermion as dark matter, with a new Z' boson mediating both its annihilation and its scattering off nuclei. Comparing the predicted nuclear recoil rate to LUX 2013 data pushes the Z' mass above about 2 TeV.","discovery_kind":"unclear","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The 2 TeV bound is a tree-level, gauge-fixed estimate robust at the factor-of-2 level; the reader's Z-Z' mixing concern is suppressed by v^2/v_chi'^2 ~ 1.5%, but the abstract's 'independently of the dark matter mass' is contradicted by the body's own M_N1-dependent statements.","rationale":"The reader's verdict CONDITIONAL is reasonable, and the presentational issues it flags (abstract vs. body on mass dependence, 'important' coannihilation vs. 'only scatter,' Fig. 7 caption attributing the excluded region to XENON100 while the text attributes it to LUX) are real. But the reader's weakest_assumption overstates the Z-Z' mixing concern: in this model the mixing angle is O(v^2/v_chi'^2) ~ 1.5%, so the cross section shifts by a few percent, not a factor of a few. The scalar-exchange concern is also weaker than the reader suggests, because the S1/S2/P1 couplings to light quarks are Yukawa-suppressed. The genuinely load-bearing issue is the scope of the central claim: the abstract's 'independently of the dark matter mass' is contradicted by Sec. III.B and Figs. 6-7, and the sentence about light N1 needing a heavier Z' appears to have the wrong sign relative to the mu^2 scaling. This is a scope overclaim, not a computational error, so it supports CONDITIONAL rather than a rejection. The bound itself is a standard tree-level, gauge-fixed calculation and is robust at the factor-of-2 level; the unshipped micrOMEGAs implementation is a replication obstacle but not a correctness concern for the bound's order of magnitude. No change to the reader's verdict is warranted, but the rationale should be re-centered on the mass-dependence inconsistency rather than on Z-Z' mixing.","tokens_in":37660,"tokens_out":49605,"duration_ms":445946,"concrete_test":"Recompute Fig. 6's SI cross section at M_N1 = 200, 600, and 1000 GeV for M_Z' = 2 TeV, and check the sign of the M_N1 dependence against the text's claim that light N1 (<600 GeV) needs a heavier Z' to evade XENON100. If the cross section decreases with M_N1 (as the mu^2 scaling implies), the text's statement is wrong and the 'independently of the dark matter mass' claim in abstract:s3 needs qualification.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim's scope, not its computation, is the soft spot. The abstract (abstract:s3) says the LUX bound is 'independently of the dark matter mass,' but Sec. III.B and Figs. 6-7 show the SI cross section scales with the WIMP-nucleus reduced mass, so the bound weakens for light N1. The text even states 'For a N1 lighter than ~600 GeV one will need a Z' much heavier than 2 TeV in order to evade the XENON100 limits' (Sec. III.B), which is the opposite of the mu^2 scaling and suggests a sign/description error in that sentence. The bound is also only meaningful where the relic density is viable, which the paper's own scan restricts to M_N1 < M_Z'/2 (resonance) or M_N1 >~ 1 TeV (coannihilation). The reader's Z-Z' mixing concern is real but small: the mixing angle is O(v^2/v_chi'^2) ~ (246/2000)^2 ~ 1.5%, so the cross section shifts by O(3%), not 'a factor of a few.' Scalar contributions (S1, S2, P1) are suppressed by the quark Yukawa y_q ~ m_q/v, so the paper's qualitative dismissal is correct. The bound is therefore robust at the factor-of-2 level (sigma ~ 1/M_Z'^4, so a factor-4 cross-section error moves 2 TeV to ~1.4-2.8 TeV), but the abstract's mass-independence claim is an overstatement that the body itself contradicts.","agreement_with_reader":"partial"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript studies the 3-3-1LHN extension of the Standard Model, in which the lightest of the new heavy neutral fermions (N1) is a viable WIMP candidate stabilized by a discrete symmetry. The authors implement the model in a customized version of micrOMEGAs, compute the N1 thermal relic density including coannihilation across the heavy fermion sector and 3- and 4-body final states, and scan the (M_Z', M_N1) plane for four values of the symmetry-breaking scale v_chi' = 2, 3, 4, 5 TeV, corresponding to M_Z' = 0.8, 1.2, 1.6, 2 TeV via Eq. (17). They then compute the spin-independent N1-nucleus scattering cross section, mediated at tree level by Z' exchange with the gauge couplings of Table I, and compare it with the LUX 2013 and XENON100 limits. The headline conclusion is a lower bound M_Z' >~ 2 TeV, stated in the abstract as holding 'independently of the dark matter mass', which through Eq. (17) translates into a bound on the symmetry-breaking scale and hence on the whole new-physics mass spectrum. The authors also argue that the bound applies, at some level, to other 331-like models with singlet neutral fermion dark matter, and comment on LHC phenomenology.","tokens_in":38410,"tokens_out":43356,"duration_ms":423415,"significance":"If the bound holds as stated, it is a useful and physically transparent result: because the Z' couplings to quarks and to N1 are fixed by gauge symmetry (Table I) rather than fitted, the spin-independent cross section is essentially a one-parameter prediction in M_Z' (modulo M_N1), and the comparison with direct detection is a genuine test rather than a fit. The mapping of the bound onto the symmetry-breaking scale, and hence onto the masses of the V+, U0, q' and heavy scalar states, makes it complementary to the collider, FCNC, STU and muon-decay limits cited in the introduction. I give credit for the micrOMEGAs implementation with 3- and 4-body final states, for the inclusion of heavy-fermion coannihilation, and for the two-dimensional scan in Fig. 7, which displays the relic-density windows, the instability region and the direct-detection exclusion on the same plane; that figure is the most informative in the paper. The result is robust at the factor-of-two level, since sigma ~ 1/M_Z'^4, so a factor-4 error in the cross section moves the quoted 2 TeV to roughly 1.4-2.8 TeV.","major_comments":[{"comment":"The abstract states that LUX puts a bound M_Z' >~ 2 TeV 'independently of the dark matter mass', but the body does not support the qualifier. The spin-independent cross section of Eqs. (25)-(27) scales with the WIMP-nucleus reduced mass squared, so for a light N1 the predicted rate falls and the bound on M_Z' weakens; the LUX 2013 limit curve itself is also mass-dependent, rising steeply at low WIMP mass. In addition, the bound is only meaningful where the thermal relic density matches the observed value, and Fig. 4 shows that for each M_Z' the viable N1 values are confined to a narrow resonance window near M_N1 ~ M_Z'/2 and to M_N1 >~ 1 TeV on the coannihilation side. The abstract and the conclusions should therefore state the bound together with the N1 mass range over which it applies, rather than claiming mass independence.","section":"Abstract (abstract:s3) and Sec. III.B, Figs. 6-7","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Fig. 6 draws the XENON100 (2012) and LUX (2013) limits as horizontal lines of constant cross section across the whole 200-1000 GeV N1 mass range shown. The published limits are not horizontal: they are quoted as a function of WIMP mass and rise substantially at low WIMP mass. Since the paper's central claim concerns the mass dependence (or lack thereof) of the bound, the comparison should use the actual published limit curves, or the authors should state explicitly that the horizontal lines are a conservative approximation and justify that approximation over the plotted range. As drawn, the figure cannot support a statement about mass independence.","section":"Sec. III.B, Fig. 6","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The sentence 'For a N1 lighter than ~600 GeV one will need a Z' much heavier than 2 TeV in order to evade the XENON100 limits' appears to have the wrong sign relative to the stated scaling. Since the predicted cross section decreases with the reduced mass, a lighter N1 gives a smaller rate and hence a weaker, not stronger, lower bound on M_Z'. The sentence also sits uneasily with the abstract's mass-independence claim and with the attribution of the exclusion to LUX rather than XENON100. The authors should recheck this statement against their own numerical scan and either correct it or explain the mechanism that reverses the naive mu^2 scaling.","section":"Sec. III.B, paragraph following Fig. 6","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract advertises 'unprecedented accuracy' and 'the important effect of coannihilation across the heavy fermion sector', but Sec. III.A concludes that coannihilation 'only produce[s] some scatter in the abundance plot' and 'do[es] not play a crucial role in setting the thermal relic abundance'. The two statements are in tension. Either the coannihilation effect should be quantified (for example, by showing the relic density with coannihilation switched off against the full result for at least one benchmark), or the abstract should be softened. Similarly, 'unprecedented accuracy' is not substantiated: no comparison with the earlier calculations of Refs. [7,8] is presented, and the improvement from 3- and 4-body final states is asserted rather than demonstrated.","section":"Sec. III.A and Abstract (abstract:s2)","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The caption attributes the red excluded region to XENON100 [36], whereas the text of Sec. III.B attributes it to LUX 2013 [35]. The caption also describes the relic-density points as 'black, blue and green', while the text describes them as green (overabundant), light blue (underabundant) and a dark blue line (correct density). Please make the caption and text consistent.","section":"Fig. 7 caption","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The table lists g'_V(NN) = -g'_A(NN), i.e. a purely chiral Z' coupling to N1. Since the spin-independent rate of Eqs. (25)-(26) is driven by the vector coupling of N1, it would help to state explicitly the value of the vector coupling that enters B_N and to confirm that the SI rate is not accidentally suppressed by this structure.","section":"Table I","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The paper asserts that 'since only gauge couplings are involved, the scattering cross section is determined by the mass of the WIMP and the Z' only', but Z-Z' kinetic mixing is never discussed. An explicit estimate of the mixing angle and of its effect on the SI cross section, even if it is at the percent level as naive v^2/v_chi'^2 power counting suggests, would make the robustness claim verifiable.","section":"Sec. III.B","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The scalar contributions from S1, S2 and P1 are dismissed qualitatively. A short quantitative estimate of the scalar-exchange contribution to the SI cross section, showing it is negligible relative to the Z' tree-level term over the scanned parameter space, would strengthen the argument.","section":"Sec. III.B","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The text states that all results were computed 'without using any assumption on the vevs or on the constant couplings', but the numerical study fixes v_chi' = 2, 3, 4, 5 TeV and assumes couplings of order one. Please state precisely which parameters are scanned and which are fixed.","section":"Sec. II, Mass Eigenstates","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The statement that 'we let all coupling constants free to vary randomly' is unclear given that the Z' couplings are fixed by gauge symmetry in Table I. Please specify which couplings are varied in the direct-detection calculation.","section":"Sec. III.B","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The claim that the bounds apply 'up to some extent' to generic 331-like models is asserted without demonstration. Either quantify the sense in which the Z' couplings of those models resemble Table I, or soften the claim.","section":"Sec. III.B and Conclusions","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The velocity distribution is assumed Maxwell-Boltzmann with rho_DM = 0.3 GeV/cm^3, but the adopted v_0 and v_esc are not stated. Please give them, since the event-rate normalization affects the comparison with the quoted limits.","section":"Sec. III.B, Eq. (18)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Fig. 1 caption reads 'total width (read)' for 'red'. In Fig. 4, please state in the caption what the vertical thickness of each band represents, since the text explains it only in the body.","section":"Figs. 1 and 4","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"There are several typographical and grammatical errors that should be corrected: '3-3-1LHC model' in the Gauge Bosons paragraph, 'exclusivley', 'On the order hand', 'symmetry symmetry', 'Techinicolor', 'it is not to relevant', 'what sort or couplings', 'know quantities', 'Maxwell-Botzmann', and 'V ariety'.","section":"Throughout","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The physics calculation is standard and the central bound is likely to survive at the factor-of-two level, but the abstract's headline qualifier ('independently of the dark matter mass') is contradicted by the paper's own figures and by the mu^2 scaling of the SI cross section, and Fig. 6 compares against horizontalized experimental limits. These are fixable, but they touch the paper's main selling point, so I would not accept until the abstract, Sec. III.B and Fig. 6 are revised consistently. The overlap with the authors' companion papers (Refs. [9] and [26]) is disclosed through citation and does not raise a novelty concern for me."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"Bottom line: the number is real and worth having — M_Z' ≳ 2 TeV in the 3-3-1LHN model from LUX 2013 — but the abstract oversells its scope, and the body knows it better than the abstract does. What is actually new: the model and its Z' couplings (Table I) come from the authors' earlier work. The additions here are a micrOMEGAs implementation that includes coannihilation and 3/4-body final states, and the spin-independent direct detection cross section with the resulting Z' mass bound. The direct detection piece is the valuable one, because the Z' couplings are fixed by gauge symmetry — nothing is tuned to LUX, so the comparison is honest. The discussion of complementarity with collider, FCNC, and STU limits is useful and correctly framed. Soft spots, in order of how much they matter. The abstract's 'independently of the dark matter mass' (abstract:s3) is wrong as stated. Sec. III.B itself says that for N1 below about 600 GeV you need a Z' well above 2 TeV, and Fig. 6 shows the usual reduced-mass dependence. The bound also only means something where the relic density is viable, which their own scan restricts to M_N1 < M_Z'/2 or M_N1 ≳ 1 TeV. The body is more careful than the abstract; the abstract is what needs fixing. Second, 'the important effect of coannihilation' (abstract:s2) does not survive Sec. III.A, which says coannihilation only thickens the curves. That is fine physics, but it is the sentence carrying the 'unprecedented accuracy' claim. Third, Fig. 7's caption says XENON100 excludes the red region while the text says LUX 2013. Those limits differ; pick one. On the reader's Z-Z' mixing worry: it does not land. The mixing is O(v^2/v_chi'^2) ~ 1%, so a few percent on the cross section, not a factor of a few. Scalar exchange is likewise Yukawa-suppressed, so the paper's qualitative dismissal is correct. The bound is robust at the factor-of-2 level, which for sigma ~ 1/M_Z'^4 is what you would expect from a tree-level estimate. Who it is for: people building 331 models or quoting Z' direct detection bounds. Modest but legitimate. Send it out; referees should push on the abstract's scope claims, not on the calculation.","headline":"A real, checkable Z' mass bound from LUX in the 3-3-1LHN model, undermined mainly by an abstract that claims more scope than the body delivers.","tokens_in":19862,"tokens_out":1698,"would_cite":true,"duration_ms":13984,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["95.35.+d","12.60.Cn","14.70.Pw"],"model":"selfhosted/deepseek-v4.1-flash","headline":"In a 331 extension of the Standard Model, the extra Z' boson must be heavier than about 2 TeV, or its exchange would have produced a dark matter signal that LUX did not see.","keywords":["331 models","Z' gauge boson","WIMP dark matter","direct detection","thermal relic density","coannihilation","spin-independent cross section","LUX"],"falsifier":"A direct-detection experiment with larger exposure, or a reanalysis that includes $Z$–$Z'$ kinetic mixing, finding a spin-independent cross section for a sub-2-TeV $Z'$ that falls below the LUX limit; alternatively, an LHC observation of this $Z'$ below 2 TeV in invisible or dilepton channels, would break the bound.","tokens_in":20181,"feed_emoji":"🌑","tokens_out":3440,"duration_ms":39826,"temperature":0.7,"pith_summary":"This paper asks whether a specific extension of the electroweak gauge group — the so-called 3-3-1LHN model, in which $SU(3)_L$ replaces $SU(2)_L$ — can supply a viable dark matter particle, and what that particle's existence implies for the extra neutral gauge boson $Z'$ the extension predicts. The candidate is $N_1$, the lightest of the new heavy neutral fermions, kept stable by a discrete parity. Because $N_1$ communicates with ordinary quarks only through $Z'$ exchange, the same coupling that fixed how much dark matter annihilated away in the early universe also fixes how hard it would recoil off a xenon nucleus today. That single link lets a null direct-detection result be converted into a limit on the $Z'$ mass, and — since every new mass in the model scales with the same symmetry-breaking vacuum expectation value — into a limit on the entire new-physics scale. The authors argue the resulting bound, $M_{Z'} > 2$ TeV, holds essentially regardless of how heavy the dark matter particle itself is.","feed_headline":"Dark matter pushes a new gauge boson above 2 TeV","feed_subtitle":"A null xenon recoil signal rules out lighter Z' mediators in a 331 model, whatever the dark matter mass.","key_machinery":"The load-bearing object is the $Z'$ itself, acting as both annihilation mediator and scattering mediator. On the relic-density side, the authors implement the model in a customized micrOMEGAs, including 3- and 4-body final states and coannihilation among $N_1$, $N_2$ and $N_3$ (with masses varied within 10% of each other), and exhibit the resonance funnel at $M_{N_1} = M_{Z'}/2$ for $M_{Z'} = 0.8, 1.2, 1.6, 2$ TeV. On the scattering side, the Dirac fermion $N_1$ has a vector coupling to quarks, giving a spin-independent cross section of the form $σ_0 = μ^2 B_N^2 / 64π$ with $B_N = α_V^u (A+Z) + α_V^d (2A - Z)$, whose $A^2$ coherence enhancement is what makes the spin-independent channel the strongest handle even though the spin-dependent cross section is numerically larger. The scalar and pseudoscalar states $S_1$, $S_2$ and $P_1$ are argued to be irrelevant: no resonance arises from a light $S_1$, and $P_1$ exchange is $p$-wave suppressed.","core_discovery":"The paper's claim is that the 3-3-1LHN model's dark matter candidate $N_1$ can reproduce the observed relic density through $Z'$-mediated annihilation (with a resonance at $M_{N_1} = M_{Z'}/2$) plus coannihilation among the heavy neutral fermions, and that the spin-independent cross section this same $Z'$ produces off nuclei is large enough that the LUX 2013 limit excludes $M_{Z'} < 2$ TeV. The authors emphasize that the exclusion is largely independent of the dark matter mass, because only gauge couplings enter the scattering: the cross section is set by the $Z'$ mass and the WIMP mass alone. Translated through the model's mass relations, the bound says the symmetry-breaking scale sits at $v_{χ'} = 4$–$5$ TeV, dragging every new fermion, quark, scalar and gauge boson of the theory up to the few-TeV range. The authors present this as complementary to collider, flavour-changing-neutral-current, electroweak-precision and muon-decay limits on the same boson, and note that the bound should carry over, at least approximately, to other 331-like models where a singlet neutral fermion is the dark matter and the $Z'$ is the mediator.","pith_inferences":["The quoted 2 TeV number is a factor-of-a-few statement: a $Z$–$Z'$ kinetic mixing term, never discussed in the paper, would rescale the spin-independent cross section and move the bound proportionally, so it would be worth quantifying before treating 2 TeV as a hard, model-independent threshold.","The near-independence from the dark matter mass follows from the pure vector coupling; any scalar-mediated contribution to the cross section would reintroduce mass dependence and could reopen sub-2-TeV $Z'$ masses near the resonance, where the relic density is anyway correct.","Since the same vacuum expectation value fixes $M_{V^\\pm}$ and $M_{U^0}$, a future measurement or exclusion of the charged gauge boson at the LHC would provide an independent cross-check on the direct-detection bound, or expose a tension between the two sectors.","A joint likelihood combining invisible-width LHC searches with the xenon recoil limit would be sharper than either alone, because the two experiments probe the same coupling in complementary kinematic regimes."],"forward_implications":["If the bound holds, the symmetry-breaking scale of the model is pushed to $v_{χ'} \\simeq 4$–$5$ TeV, so all the new quarks, neutral fermions, scalars and the charged gauge bosons $V^\\pm$ and $U^0$ sit at a few TeV and are, in principle, within reach of the LHC.","For $M_{N_1} < M_{Z'}/2$ the $Z'$ decays predominantly invisibly into $N_1 \\bar{N}_1$ pairs, so the dilepton searches that constrain the right-handed-neutrino version of the model lose sensitivity and missing-energy searches become the relevant channel.","The direct-detection bound is complementary to, and of comparable reach as, limits from colliders, flavour-changing neutral currents, $S$, $T$, $U$ oblique corrections and muon decay, so a future $Z'$ discovery would need to satisfy all of them at once.","Because the scattering is governed by gauge couplings alone, the exclusion can be stated as a bound in the $(M_{Z'}, M_{N_1})$ plane rather than as a bound at one benchmark dark matter mass."],"supporting_citations":[{"why":"Supplies the LUX 2013 spin-independent limit that the entire 2 TeV exclusion is read against.","marker":"[35]"},{"why":"The micrOMEGAs package used to compute both the thermal relic density and the direct-detection rate.","marker":"[32]"},{"why":"Earlier analysis identifying the two possible dark matter candidates of the 3-3-1LHN model, which this paper builds on.","marker":"[7]"},{"why":"Prior study of the model's spectrum and Higgs-sector consistency that the present calculation extends to direct detection.","marker":"[8]"},{"why":"The XENON100 2012 limit used as the weaker comparison benchmark in the cross-section figures.","marker":"[36]"},{"why":"Establishes the minimal 331 construction and the anomaly-cancelling generation assignment that the LHN variant inherits.","marker":"[12]"},{"why":"Argues that minimal 331 models need an extended scalar or gauge sector to host dark matter, motivating the LHN variant studied here.","marker":"[19]"},{"why":"The CMS-based $M_{Z'} > 2.2$ TeV limit for the right-handed-neutrino 331 model, which the authors argue does not directly apply here because their $Z'$ decays invisibly.","marker":"[22]"}],"fun_headline_variants":["LUX data push this 331 model's Z' mass above 2 TeV","331 dark matter needs a Z' above 2 TeV to pass LUX","Coannihilation sets the 331 relic density; LUX sets the Z' floor","The same Z' sets 331 relic density and the LUX scattering bound"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The whole bound rests on the spin-independent cross section being set entirely by tree-level $Z'$ exchange with the couplings listed in the paper's Table I, with no $Z$–$Z'$ mixing and with scalar exchange genuinely negligible.","fun_headline_variants_meta":{"raw":{"variants":["LUX data push this 331 model's Z' mass above 2 TeV","331 dark matter needs a Z' above 2 TeV to pass LUX","Coannihilation sets the 331 relic density; LUX sets the Z' floor","The same Z' sets 331 relic density and the LUX scattering bound"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":1693,"prompt_tokens":988,"completion_tokens":705,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":628}},"tokens_in":988,"tokens_out":705,"duration_ms":8994,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":628,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-11-10T10:13:11.369845+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"A direct-detection experiment with larger exposure, or a reanalysis that includes $Z$–$Z'$ kinetic mixing, finding a spin-independent cross section for a sub-2-TeV $Z'$ that falls below the LUX limit; alternatively, an LHC observation of this $Z'$ below 2 TeV in invisible or dilepton channels, would break the bound.","supporting_citations":[{"cited_title":"First results from the LUX dark matter experiment at the Sanford Underground Research Facility","cited_arxiv_id":"1310.8214","evidence_quote":"Supplies the LUX 2013 spin-independent limit that the entire 2 TeV exclusion is read against."},{"cited_title":"micrOMEGAs3.1 : a program for calculating dark matter observables","cited_arxiv_id":"1305.0237","evidence_quote":"The micrOMEGAs package used to compute both the thermal relic density and the direct-detection rate."},{"cited_title":"WIMPs in a 3-3-1 model with heavy Sterile neutrinos","cited_arxiv_id":"1010.4097","evidence_quote":"Earlier analysis identifying the two possible dark matter candidates of the 3-3-1LHN model, which this paper builds on."},{"cited_title":"On the connection of Gamma-rays, Dark Matter and Higgs searches at LHC","cited_arxiv_id":"1206.5779","evidence_quote":"Prior study of the model's spectrum and Higgs-sector consistency that the present calculation extends to direct detection."},{"cited_title":"Dark Matter Results from 225 Live Days of XENON100 Data","cited_arxiv_id":"1207.5988","evidence_quote":"The XENON100 2012 limit used as the weaker comparison benchmark in the cross-section figures."},{"cited_title":"A minimal 3-3-1 model with naturally sub-eV neutrinos","cited_arxiv_id":"1003.1270","evidence_quote":"Establishes the minimal 331 construction and the anomaly-cancelling generation assignment that the LHN variant inherits."},{"cited_title":"3-3-1-1 model for dark matter","cited_arxiv_id":"1305.0369","evidence_quote":"Argues that minimal 331 models need an extended scalar or gauge sector to host dark matter, motivating the LHN variant studied here."},{"cited_title":"Bounds on $Z^\\prime$ from 3-3-1 model at the LHC energies","cited_arxiv_id":"1304.7907","evidence_quote":"The CMS-based $M_{Z'} > 2.2$ TeV limit for the right-handed-neutrino 331 model, which the authors argue does not directly apply here because their $Z'$ decays invisibly."}],"review_version":1}