Forbidden Dark Matter at the Weak Scale via the Top Portal

The thing worth knowing: this is a competent, well-executed simplified-model paper. Forbidden annihilation has been around since Griest–Seckel, and the detailed-balance relic calculation follows D'Agnolo–Ruderman, but nobody had done the weak-scale version with SM final states. The authors do that, argue by elimination that the top quark is the only portal, and build two explicit models (s-channel pseudoscalar, t-channel scalar or fermion mediator) with relic density, monojet, stop-search, and direct-detection constraints all mapped on the same mDM–mMED plane. Appendix B gives explicit a and b coefficients, which is what makes the paper reusable. The relic calculation is cross-checked against MicrOmegas. The observation that forbidden WIMPs are structurally the opposite of secluded WIMPs — colliders and direct detection instead of indirect detection — is a genuinely useful framing point, and the indirect-detection immunity argument holds up on reading it (abstract:s2 is the claim; Sec. III.3 is the support). The paper is also unusually candid about its own approximations, which I count in its favor rather than against it: the EFT monojet recasting is flagged as crude, the Taylor expansion near the pole is marked with dashed lines, and the perturbativity bound is presented as an estimate. Those are acknowledged limitations, not new findings, and I would not hold them against the paper beyond what the authors already say. Soft spots, in order of how much they matter. First, the bottom-portal paragraph at the end of Sec. III.2 has a real error: it sets m_~B = 10⁴ GeV and calls it 'the edge of the LEP limit.' LEP's reach on pair-produced colored mediators in missing-energy is O(100 GeV), not 10 TeV, and the same 10⁴ GeV number appears in Sec. II.2 as the reason light-fermion mediators are excluded. If the true edge is ~100 GeV, the bottom portal has a much wider window than the quoted m_DM ≈ 4.0 GeV, and the 'must couple to top' claim is correspondingly softer. One correction to the stress-test note: its second point — that 10⁴ GeV minimizes rather than maximizes the cross-section — does not land, because given the paper's (wrong) LEP premise, 10⁴ GeV is the smallest allowed mass and hence does maximize. The error is the LEP number, not the logic. Second, the λ ≤ 1.12 perturbativity bound rests on v/Λ ≤ 1/10; the authors say so, but it moves the boundary of Fig. 3 and the quoted allowed ranges, so it is worth a sentence of scrutiny. Who should read it: anyone working on non-standard freezeout or simplified DM models with top couplings. It is a solid reference point. Recommendation: send it out. The bottom-portal error needs fixing, but it is a paragraph the authors already say they do not pursue, and the core construction stands.

The paper's headline claim (abstract:s2) is that forbidden annihilation 'requires' DM to couple predominantly to top quarks. This is an argument by elimination (Sec. II.2), and the one surviving exception is the bottom portal, discussed at the end of Sec. III.2. That discussion sets m_B = 10^4 GeV, calling it 'the edge of the LEP limit,' and states this choice 'maximizes the forbidden annihilation cross-section.' Both statements are suspect. LEP's reach on pair-produced colored mediators is ~10^2 GeV, not 10^4 GeV, so 10^4 GeV is far above the LEP edge, not at it. Moreover, since the t-channel cross-section scales as 1/m_B^4, a smaller m_B gives a larger cross-section; setting m_B = 10^4 GeV minimizes, not maximizes, the annihilation rate. The quoted viable point (m_DM = 3.95 GeV for scalar DM) should therefore be re-derived. If the correct LEP edge is ~10^2 GeV, the bottom-portal window is different from the one quoted, and the 'must couple to top' universality is correspondingly less secure. This is not merely a typo: the elimination argument in Sec. II.2 assumes light-fermion mediators are ≤ O(10 GeV), which the paper's own 10^4 GeV example contradicts, so the two sections are in tension about how heavy a light-fermion mediator can be.

The paper is a competent simplified-model study, and the reader's verdict (CONDITIONAL) is broadly appropriate. I agree with the reader that the perturbativity bound λ ≤ 1.12 in Sec. III.1 is an estimate, not a derivation, and that it shapes the claimed s-channel parameter space. But I think the more load-bearing concern for the headline claim is the treatment of the bottom portal, because that is the one explicit exception to 'DM must couple predominantly to top quarks.' The reader's concern affects the size of the viable region; the bottom-portal concern affects whether the universality claim holds at all. The paper does acknowledge the bottom portal as a special case, so I do not present it as a new finding; what I flag is the internal tension between Sec. II.2 (light-fermion mediators ≤ O(10 GeV)) and Sec. III.2 (m_B = 10^4 GeV), together with the apparent misidentification of 10^4 GeV as the LEP edge. These are concrete and checkable. If the bottom-portal window is larger than quoted, the 'must' in abstract:s2 weakens to 'typically'; if it is smaller, the paper's conclusion is strengthened. Either way, the top-portal models themselves (Figs. 3 and 4) are unaffected, so the verdict level does not change. I also note that the paper's own caveats — the EFT monojet recasting, the Taylor-expansion breakdown near the pole, and the overestimated scalar-DM direct-detection cross-section in Appendix B — are acknowledged and appropriately scoped, so I do not count them as new concerns. The relic-density calculation (Appendix A) is standard detailed-balance and cross-checked against MicrOmegas, so I see no issue there.

The paper addresses an under-explored freezeout mechanism with a clear and concrete simplified-model framework. The relic-density calculation is transparent, the detailed-balance derivation in Appendix A is a useful service to the community, and the explicit a and b coefficients in Appendix B make the results reproducible. The collider and direct-detection recasts are appropriate and the models are falsifiable. The central claim that the top quark is the only viable SM portal for a principally forbidden WIMP is interesting, but it rests on an elimination argument whose one acknowledged exception, the bottom portal, is dismissed using a collider reach that appears to be misquoted by two orders of magnitude. That issue is load-bearing for the abstract's 'must couple predominantly to top quarks' and should be corrected before the paper's conclusion can be regarded as established.

Most dark matter models assume the particle annihilates into lighter things, which is why the relic abundance is tied to a simple ratio of coupling squared over mass squared. This paper asks the opposite: what if the annihilation products are heavier than the dark matter itself, so that only the fast tail of the velocity distribution can supply the energy? That 'forbidden' annihilation is Boltzmann-suppressed, so the underlying cross-section must be large to compensate. Working through every massive Standard Model final state, the authors argue that the only viable option is the top quark, because electroweak bosons and the Higgs always drag along light-fermion channels, and light fermions require mediators already excluded by LEP and di-fermion resonance searches. The payoff is a dark matter candidate a few GeV below the top mass whose abundance is set by top-quark annihilation, which makes it essentially invisible to indirect detection while remaining squarely in range of LHC stop-like searches and nuclear recoil experiments.

What carries the argument. The load-bearing device is a detailed-balance identity that converts the forbidden cross-section into the cross-section of the reverse process. Because the top quarks in the bath are in equilibrium, one can write $⟨σv⟩_{χχ→t̄t} = (g_t/g_χ)^2 (1+δ)^3 e^{-2δx} ⟨σv⟩_{t̄t→χχ}$, with $δ = (m_t - m_{DM})/m_{DM}$ and $x = m_{DM}/T$. The exponential is the Boltzmann penalty for reaching a final state heavier than the initial one; the prefactor and the reverse cross-section, Taylor-expanded as $a + b v^2$ and integrated against the thermal history, are what must be made large enough. Two mechanisms supply that size: a pseudoscalar $s$-channel mediator tuned near the $2m_t$ resonance, and a $t$-channel mediator with a coupling that simplified-model logic permits to be order one or larger. The same identity explains why the models are blind to indirect detection: at $T = 2.7$ K the exponential is vanishingly small, so the present-day annihilation rate is many orders of magnitude below the Fermi-LAT dwarf-spheroidal bound.

Core claim. The paper's central claim is that forbidden annihilation can be the principal setter of the dark matter relic abundance at the electroweak scale, and that demanding Standard Model annihilation products forces the dark matter to couple predominantly, if not solely, to top quarks. The argument proceeds by elimination: $ZZ$ and $WW$ final states always come with an $s$-channel $Z$ that also yields light fermions; Higgs final states require $m_{DM}$ within a few percent of $125$ GeV, where Higgs-portal models without parity violation are already in tension with LUX and PandaX-II; and bottom or lighter fermion final states need mediators below roughly $10$ GeV or $10^4$ GeV that would have shown up as di-fermion resonances or missing-energy signals. The top quark is what remains. The authors then build two simplified models that reach the observed $Ω_χ h^2 = 0.1197$: an $s$-channel CP-odd singlet mediator, where the enhancement comes from annihilation near the $2m_t$ pole, and a $t$-channel mediator, where the coupling $λ$ itself is allowed to be larger than one. Flavor safety is handled by Minimal Flavor Violation, so the mediator couples to fermions in proportion to Higgs Yukawas and the light-quark channels stay negligible. The resulting viable windows are $m_{DM} ∈ [145, 170]$ GeV with $m_{MED} ∈ [175, 725]$ GeV in the $s$-channel, and $m_{DM} ∈ [150, 170]$ GeV with $m_{MED}$ up to about $1000$ GeV in the $t$-channel.

The premise it rests on. The size of the allowed parameter space rests on a perturbativity estimate rather than a derivation: the authors assume the top-mediator coupling descends from an operator suppressed by a scale at least ten times the Higgs vacuum expectation value, giving $λ_t ≤ 0.1$ and hence $λ ≤ 1.12$ in the $s$-channel, and a different ultraviolet completion would move that boundary and change which masses are claimed viable.

The $s$-channel pseudoscalar model survives the 8 TeV monojet search almost entirely, and even the 14 TeV, $3000$ fb$^{-1}$ projection only grazes its parameter space, so a forbidden WIMP of this type could be sitting just under current LHC reach.

In the $t$-channel models the mediator is QCD-produced and decays to a top plus missing energy, so existing stop searches recast directly: $m_{MED} ∈ [380, 690]$ GeV is excluded for fermionic dark matter and $m_{MED} ∈ [310, 920]$ GeV for scalar dark matter.

The scalar-dark-matter version scatters off nuclei strongly enough that LUX and PandaX-II already cover a wide band, and the residual region has a spin-independent cross-section around $2 × 10^{-45}$ cm$^2$, within reach of XENON1T.

Because the abundance is fixed by forbidden top annihilation, any loop-induced light final states are automatically far below the thermal cross-section, so the models cannot produce a detectable indirect-detection signal.

Three-body final states such as $tWb$ are shown to contribute at the ten-percent level or less for $m_{DM} \gtrsim 150$ GeV, so the two-body treatment of freezeout is adequate wherever the coupling stays perturbative.

The spectral tuning that forbidden models require — dark matter sitting a few GeV below the top — is the same kind of coincidence that co-annihilation and resonance models need, which suggests a common ultraviolet origin; a flavor symmetry tying the dark sector to the top Yukawa would be the natural place to look.

If the $t$-channel mediator is really a top-flavored scalar, the compressed region $m_{MED} \approx m_{DM} + m_t$ is the sharpest place to test the idea, since the recoil-against-ISR strategy proposed for compressed stops applies unchanged and has not yet been run as a dedicated search.

The authors note that a bino just below the top mass annihilating only through forbidden channels would overclose the universe unless a gluino sits within about ten percent in mass; this makes the gluino-bino compressed spectrum a concrete supersymmetric target that existing jets-plus-missing-energy searches are poorly suited to cover.

A cleaner experimental discriminator between the $s$- and $t$-channel versions would be the shape of the missing-energy spectrum in monojet events: the $t$-channel mediator is QCD-produced and gives harder top-associated activity, while the pseudoscalar gives the contact-operator-like monojet shape the EFT recasts assume.

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