On the Validity of the Effective Field Theory for Dark Matter Searches at the LHC Part III: Analysis for the t-channel

This is Part III of the Busoni–De Simone–Morgante–Riotto EFT-validity series, now for a t-channel scalar mediator. The genuinely useful content is the explicit three-body calculation in Appendix A: matrix elements, phase space, differential cross sections, and the four transferred-momentum expressions. That is real work, laid out so it can be rebuilt, and the MadGraph cross-check in Fig. 8 is the right kind of external benchmark. The headline result — that R_Λ stays well below one over most of the (Λ, m_DM) plane at both 8 and 14 TeV — looks robust and is what most readers will take away. The observation that t-channel contours can cross the Λ < m_DM/(2π) line, unlike the s-channel case, is a nice, correct point about kinematics that is easy to miss. The authors are also upfront that g ≳ 1 is a benchmark, not a derivation, and they show the g = 4π variant in Fig. 6. That is acknowledged, not a hidden flaw, and I would not hold it against them beyond noting the contours are benchmark-dependent by construction. The one soft spot with teeth is the relic-density corollary in the abstract. Fig. 5 overlays the Ωh² = 0.12 curve on the g~1 contours only. The relic curve depends on Λ alone, while the EFT-valid region grows with g; at g = 4π the 50% contour moves to smaller Λ by roughly a factor of 4π, and the paper never checks whether it then crosses the relic line. If it does, the 'typically large' trend fails exactly where the EFT is hardest to dismiss. This is a one-line overlay of two curves they already have, so it is a modest gap, not a load-bearing error — and the text does hedge it as a 'general trend' with extra annihilation channels as an escape. Minor: no code or event samples shipped, so Fig. 8 would need rebuilding. Worth a referee report; I would expect minor revision at most. Cite it if you work on mono-jet EFT validity.

The central claim has two parts: (i) the EFT is valid only in a restricted region (R_Λ well below one over most of the (Λ, m_DM) plane), and (ii) that region typically has an unacceptably large relic abundance [abstract:s3]. Part (i) is robust: the analytic R_Λ is derived in Appendix A and cross-checked against a MadGraph simulation (Section 2.3, Fig. 8). Part (ii) is established in Fig. 5 by overlaying the Ω_DM h² = 0.12 curve on the g~1 contours (Q_tr < Λ). But the authors themselves identify g = 4π as the most optimistic case for EFTs (Section 2.2) and show in Fig. 6 that the R = 50% contour shifts when the cut is relaxed to Q_tr < 4πΛ. The relic curve depends only on Λ (the operator coefficient is 1/Λ², independent of g), whereas the EFT-valid region grows as g increases. A larger EFT-valid region (extending to smaller Λ) is therefore more likely to intersect the relic curve. The paper does not overlay the relic curve on the g = 4π contour, so it does not check whether the EFT-valid region still has large relic abundance in the coupling regime where the EFT is most defensible. If it does not, the 'general trend' of [abstract:s3] is not universal, and the cosmological-exclusion argument for the EFT-valid region weakens precisely where the EFT is hardest to dismiss. This is a gap in the paper's own logic, not a request to re-derive a cited result: the relic calculation is the authors' own, and the missing step is a one-line overlay of two curves they already have.

The reader correctly identifies the g ≳ 1 benchmark (Section 1, Eq. 1.3) as the load-bearing premise and correctly notes that the authors acknowledge it and vary it to g = 4π in Fig. 6. I agree that this is the central soft spot, and I do not present it as a new finding. What the reader does not flag is the specific consequence for the paper's second claim: the relic-density corollary [abstract:s3] is derived only for the g~1 contours of Fig. 5, and the g = 4π case of Fig. 6 is shown without the relic curve. Because the relic curve is g-independent while the EFT-valid region grows with g, the most optimistic coupling is exactly the case where the corollary is most likely to fail, and the paper does not check it. This is a concrete, one-line check using curves the authors already have, not a demand for new physics. The main claim (i), that the EFT validity region is restricted, is well supported by the analytic derivation and the MadGraph cross-check, and I do not see a load-bearing objection to it. The paper is careful, the limitations are stated, and the qualitative conclusion survives even if the relic-density corollary needs qualification. I therefore recommend UNCHANGED: the concern sharpens the scope of the secondary claim but does not undermine the central result. The reader's soundness score of 7 and reproducibility score of 5 seem appropriate; the missing simulation artifacts are a real but minor shortcoming, and the g benchmark is handled as transparently as the present framing allows.

The paper is a timely and technically careful extension of the authors' earlier s-channel analyses to the t-channel case, which is well motivated by simplified DM models and by supersymmetric analogues. The complete analytic derivation in Appendix A and the independent Monte Carlo cross-check in Fig. 8 are genuine strengths: the two tool chains do not share the same calculational route, so the agreement in Fig. 8 is meaningful evidence that the R_Λ contours are under control. The result reinforces the growing case that EFT limits on DM at the LHC must be interpreted with care and that simplified models are preferable. If the central EFT-validity claim holds, it is a useful reference for the community.

The paper asks whether the effective-field-theory description of dark matter production at the LHC remains trustworthy when dark matter couples to quarks through a $t$-channel scalar mediator. It defines a ratio $R_Lambda$: the fraction of mono-jet events whose mediator momentum transfer stays below the cutoff $Lambda$, divided by all such events. Using analytical three-body cross sections at $sqrt{s}=8$ and $14$ TeV, and checking them with a Monte Carlo event generator, the authors find that this fraction is well below one over most of the $(Lambda,m_{rm DM})$ plane. In the small region where the EFT passes the test, the thermal relic abundance computed from the same operator is typically larger than the observed value. The practical point is that LHC limits quoted in $Lambda$ alone can describe a theory that the data never actually tested.

What carries the argument. The load-bearing object is $R_Lambda$, the ratio of the mono-jet cross section restricted to events with $Q_{rm tr}<Lambda$ to the unrestricted cross section, with $Q_{rm tr}$ the momentum carried by the integrated-out mediator. The authors compute the $2to3$ matrix elements for $qbar qtochibar{chi} g$ and the subdominant $qg$ and $bar qg$ channels, boost them to the lab frame, and integrate over the jet $p_T$ and pseudorapidity ranges used in LHC searches. A Fierz transformation rewrites the $t$-channel operator as a sum of $s$-channel operators $D5$-$D8$, but the paper argues that the $t$-channel kinematics, especially the different $Q_{rm tr}$ distribution, prevent one from reading off the $t$-channel validity from any single $s$-channel result.

Core claim. The central claim is that for Dirac dark matter coupled to left-handed quarks by $mathcal{O}=(bar{chi} P_L q)(bar{q} P_Rchi)/Lambda^2$, the EFT is valid only in a restricted corner of parameter space. The mediator mass $M$ and coupling $g$ are combined into $Lambda=M/g$; the propagator expansion requires $Q_{rm tr}^2ll M^2$, and with the benchmark $ggtrsim 1$ the authors impose $Q_{rm tr}^2<Lambda^2$ event by event. Because the mono-jet process has two diagrams, they require both transferred-momentum values to pass. The resulting $R_Lambda$ contours at 8 and 14 TeV show that the EFT-valid region is small, and the contour where $R_Lambda=50%$ lies where the relic density exceeds $Omega_{rm DM}h^2simeq0.12$. A MadGraph simulation reproduces the analytic contour, so the conclusion is not an artifact of the hand calculation.

The premise it rests on. The load-bearing premise is that the unknown mediator coupling satisfies $ggtrsim1$, which turns the condition $Q_{rm tr}^2ll M^2$ into the benchmark $Q_{rm tr}^2<Lambda^2$; since $Lambda=M/g$, a smaller coupling would move the validity boundary and make the EFT fail even earlier.

LHC bounds on $Lambda$ for this $t$-channel operator should be quoted together with the event-level cut $Q_{rm tr}<Lambda$; otherwise the bound may cover a region where the EFT expansion is uncontrolled.

In the region where the EFT is valid, the relic abundance from this operator alone is typically above the observed $Omega_{rm DM}h^2simeq0.12$, so a viable thermal history needs another annihilation channel.

The $t$-channel case cannot be inferred from a single $s$-channel operator despite the Fierz decomposition, because the transferred-momentum distributions differ.

Direct mediator production and mediator pair production add mono-jet and dijet signals that the EFT omits, so simplified-model searches can constrain the model where EFT limits cannot.

The Monte Carlo check supports the analytic $R_Lambda$ contours, so the small valid fraction is not an artifact of the phase-space treatment.

Because the EFT validity condition depends on $g$, any LHC limit expressed only in $Lambda$ implicitly assumes a strongly coupled mediator; a weakly coupled mediator with the same $Lambda$ can evade the EFT logic entirely.

The relic-density tension suggests a testable correlation: a mono-jet excess in the EFT-valid region would require a second dark-matter annihilation channel or a nonthermal history, which could show up in indirect-detection or cosmological data.

The usual $s$-channel benchmark $Lambda<m_{rm DM}/(2pi)$ is not a universal validity boundary; $t$-channel events can have $Q_{rm tr}<2m_{rm DM}$, so an event-level cut is the appropriate diagnostic.

A combined fit to mono-jet and dijet mediator searches could map the actual $(M,g)$ region and test whether any EFT-valid point survives both.

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