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Light top-flavoured dark matter in dark SMEFT: one-loop matching and phenomenology

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Meng-Chao Gao, Xin-Qiang Li, Ya-Dong Yang, Xing-Bo Yuan, Xin Zhang

High Energy Physics - Phenomenology · Submitted 26 Oct 2026 · 143 references

Pith's verdict: One-loop DSMEFT matching for top-philic dark matter, applied to the Belle II excess – solid calculation, honest about its scope.

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arXiv ID2610.34880 (version 1)
Pith IDN352OJOQ, Pith's permanent record of this paper and its review
CitationMeng-Chao Gao, Xing-Bo Yuan, Xin-Qiang Li, Xin Zhang, Ya-Dong Yang. "Light top-flavoured dark matter in dark SMEFT: one-loop matching and phenomenology." arXiv:2610.34880 (2026). https://pith.science/paper/N352OJOQ
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The paper

The paper claims

Light dark matter that talks only to the top quark can explain the Belle II excess in B→Kνν, but only through tree-level operators with O(1) couplings.

The reading

This paper argues that a light dark-matter particle (below a few GeV) that interacts exclusively with top quarks could be responsible for the anomalous B+→K+νν signal seen at Belle II. The authors build a complete effective-field-theory chain linking high-energy dark-matter–top-quark operators down to low-energy processes: rare meson decays, dark-matter–nucleus scattering, and dark-matter annihilation in the early Universe. By performing the one-loop matching at the electroweak scale for the first time, they show that the low-energy couplings are universally controlled by CKM factors and, for scalar currents, by the external quark masses. The key phenomenological result is that only the operators that already contribute at tree level can accommodate the Belle II excess with O(1) Wilson coefficients for a new-physics scale of 1 TeV; loop-induced operators require coefficients of O(10–100) and are not natural. The analysis simultaneously constrains the favoured parameter space with other flavour observables—especially B0→K*0+inv—and with direct-detection experiments like CRESST-III and DarkSide-50, which exclude the Belle II band for dark-matter masses above about 1–2 GeV for scalar-current operators.

What carries the argument

The EFT chain consisting of the dark SMEFT (DSMEFT) matched at one loop onto the dark low-energy effective field theory (DLEFT) at the electroweak scale, followed by QCD evolution and a final matching onto a non-relativistic EFT (NREFT) for dark-matter–nucleus scattering. The central object is the top-flavoured Wilson coefficient [Ci]33, whose CKM structure VtjV*ti controls all down-type flavour-changing neutral currents and correlates flavour, direct-detection, and cosmological observables through a single coupling per operator.

Extended reading notes

Core claim

The paper establishes a consistent EFT framework for light top-flavoured dark matter and uses it to show that the Belle II excess in B+→K+νν can be interpreted as a decay into dark matter only if the underlying UV operator contributes at tree level to the transition, with O(1) couplings at a 1 TeV scale. Loop-induced operators are too weak, requiring couplings of O(10–100). The low-energy effects of any top-flavoured operator are universally governed by the CKM matrix elements VtjV*ti and, for scalar quark currents, by the mass of the external down-type quark. This CKM structure correlates b→s, b→d, and s→d transitions through a single coupling per operator, making rare kaon decays competitive in spite of the small CKM factor because of their extreme experimental precision. Direct detection is competitive for scalar and tensor operators because their gluonic couplings avoid CKM suppression.

Load-bearing premise

The Wilson coefficients of the DSMEFT operators are fixed at the electroweak scale, neglecting the renormalization-group evolution from the new-physics scale Λ down to that scale, which could mix top-quark operators into operators involving Higgs and gauge bosons and thereby alter the matching coefficients and the conclusions.

Editorial extensions

If this is right

  • If the Belle II excess persists, only UV completions with tree-level couplings of dark matter to left-handed quark doublets (or right-handed up-type singlets) can provide a natural explanation at the TeV scale; loop-level completions are fine-tuned.
  • The prediction that B0→K*0+inv is the leading constraint for most of the favoured parameter space will be tested with high statistics at Belle II and at Tera-Z factories.
  • Direct-detection experiments with sub-GeV thresholds can fully test the scalar-current explanation, as they already exclude the Belle II band for dark-matter masses above about 1.35 GeV (for scalar DM), 2.3 GeV (for fermionic DM), and 1.8 GeV (for vector DM).
  • Future measurements of Bs→φsνν with 2% precision at the CEPC or FCC-ee would cover the Belle II band for most two-DM operators up to the kinematic endpoint.
  • For most operators, the thermal relic abundance from top-flavoured interactions alone overproduces dark matter, implying that additional annihilation channels (e.g., into dark-sector states) are necessary for a consistent cosmological history.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's framework suggests that any UV model of top-philic light dark matter should predict a specific pattern of correlated flavour signals: rare kaon decays become a sensitive probe for scalar-type operators because the ms/mb suppression is compensated by the enormous precision of NA62.
  • Because the CKM structure is identical to that of the SM top loops, the authors' results imply that even a dark-matter coupling that is purely third-generation at high energies unavoidably generates couplings to light quarks at low energies—a feature that generic simplified models may miss.
  • A testable extension would be to include the RG running from the new-physics scale down to the electroweak scale, which could mix top-quark operators into Higgs and gauge operators and potentially strengthen or weaken the constraints. The authors flag this as a future direction.
Original abstract

We study light top-flavoured dark matter (DM) below the electroweak (EW) scale within the dark Standard Model effective field theory (DSMEFT). We perform the one-loop matching of the DSMEFT onto the dark low-energy effective field theory (DLEFT) at the EW scale for all relevant operators that couple scalar, fermionic or vector DM, as well as axion-like particles, exclusively to third-generation quarks. After QCD evolution to the relevant low-energy scales, we match the DLEFT onto the non-relativistic EFT for DM-nucleus scattering. This EFT chain provides a unified framework for phenomenological studies of rare $B$- and $K$-meson decays with missing energy, direct and indirect detection, and the thermal relic abundance. Interpreting the Belle II excess in $B^+\to K^+\nu\bar\nu$ as a decay into DM, we find that only the DSMEFT operators contributing at tree level can accommodate it with $O(1)$ couplings for a new-physics scale of $1\,\mathrm{TeV}$. The decay $B^0\to K^{*0}+\mathrm{inv}$ provides the strongest constraint over large portions of the Belle II-favoured parameter space, while $K^+\to\pi^++\mathrm{inv}$ can dominate at low and $B_s\to\mathrm{inv}$, $B^+\to\pi^++\mathrm{inv}$ and $\Upsilon(1S)\to\mathrm{inv}$ become important at high DM masses, respectively. Direct-detection searches by CRESST-III and DarkSide-50 are competitive for operators involving scalar quark currents and, depending on the operator, exclude the Belle~II-favoured band for $m_{\mathrm{DM}}\gtrsim1$-$2\,\mathrm{GeV}$. We also perform detailed analyses of the thermal relic abundance and the indirect-detection constraints from the CMB and Fermi-LAT.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-27: 1 request, 6,824 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.45 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.35 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study light top-flavoured dark matter (DM) below the electroweak (EW) scale within the dark Standard Model effective field theory (DSMEFT). We perform the one-loop matching of the DSMEFT onto the dark low-energy effective field theory (DLEFT) at the EW scale for all relevant operators that couple scalar, fermionic or vector DM, as well as axion-like particles, exclusively to third-generation quarks. After QCD evolution to the relevant low-energy scales, we match the DLEFT onto the non-relativistic EFT for DM-nucleus scattering. This EFT chain provides a unified framework for phenomenological studies of rare $B$- and $K$-meson decays with missing energy, direct and indirect detection, and the thermal relic abundance. Interpreting the Belle II excess in $B^+\to K^+\nu\bar\nu$ as a decay into DM, we find that only the DSMEFT operators contributing at tree level can accommodate it with $O(1)$ couplings for a new-physics scale of $1\,\mathrm{TeV}$. The decay $B^0\to K^{*0}+\mathrm{inv}$ provides the strongest constraint over large portions of the Belle II-favoured parameter space, while $K^+\to\pi^++\mathrm{inv}$ can dominate at low and $B_s\to\mathrm{inv}$, $B^+\to\pi^++\mathrm{inv}$ and $\Upsilon(1S)\to\mathrm{inv}$ become important at high DM masses, respectively. Direct-detection searches by CRESST-III and DarkSide-50 are competitive for operators involving scalar quark currents and, depending on the operator, exclude the Belle~II-favoured band for $m_{\mathrm{DM}}\gtrsim1$-$2\,\mathrm{GeV}$. We also perform detailed analyses of the thermal relic abundance and the indirect-detection constraints from the CMB and Fermi-LAT.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study light top-flavoured dark matter (DM) below the electroweak (EW) scale within the dark Standard Model effective field theory (DSMEFT). contribution 0.93 0.92 0.04 asserted 0.90
s1 We perform the one-loop matching of the DSMEFT onto the dark low-energy effective field theory (DLEFT) at the EW scale for all relevant operators that couple scalar, fermionic or vector DM, as well as axion-like particles, exclusively to third-generation quarks. method 0.65 0.97 0.06 asserted 1.00
s2 After QCD evolution to the relevant low-energy scales, we match the DLEFT onto the non-relativistic EFT for DM-nucleus scattering. method 0.96 0.94 0.04 asserted 1.00
s3 This EFT chain provides a unified framework for phenomenological studies of rare $B$- and $K$-meson decays with missing energy, direct and indirect detection, and the thermal relic abundance. contribution 0.60 0.61 0.13 asserted 1.00
s4 Interpreting the Belle II excess in $B^+\to K^+\nu\bar\nu$ as a decay into DM, we find that only the DSMEFT operators contributing at tree level can accommodate it with $O(1)$ couplings for a new-physics scale of $1\,\mathrm{TeV}$. result 0.83 0.96 0.29 asserted 1.00
s5 The decay $B^0\to K^{*0}+\mathrm{inv}$ provides the strongest constraint over large portions of the Belle II-favoured parameter space, while $K^+\to\pi^++\mathrm{inv}$ can dominate at low and $B_s\to\mathrm{inv}$, $B^+\to\pi^++\mathrm{inv}$ and $\Upsilon(1S)\to\mathrm{inv}$ become important at high DM masses, respectively. result 0.99 0.86 0.18 asserted 0.98
s6 Direct-detection searches by CRESST-III and DarkSide-50 are competitive for operators involving scalar quark currents and, depending on the operator, exclude the Belle~II-favoured band for $m_{\mathrm{DM}}\gtrsim1$-$2\,\mathrm{GeV}$. result 0.99 0.84 0.11 asserted 0.89
s7 We also perform detailed analyses of the thermal relic abundance and the indirect-detection constraints from the CMB and Fermi-LAT. contribution 0.96 0.95 0.05 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.47.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Feynman diagrams involved in the top-flavoured DSMEFT during the one-loop matching in unitary gauge. The green lines represent the DM particles, and the DSMEFT operator is represented by the black square. integrated out. The matching is carried out using the standard off-shell matching approach [104, 105]. The relevant one-loop Feynman diagrams are shown in figure 1 and can be di￾vided into two categories. The first category contains the diagrams shown in fig￾ures 1a, 1d, 1e, and 1f. For these diagrams, the calculation can be performed within the naive dimensional regularization…
Figure 2. Flavour constraints on the Wilson coefficients of the DSMEFT operators with two scalar (upper four) or two fermionic (lower two) DM fields as functions of the DM mass, at the NP scale Λ = 1 TeV. The band is allowed by the Belle II measurement of B(B+ → K+νν¯) at the 2σ level, and the solid lines correspond to the 90% CL upper bounds from the other observables in table 3. – 16 –
Figure 3. Same as in figure 2, but for the DSMEFT operators with two vector DM fields. of the Belle II band is excluded by B(B0 → K∗0+inv). This can be understood from the fact that the induced left-handed quark current has the same structure – 17 –
Figure 4. Same as in figure 2, but for the DSMEFT operators with a single DM field. Unlike Qϕq, however, QuHX2 matches onto the tensor DLEFT operator OT dX2 . Since the hadronic matrix element ⟨0|qσ¯ µνb|B¯ q⟩ vanishes, this operator does not contribute to Bq → inv. Its high-mass range is instead constrained by B(B+ → π + + inv). We note that only the tree-level operators can accommodate the Belle II excess with O(1) coefficients at the TeV scale. The loop-induced operators generally require coefficients of O(10–100), e.g., Cuϕ2 ≃ 25–45.5 This would imply strongly coupled NP close to the EW
Figure 5. Projected sensitivities of the b → s observables for some representative DSMEFT operators. The dotted lines show the projected 90% CL bounds at Belle II with 5 ab−1 and, for Bs → ϕsνν¯, at the Tera-Z phase of the CEPC, assuming the SM-like central values. The band and the solid lines are the same as in figures 2–4. 5 Direct detection Direct-detection experiments use different targets to determine the precise interac￾tions of a DM particle with nuclei. This is achieved by looking for nuclear recoils induced by the scattering of halo DM particles off the target nuclei. In the…
Figure 6. Thermally averaged cross-section of the annihilation process ¯χχ → qiqj with i, j = d, s, b and the effective Hubble rate Heff(x) = H(x)/neq, as a function of the variable x = mχ/T, with five different DM masses. Their intersection point corresponds to the decoupling temperature of the process. benchmarks above this threshold, the s ¯b and d ¯b channels remain kinematically accessible at freeze-out, with their rates being two to three orders of magnitude larger than that of ss¯. The s ¯b channel is consequently the last to decouple. In contrast, the b ¯b channel is kinematically fo
Figure 7. Combined constraints on the Wilson coefficients of the DSMEFT opera￾tors involving scalar (upper left) and fermionic (other panels) DM, as a function of the DM mass, for Λ = 1 TeV. The gray band is the 2σ region favoured by the Belle II measurement of B(B+ → K+ + inv), and the black line is the upper limit from the other flavour observables in table 3. The red and blue lines are the upper limits from DM direct detection (CRESST-III and DarkSide-50) and from the CMB and Fermi-LAT bound, respectively. The green line is the contour required for reproduc￾ing the observed relic density…
Figure 8. Same as in figure 7, but for the DSMEFT operators involving vector DM, in terms of the rescaled Wilson coefficients C˜ i defined in eq. (2.2). The CMB and Fermi-LAT bound is shown only for QuX2 , the only vector-DM operator that induces XX → γγ at leading order in the relative velocity expansion. flavour-diagonal light-quark operators and gluon operators. The light-quark inter￾actions can arise at tree level with CKM suppression or be loop-induced, while the gluon interactions are generated at one-loop level. We find that the strength of the constraints from DM direct detection…
Figure 9. Same as in figure 5, but for the projected sensitivities to the corresponding operators in figure 2. – 40 –
Figure 10. Same as in figure 5, but for the projected sensitivities to the correspond￾ing operators in figure 3. C.2 Transition form factors For FCNC transitions of a B¯ meson into a light pseudoscalar meson P (e.g., B¯ → K¯ ), the form factors are defined as [162, 163] cP ⟨P(p ′ )|qγ¯ µ b|B¯(p)⟩ = f+(q 2 )  P µ − m2 B − m2 P q 2 q µ  + f0(q 2 ) m2 B − m2 P q 2 q µ , – 41 –
Figure 11. Same as in figure 5, but for the projected sensitivities to the correspond￾ing operators in figure 4. cP ⟨P(p ′ )|qb¯ |B¯(p)⟩ = m2 B − m2 P mb(µ) − mq(µ) f0(q 2 ), cP ⟨P(p ′ )|qσ¯ µνb|B¯(p)⟩ = i P µ q ν − P ν q µ mB + mP fT (q 2 ), (C.3) with q = p−p ′ and P = p+p ′ ; the isospin factor is cP = − √ 2 for P = π 0 and cP = 1 otherwise. For B¯ → V transitions, with V a light vector meson, the form factors are defined through the Lorentz decompositions [162, 164] cV ⟨V (p ′ , ε∗ )|qγ¯ µb|B¯(p)⟩ = −ϵµνρσε ∗νP ρ q σ V (q 2 ) mB + mV , cV ⟨V (p ′ , ε∗ )|qγ¯ µ γ 5 b|B¯(p)⟩ = iε∗µ (mB + mV…

Figures reproduced from arXiv:2610.34880 by the authors.

References

Discussion

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