Dark Matter Inelastic Scattering with Nuclei for Direct Detection

Oleg Titov; Shao-Feng Ge; Yakun Wang

REVIEW

Dark Matter Inelastic Scattering with Nuclei for Direct Detection

Shao-Feng Ge, Oleg Titov, Yakun Wang

High Energy Physics - Phenomenology · Submitted 15 Sep 2026

Pith's verdict: First systematic calculation of inelastic DM scattering to higher excited states in xenon using ReCD theory; nuclear model uncertainty is the main caveat.

T0 · AI review

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arXiv ID2609.16529 (version 2)

Pith ID6TUKB7FJ, Pith's permanent record of this paper and its review

CitationOleg Titov, Shao-Feng Ge, Yakun Wang. "Dark Matter Inelastic Scattering with Nuclei for Direct Detection." arXiv:2609.16529 (2026). https://pith.science/paper/6TUKB7FJ

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Claim paper

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Editor's note

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This paper is the first to systematically compute inelastic dark matter scattering to all kinematically accessible excited states in xenon using a nuclear many-body method beyond the shell model. The formalism is well executed: the multipole expansion, selection rules, and response function decomposition are correctly applied, and the ReCD theory is a legitimate choice for heavy nuclei. The key new results—that for operators O7, O13, and O14 the inelastic rate can dominate elastic by up to three orders of magnitude, and that second excited states can rival the first for O6 and O9—are genuinely interesting and directly relevant to experiments like LZ, PandaX, and XENONnT.

The paper’s main soft spot is one it partially acknowledges but does not resolve: the ReCD nuclear response functions are not validated against measured nuclear data for the specific transitions in 129Xe and 131Xe. Comparisons with the nuclear shell model show differences of factors up to ~25 (e.g., Fig. 5 for O13), yet no independent experimental cross-check (electromagnetic transitions, magnetic moments, spectroscopic factors) is provided. This leaves the central quantitative claims vulnerable to a large, unquantified systematic uncertainty. The paper would be stronger with either validation or a frank discussion of what experimental observables could discriminate between the models.

That said, the work is a serious theoretical contribution that opens a new direction. The authors do not overclaim: they present ReCD and NSM results side by side and note the differences. The paper deserves a careful referee because the topic is important and the calculation, while model-dependent, is technically sound and clearly documented. I would recommend accepting peer review, with the expectation that the authors will address the model uncertainty in revision or in follow-up work.

Bottom line: This paper is for direct detection theorists and experimentalists who need more complete nuclear inputs. It advances the conversation, even if the numbers come with caveats. I would cite it for the formalism and the new inelastic response functions, but I would note the nuclear model dependence in any use.

Referee report

Major objections (3)

[§4 and §5] The paper lacks any comparison with experimental nuclear data (e.g., electromagnetic transition strengths, magnetic moments, spectroscopic factors) for the specific excited states of 129Xe and 131Xe. While the ReCD and NSM results are compared, no independent benchmark is provided to assess which model is more reliable. This is critical because the central quantitative claims—e.g., the dominance of inelastic scattering for O7, O13, O14 and the factor--25 difference in the LZ event analysis—depend entirely on the nuclear model. The authors should either provide such validation (e.g., from known gamma transitions) or clearly state that the predictions carry large, unquantified systematic uncertainty and that experimental input is needed to resolve the model discrepancy.
[§5.3] The discussion of the LZ event (Sec 5.3) uses ReCD and NSM predictions to suggest that the DM interpretation changes dramatically with the model. However, the paper does not test whether the ReCD-based prediction can actually fit the LZ data under any reasonable DM parameters. The authors should either perform a fit or explicitly state that their calculation is only demonstrative and not a direct test of the DM hypothesis. As it stands, the conclusion that 'it would be very difficult to interpret the LZ event by a DM signal if the ReCD calculation is adopted' is too strong given the lack of a full analysis.
[§4.5] The paper repeatedly describes ReCD as 'state-of-the-art' and implies it is superior to NSM for heavy nuclei, but no evidence is given that ReCD's specific predictions for the relevant transitions are more accurate. The comparative statement in §4.5 is qualitative only. The authors shoul either provide quantitative evidence (e.g., agrreement with measured nuclear properties) or tone down the claims of superiority, framing the results as complementary rather than definitive.

Minor objections (5)

[Table 2] The meaning of the numbers in the cells (e.g.,'0','1','2', etc) is not clear from the caption. Are they the minimum allowed multipole rank J? Please add an explanatory note.
[Eq. (3.35)] The quadruple sum runs over τ,τ' but the prefactor 4π/(2J_i+1) should appear before the summation; currently it is outside, which is correct, but a brief note explaining its origin from angular averaging would help the reader.
[§3.1.1] Typo: 'bieng' should be 'being'.
[Ref. [43]] The reference for the textbook by Walecka is incomplete; the publisher and year are given but the full title is missing. Please check the entry.
[Throughout] The notation for the transverse velocity v^⊥ is used both for the elastic and inelastic definitions. In §3.2.1, the substitution v^⊥_N ≈ v_N is justified only for the inelastic correction; a brief remark that this approximation is used in the subsequent numerics would improve clarity.

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The paper

The paper claims

Inelastic nuclear excitation can dominate dark matter scattering rates in xenon by orders of magnitude.

The reading

This paper argues that weakly interacting massive particles (WIMPs) scattering off xenon nuclei can excite the nucleus to a low-lying excited state, and that for several common effective interaction operators this inelastic signal can be as large as or even larger than the conventional elastic scattering rate. The authors compute both elastic and inelastic nuclear response functions for 129Xe and 131Xe using a sophisticated relativistic configuration-interaction density functional theory (ReCD) rather than the nuclear shell model. They find that for operators O7, O13, and O14 the inelastic rate can exceed the elastic by up to three orders of magnitude. They also show that for some operators the second excites state contributes at the same level as the first. The differences between ReCD and shell-model predictions are large enough to change the interpretation of recent experiment events, such as the LZ excess at 248 keV.

What carries the argument

The machinery is the multipole expansion of 15 non-relativistic effective field theory operators, combined with nuclear response functions computed from one-body density matrices. The density matrices are obtained from the ReCD theory, which starts from a relativistic density functional (PC-PK1) with finite-range separable pairing, performs angular-moment projection and configuration mixing via the Hill-Wheeler equation. The resulting nuclear states are used to evaluate reduced matrix elements for charge, spin, current, and velocity multipole operators that enter the spin-averaged squared amplitude.

Extended reading notes

Core claim

For the effective non-relativistic dark matter-nucleon operators O7, O13, and O14, the inelastic scattering rate to the first excited states of 129Xe and 131Xe is comparable to or dominates over the elastic rate, with enhancements up to a factor of $10^{3}$. For operators O6 and O9, the second excited state contributes at the same level as the first. These results are obtained using the Relativistic Configuration-interaction Density functional (ReCD) theory, which treats all nucleons actively and avoids the tight model-space truncations required in nuclear shell model calculations. The paper demonstrates that ReCD and shell-model nuclear response functions differ significantly, leading to a factor-of-25 discrepancy in the expected event rate at the recoil energy of the recent LZ event.

Load-bearing premise

The ReCD theory, with the PC-PK1 functional and a finite-range separable pairing force, gives an accurate description of the low-lying states of 129Xe and 131Xe and of the nuclear response functions for inelastic dark matter scattering.

Editorial extensions

If this is right

Dark matter direct detection experiments using natural xenon should observe an inelastic signal for operators O7, O13, and O14 that is much larger than expected from elastic scattering alone.
Limits on dark matter-nucleon couplings derived assuming only elastic scattering may be too weak for these operators; including inelastic scattering would strengthen the constraints.
For spin-dependent operators O6 and O9, the second excited state of 131Xe contributes at the same level as the first, roughly doubling the inelastic rate.
The large difference between ReCD and shell-model predictions implies that nuclear structure uncertainties must be accounted for when interpreting experiment events, particulary for the LZ event at 248 keV.

Reading between the lines

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

The ReCD calculations predict a broad, featureless recoil spectrum for O13, whereas the shell model predicts a peak near 200 keV; this distinction could be tested by searching for multiple events at low recoil energies in future LZ or XENONnT data.
If the inelastic channel dominates for O7 and O14, experiments sensitive only to nuclear recoil (not de-excitation photons) may miss a large fraction of the signal; a coincident de-excition gamma search could dramatically increase sensitivity to these operators.
The paper implicitly assumes isoscalar couplings (c_p = c_n); the conclusions for operators that couple differently to protons and neutrons might differ and should be explored.
The ReCD method still relies on the PC-PK1 functional; a comparison with other density functionals (e.g., DD-ME2) would test the robustness of the predictions.

Original abstract

We investigate the nuclear responses for the WIMP-nucleus scattering in the dark matter direct detection with particular emphasis on the inelastic channel for the $^{129}$Xe and $^{131}$Xe isotopes. Our generalization incorporates both the elastic and inelastic scattering channels. With multipole expansion of the effective operators, the angular momentum, parity and time-reversal selection rules can effectively determine the allowed transitions. Instead of the nuclear shell model, we use the state-of-the-art relativistic configuration-interaction density functional theory, which is more suitable for heavy nuclei such as xenon isotopes, to calculate the nuclear response functions. For certain interaction operators, the inelastic contribution can be comparable as its elastic counterpart and some can even dominate by up to three orders of magnitude. Additionally, the higher excited nuclear states can have comparable signal rate as the first excited states. We compare our results with the nuclear shell model calculation. The differences would have significant effects for interpreting the dark matter direct detection searches.

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, 2026-09-23: 1 request, 6,168 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.30 · randomized assignment 0.01 · states quantitative result 0.91 · compares with prior results 0.98 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We investigate the nuclear responses for the WIMP-nucleus scattering in the dark matter direct detection with particular emphasis on the inelastic channel for the $^{129}$Xe and $^{131}$Xe isotopes. Our generalization incorporates both the elastic and inelastic scattering channels. With multipole expansion of the effective operators, the angular momentum, parity and time-reversal selection rules can effectively determine the allowed transitions. Instead of the nuclear shell model, we use the state-of-the-art relativistic configuration-interaction density functional theory, which is more suitable for heavy nuclei such as xenon isotopes, to calculate the nuclear response functions. For certain interaction operators, the inelastic contribution can be comparable as its elastic counterpart and some can even dominate by up to three orders of magnitude. Additionally, the higher excited nuclear states can have comparable signal rate as the first excited states. We compare our results with the nuclear shell model calculation. The differences would have significant effects for interpreting the dark matter direct detection searches.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the nuclear responses for the WIMP-nucleus scattering in the dark matter direct detection with particular emphasis on the inelastic channel for the $^{129}$Xe and $^{131}$Xe isotopes.	contribution 0.98	0.89	0.06	asserted 0.90
s1	Our generalization incorporates both the elastic and inelastic scattering channels.	contribution 0.92	0.86	0.04	asserted 0.98
s2	With multipole expansion of the effective operators, the angular momentum, parity and time-reversal selection rules can effectively determine the allowed transitions.	method 0.95	0.30	0.04	asserted 0.64
s3	Instead of the nuclear shell model, we use the state-of-the-art relativistic configuration-interaction density functional theory, which is more suitable for heavy nuclei such as xenon isotopes, to calculate the nuclear response functions.	method 0.99	0.89	0.05	asserted 1.00
s4	For certain interaction operators, the inelastic contribution can be comparable as its elastic counterpart and some can even dominate by up to three orders of magnitude.	result 1.00	0.90	0.45	asserted 0.70
s5	Additionally, the higher excited nuclear states can have comparable signal rate as the first excited states.	result 1.00	0.88	0.10	asserted 0.92
s6	We compare our results with the nuclear shell model calculation.	method 0.64	0.90	0.03	asserted 0.90
s7	The differences would have significant effects for interpreting the dark matter direct detection searches.	interpretation 1.00	0.50	0.33	asserted 0.60

What kind of paper the classifier reports this is: simulation study 0.58 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

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.** Intuitive pictures for the nucleon occupation in a mean-field potential (left) and the rearranged occupation

**Figure 2.** The nuclear response W00 T for T = Σ′′ and Σ′ as functions of momentum transfer amplitude |q| calculated by the ReCD theory and their comparison to the NSM results [22]. sically incorporated, the dimension of the configuration space in the ReCD theory is much smaller than that in the NSM, and one does not need to introduce any nonphysical truncation that may influence the accuracy of theoretical calculations into the configuration space. The NSM and the ReCD are two widely used many-body approaches in the field of nuclear structures. Since some approximations are indeed employed in…

**Figure 3.** Differential event rates due to the WIMP-nucleus elastic (blue) and inelastic (orange) scatterings to

**Figure 4.** Left: Expected differential event rates of a WIMP DM with mass mχ = 10 TeV scattering on 131Xe via operator O9 at PandaX-4T. We show the recoil spectrum for elastic scattering (blue) and inelastic contributions of all four kinematically accessible excited nuclear states (orange, green, red, and purple). Right: Elastic and inelastic spin nuclear responses of 131Xe as functions of the recoil energy ER. energy at 236 keV (164 keV) for the second excitation, 129Xe (131Xe) requires the DM mass to be mχ ≳ 182 GeV (86 GeV), respectively. For a TeV scale DM, even the fifth (fourth) energy…

**Figure 5.** Differential event rates due to the WIMP-nucleus elastic (blue) and inelastic (orange) scatterings via

Figures reproduced from arXiv:2609.16529 by the authors.

References

Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The Electron-Recoil Response Tail and the LZ High-Energy Event Background
hep-ex 2026-10 accept novelty 7.0 of 10

The published LZ electron-recoil response characterization does not determine the tail probability needed for the background estimate; tiny quantile shifts (0.14%) can change the ER contribution by a factor of 13.
Testing the inelastic dark matter interpretation of the LZ event with heavy-element experiments
hep-ph 2026-10 conditional novelty 6.0 of 10

The thermal Higgsino dark matter model can fit the LZ 248 keV event only if the dark matter velocity distribution has an extreme high-velocity tail, and heavy-element experiments can test this scenario.
Decaying Dark Matter for the Exothermic Recoil at LZ
hep-ph 2026-09 conditional novelty 6.0 of 10

Decay regeneration of a GeV-scale excited dark state produces the LZ 248 keV recoil as an exothermic downscattering line and predicts argon lines at 700 to 810 keV.
The high-velocity dark matter halo of the Milky Way in light of the LZ 248 keV event
hep-ph 2026-09 accept novelty 6.0 of 10

Using Milky Way analogues from TNG-50 and FIRE-2, the maximum laboratory-frame dark matter speed on June 16 is 793 km/s with 95% containment from 697 to 876 km/s, and the co-rotation of the dark matter halo does not l...
Endothermic Dark Matter at LZ from a Decaying Parent
hep-ph 2026-09 conditional novelty 5.0 of 10

A decaying dark parent can supply both the energy and the flux for an endothermic dark matter interpretation of the LZ 248 keV nuclear recoil candidate, fixing the required lifetime at about 4.4 x 10^20 seconds.

Show 5 more citing papers

GAIA meets LZ: a high velocity tail-tale sign for dark matter
hep-ph 2026-09 conditional novelty 5.0 of 10

Using a Gaia-informed velocity distribution with a lower escape speed than the Standard Halo Model, the endothermic dark matter interpretation of LZ's 248 keV event requires roughly 100 times larger cross sections and...
Environment-dependent mass splitting to suppress solar capture in the inelastic-doublet interpretation of the LZ event
hep-ph 2026-09 conditional novelty 5.0 of 10

A density-dependent scalar field value is shown to enlarge the inelastic dark matter mass splitting inside the Sun, suppressing solar capture while keeping the laboratory value at 350 keV, at the price of severe fine-tuning.
The LHC is not enough: the LZ High-Recoil Event at FCC-hh and a Muon Collider
hep-ph 2026-09 conditional novelty 5.0 of 10

The LZ 248 keV recoil, read as inelastic electroweak dark matter, is beyond HL-LHC reach but coverable by FCC-hh and a multi-TeV muon collider.
Inelastic Dark Matter from a Higher-Dimensional Operator: The LUX-ZEPLIN High-Recoil Event and Thermal Relic
hep-ph 2026-09 conditional novelty 4.0 of 10

A single dimension-6 Z-portal operator can simultaneously explain the 248 keV LZ recoil event via inelastic dark matter and the observed thermal relic density for a dark matter mass of roughly 0.2-1 TeV.
Inelastic dark matter mediated by natural dark photon
hep-ph 2026-09 reject novelty 4.0 of 10

A Z2-breaking dark sector with two nearly degenerate scalar dark matter states and a GeV-scale, weakly mixed dark photon is proposed as an exothermic inelastic explanation of the LZ 248 keV event.

Discussion

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