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Exothermic dark-photon dark matter and the LZ high-recoil event: finite-reheating constraints

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Kuldeep Deka

High Energy Physics - Phenomenology · Submitted 13 Oct 2026 · 52 references

Pith's verdict: Careful finite-reheating freeze-in calculation for the LZ exothermic benchmark, with honest limitations but no sensitivity test for its central reheating assumptions.

T0 · AI review

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arXiv ID2610.18974 (version 1)
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CitationKuldeep Deka. "Exothermic dark-photon dark matter and the LZ high-recoil event: finite-reheating constraints." arXiv:2610.18974 (2026). https://pith.science/paper/PO4N3AER
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The paper

The paper claims

Finite-reheating freeze-in of exothermic dark-photon dark matter yields specific reheating temperatures for the LZ 248 keV candidate.

The reading

This paper calculates how a specific exothermic dark-photon dark-matter candidate—a 45 GeV pseudo-Dirac fermion with a 1 MeV mass splitting and a 1 GeV dark photon—could have been produced through freeze-in during a non-instantaneous reheating phase after inflation. The same interaction that produces the relic also gives a nuclear-recoil signal consistent with the LZ 248 keV candidate event. The required reheating completion temperature depends on the expansion history during reheating: for a matter-like constant-width history it is 1.32 GeV, for quartic oscillations with scalar decay it is 3.09 GeV, and for quartic oscillations with constant width it is 0.588 GeV, compared with 4.10 GeV for instantaneous reheating. Adiabatic kination cannot accommodate the observed abundance above the BBN lower limit. The result connects a terrestrial direct-detection hint to the early universe's thermal history before radiation domination.

What carries the argument

The central object is a pseudo-Dirac fermion dark sector with a 1 GeV dark photon mediator, where the mass splitting δ=1 MeV makes scattering exothermic. Freeze-in production is computed using a parameterized reheating background described by T∝$a^{{-α}}$ and ρφ∝$a^{{-3(1+ω)}}$, which determines both the Hubble rate and the comoving-volume dilution factor (Trh/T)^{3/α} in the yield integral. The Standard Model fermion source is given by a spin-averaged cross section for f¯f→χLχH via off-shell A' and Z exchange, including on-shell Z→χLχH. The three-photon decay width of the excited state, evaluated through a one-loop electron diagram, provides the INTEGRAL/SPI constraint that sets the normalization. Self-conversion HH→LL is estimated but found negligible.

Extended reading notes

Core claim

For an exothermic dark-photon benchmark with mχ=45 GeV, δ=1 MeV, mA'=1 GeV, and a signal normalization CLZ=7.0×$10^{{-18}}$ that satisfies the INTEGRAL/SPI three-photon decay limit, the relic abundance from freeze-in requires a reheating temperature Trh that varies strongly with the reheating equation of state and cooling exponent. At Tmax=mχ, quadratic constant-width reheating gives Trh=1.32 GeV, quartic scalar-decay reheating gives 3.09 GeV, and quartic constant-width reheating gives 0.588 GeV, while instantaneous reheating gives 4.10 GeV. These solutions are insensitive to raising Tmax above mχ. Adiabatic kination (ω=1, α=1) yields no viable Trh above the 5.96 MeV BBN cutoff for Tmax≥mχ. The calculation includes both dark-photon and Z exchange in the production kernel, entropy dilution during reheating, and a threshold estimate of the thermal-mediator source, which contributes less than 0.2% of the Standard Model fermion yield at αD=$10^{{-10}}$.

Load-bearing premise

The calculation assumes that the visible decay products of the inflaton thermalize rapidly, that the inflaton does not decay directly into the dark sector, and that hard nonthermal primaries make a negligible contribution to dark matter production; if any of these fail, the freeze-in yield would be significantly different and the quoted reheating temperatures would no longer hold.

Editorial extensions

If this is right

  • The LZ event alone does not select a specific reheating history, but if additional recoil events appear, the required Trh from a production calculation can be compared with independent probes of early-universe expansion (e.g., primordial gravitational waves or BBN).
  • The same benchmark predicts a diffuse X-ray flux from χH→χL+3γ at about 78% of the INTEGRAL/SPI limit; improved photon measurements could either confirm a signal or push CLZ below the adopted value.
  • Future detector-level likelihood fits for exothermic benchmarks should incorporate the finite-reheating dependence of the excited fraction and the relic density, not just the instantaneous-reheating approximation.
  • The absence of a kination solution implies that if dark matter is this exothermic vector-portal particle, the early universe could not have passed through a period of adiabatic kination after inflation, unless Tmax is below mχ.

Reading between the lines

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

  • If the LZ candidate is confirmed and attributed to this model, the dark matter relic density would constrain the reheating temperature to be below about 4 GeV, which is far lower than the reheating scale in many inflationary models, pointing to low-reheating cosmologies.
  • The strong dependence of Trh on ω and α means that dark matter freeze-in could become a probe of the inflaton decay mechanism: measuring both the relic density and the direct-detection rate would narrow the allowed (ω,α) region.
  • The three-photon decay lifetime (∼2×10^22 s) is long enough that the excited state survives to the present; future MeV gamma-ray telescopes (e.g., AMEGO, e-ASTROGAM) could detect the diffuse signal and distinguish this scenario from other inelastic dark matter models.
  • The negligible self-conversion implies that the local excited fraction remains near 1/2, so the direct-detection rate is directly tied to the total local density, simplifying comparisons with halo-independent analyses.
Original abstract

An excited dark-matter state can produce a high-energy nuclear recoil by releasing its mass splitting in a collision. Motivated by the $248$~keV LUX--ZEPLIN candidate, we study freeze-in of a $45$~GeV pseudo-Dirac particle with a $1$~MeV splitting and a $1$~GeV dark photon during non-instantaneous reheating. We choose a recoil normalization compatible with the published INTEGRAL/SPI three-photon decay limit. It predicts $0.43$ events in the LZ window and retains the reference recoil shape. Including both dark-photon and $Z$ exchange, we calculate production and entropy dilution for backgrounds with $T\propto a^{-\alpha}$ and $\rho_\phi\propto a^{-3(1+\omega)}$. For $\Tmax=m_\chi$, the observed abundance requires $\Trh=1.32$~GeV for matter-like constant-width reheating, $3.09$~GeV for quartic oscillations with scalar decay, and $0.588$~GeV for quartic oscillations with constant width, compared with $4.10$~GeV for instantaneous reheating. These finite-reheating solutions are insensitive to increasing $\Tmax$ above $m_\chi$. For $\Tmax\geq m_\chi$, adiabatic kination has no solution with $\Trh>5.96$~MeV, the BBN-motivated cutoff adopted for our scans. At $\alpha_D=10^{-10}$, the estimated thermal-mediator source is below $0.2\%$ of the Standard Model source, and self-conversion does not appreciably deplete the excited population. The calculation relates an exothermic recoil benchmark to the production and dilution history before radiation domination.

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, 2026-10-15: 1 request, 7,886 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.75 · human participants 0.01 · controlled comparison 0.27 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

An excited dark-matter state can produce a high-energy nuclear recoil by releasing its mass splitting in a collision. Motivated by the $248$~keV LUX--ZEPLIN candidate, we study freeze-in of a $45$~GeV pseudo-Dirac particle with a $1$~MeV splitting and a $1$~GeV dark photon during non-instantaneous reheating. We choose a recoil normalization compatible with the published INTEGRAL/SPI three-photon decay limit. It predicts $0.43$ events in the LZ window and retains the reference recoil shape. Including both dark-photon and $Z$ exchange, we calculate production and entropy dilution for backgrounds with $T\propto a^{-\alpha}$ and $\rho_\phi\propto a^{-3(1+\omega)}$. For $\Tmax=m_\chi$, the observed abundance requires $\Trh=1.32$~GeV for matter-like constant-width reheating, $3.09$~GeV for quartic oscillations with scalar decay, and $0.588$~GeV for quartic oscillations with constant width, compared with $4.10$~GeV for instantaneous reheating. These finite-reheating solutions are insensitive to increasing $\Tmax$ above $m_\chi$. For $\Tmax\geq m_\chi$, adiabatic kination has no solution with $\Trh>5.96$~MeV, the BBN-motivated cutoff adopted for our scans. At $\alpha_D=10^{-10}$, the estimated thermal-mediator source is below $0.2\%$ of the Standard Model source, and self-conversion does not appreciably deplete the excited population. The calculation relates an exothermic recoil benchmark to the production and dilution history before radiation domination.

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 An excited dark-matter state can produce a high-energy nuclear recoil by releasing its mass splitting in a collision. background 1.00 0.07 0.04 asserted 0.74
s1 Motivated by the $248$~keV LUX--ZEPLIN candidate, we study freeze-in of a $45$~GeV pseudo-Dirac particle with a $1$~MeV splitting and a $1$~GeV dark photon during non-instantaneous reheating. contribution 0.96 0.76 0.06 asserted 0.90
s2 We choose a recoil normalization compatible with the published INTEGRAL/SPI three-photon decay limit. method 0.94 0.81 0.03 asserted 0.98
s3 It predicts $0.43$ events in the LZ window and retains the reference recoil shape. result 1.00 0.86 0.19 asserted 0.99
s4 Including both dark-photon and $Z$ exchange, we calculate production and entropy dilution for backgrounds with $T\propto a^{-\alpha}$ and $\rho_\phi\propto a^{-3(1+\omega)}$. method 0.96 0.92 0.04 asserted 0.99
s5 For $\Tmax=m_\chi$, the observed abundance requires $\Trh=1.32$~GeV for matter-like constant-width reheating, $3.09$~GeV for quartic oscillations with scalar decay, and $0.588$~GeV for quartic oscillations with constant width, compared with $4.10$~GeV for instantaneous reheating. result 1.00 0.91 0.40 asserted 1.00
s6 These finite-reheating solutions are insensitive to increasing $\Tmax$ above $m_\chi$. result 0.95 0.90 0.14 asserted 1.00
s7 For $\Tmax\geq m_\chi$, adiabatic kination has no solution with $\Trh>5.96$~MeV, the BBN-motivated cutoff adopted for our scans. result 0.92 0.85 0.08 asserted 1.00
s8 At $\alpha_D=10^{-10}$, the estimated thermal-mediator source is below $0.2\%$ of the Standard Model source, and self-conversion does not appreciably deplete the excited population. result 0.93 0.84 0.05 asserted 0.93
s9 The calculation relates an exothermic recoil benchmark to the production and dilution history before radiation domination. contribution 0.90 0.86 0.15 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from simulation or computation 0.51.

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. Illustrative true-recoil spectra for xenon, germanium and argon. Dotted lines mark the kinematic centers from Eq. (2.4). The LZ signal window, high-energy sideband and candidate-energy interval are distinguished by the shaded and hatched regions. Each target curve is normalized to the corresponding rate in Ref. [8] multiplied by 7/17. Detector efficiency, energy reconstruction and smearing are not included. The vector-mediator limit in the left panel of
Figure 2. Temperature distribution (1/Yobs) dY /d ln T for the instantaneous calculation and the viable reheating histories at Tmax = mχ. Each finite-reheating curve includes production during reheating and the subsequent radiation-dominated contribution. The displayed curves integrate to unity over ln T to plotting accuracy. The vertical line marks the calculated instantaneous result 4.10 GeV at the normalization in Eq. (2.7)
Figure 3. Source and self-conversion diagnostics for quadratic, constant-width reheating at Tmax = mχ. Top: thermal-mediator yield relative to the Standard Model fermion yield. Bottom: HH-only depletion retaining equal-state production but omitting reverse conversion (solid), and its source-free upper bound (dashed). Both panels use the same relic-density solution and portal normalization at each αD. Electron conversion and radiative decay are omitted from the bottom panel. The vertical line marks αD = 10−10, where the yield ratio is 9.88 × 10−4 . Horizontal lines mark 0.1 and 1 where…
Figure 4. Reheating-completion temperature required by the relic abundance as a function of Tmax. Crosses mark the last viable scan point when no solution exists at larger Tmax above the adopted 5.96 MeV lower limit. The dotted vertical line marks Tmax = mχ. Points to its left describe production from the Boltzmann tail with Tmax < mχ. The Standard Model fermion source uses the collision term in Eq. (2.13). All curves include the threshold estimate of the thermal-mediator source. 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Tmax/m 10 2 10 1 10 0 10 1 r e q uir e d TR H [G e V] (a) 45 GeV, 1.0 MeV 200…
Figure 5. Adiabatic-kination comparison. Left: required Trh for the 45 GeV point (solid) and the 200 GeV point (dashed). Crosses mark where the solution reaches the adopted BBN lower limit. Right: largest viable Tmax/mχ for each point, compared with Tmax = mχ. Both source terms and the entropy-conserving kination background are evaluated at the corresponding dark-matter mass. The 200 GeV point is evaluated with the same CLZ and αD as the 45 GeV point. – 12 –
Figure 6. Required Trh at Tmax = mχ. The hatched region lies outside the physical domain in Eq. (3.6). The separately shaded region has no relic-density solution above Trh = 5.96 MeV. The dashed curve is α = 3(1 + ω)/4, and labeled symbols mark the histories in

Figures reproduced from arXiv:2610.18974 by the authors.

References

Discussion

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