Gauged $U(1)_{L_\mu-L_\tau}$ Scotogenic Model in light of $R_{K^{(*)}}$ Anomaly and AMS-02 Positron Excess

Bin Zhu; Ran Ding; Su-Jie Lin; Zhi-Long Han

REVIEW 2 major objections 5 minor 106 references

Gauged $U(1)_{L_\mu-L_\tau}$ Scotogenic Model in light of $R_{K^{(*)}}$ Anomaly and AMS-02 Positron Excess

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A single gauged mu-minus-tau symmetry, embedded in the scotogenic model with vector-like quarks, can explain both the LHCb $R_{K^{(*)}}$ anomaly and the AMS-02 positron excess at the same time.

desk verdict The model-building and constraint work are genuinely useful, but the AMS-02 positron claim does not survive contact with the paper's own couplings: the advertised Z'H0 channel cannot produce the quoted annihilation rate. read the letter →

arxiv 1908.07192 v1 pith:6SWTLVH3 submitted 2019-08-20 hep-ph

Zhi-Long Han , Ran Ding , Su-Jie Lin , Bin Zhu This is my paper · ORCID

classification hep-ph

keywords scotogenicmodelU(1)L_mu-L_tauR_KanomalyAMS-02positronexcessZ-primebosonvector-likequarkSommerfeldenhancementMajoranadarkmatter

topics Dark Matter

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that one extension of the Standard Model, the scotogenic radiative neutrino-mass model with a gauged $U(1)_{L_\mu-L_\tau}$ symmetry, can account for two unexplained observations at once: the LHCb measurement of $B$ meson decays that deviate from lepton-flavor universality, and the high-energy positron excess reported by AMS-02. The key is a $Z'$ boson that couples to muons and taus; once heavy vector-like quarks are added, it also develops a loop-level $b$-$s$ coupling, producing the observed $R_{K^{(*)}}$ effect. The same $Z'$ mediates dark-matter annihilation into leptons, so the particle that sets the relic density can also be the source of the positron excess. The authors give explicit benchmark masses, mostly with dark matter near 1 to 1.5 TeV and $Z'$ between roughly 10 GeV and 1.3 TeV, that pass neutrino, meson-mixing, direct-detection, antiproton, gamma-ray, and CMB constraints.

What carries the argument

The load-bearing object is the massive $Z'$ gauge boson of $U(1)_{L_\mu-L_\tau}$, together with the singlet scalar $H_0$ that arises when the new symmetry breaks. The $Z'$ does double duty: through heavy vector-like quarks it generates the flavor-changing $Z'bs$ coupling that sets $C_9^\mu$, and through its couplings to muons and taus it mediates leptophilic dark-matter annihilation. The $H_0$ is the second piece of machinery, as its lightness provides a Yukawa-type potential that gives a velocity-dependent Sommerfeld enhancement to the annihilation cross section, converting the freeze-out cross section into the much larger boost factor required by the positron data.

What would settle it

Measure the local dark matter density to a precision that excludes the high side of the current range, say by pinning it at the nominal $0.4\text{ GeV cm}^{-3}$; the paper's own benchmark tables show the required annihilation cross sections would then exceed the CMB limit by factors of about two to three, removing the AMS-02 interpretation. A second decisive check is the LHC search for $Z'\to \mu^+\mu^-$ in the 10 GeV mass range and for $t\to cZ'$ above a branching ratio of roughly $10^{-4}$.

Watch

Extended reading notes

Core claim

The paper's central claim is that the $R_{K^{(*)}}$ anomaly and the AMS-02 positron excess can be explained simultaneously within the gauged $U(1)_{L_\mu-L_\tau}$ scotogenic model. Neutrino masses are generated at one loop with $Z_2$-odd right-handed neutrinos and an inert scalar doublet, while spontaneous symmetry breaking of the new gauge group by a singlet scalar produces a massive $Z'$. With heavy vector-like quarks, an effective $Z'bs$ coupling arises, yielding the Wilson coefficient $C_9^\mu\simeq -0.95$ that fits the LHCb data for $Y_Q=0.122$ and $M_Q=10$ TeV. For the Majorana dark-matter fermion $N$, annihilation through $NN\to Z'Z'$ and $NN\to Z'H_0(\to Z'Z')$ produces muon and tau final states that fit the AMS-02 positron flux for $M_N\sim 1$ to 1.5 TeV; the 2 TeV benchmark overshoots the data. A Sommerfeld enhancement driven by a light singlet Higgs $H_0$ with mass around 30 to 75 GeV supplies the large boost factor needed, and the combination satisfies the main existing constraints, with the CMB bound the tightest.

Load-bearing premise

The positron interpretation rests on a light singlet Higgs boson near 30 to 75 GeV providing a large Sommerfeld enhancement to dark-matter annihilation, and on the local dark matter density being near the upper end of its measured uncertainty so that the required cross section slips under the CMB bound.

Editorial extensions

If this is right

If the model is right, the $R_{K^{(*)}}$ anomaly is a sign of a new $C_9^\mu$ contribution around $-0.95$, produced by $Z'$ exchange whose strength is fixed by the ratio $Y_Q/M_Q$ and is otherwise independent of the $Z'$ mass and gauge coupling.
The viable $Z'$ parameter region is bounded by neutrino trident production and $B_s$ mixing, leaving roughly $550\text{ GeV}\lesssim M_{Z'}/g'\lesssim 4\text{ TeV}$, with very light $Z'$ masses near 10 GeV allowed at $g'\simeq 3\times10^{-3}$.
Dark matter with mass between about 1 and 1.5 TeV annihilating into $Z'Z'$ or $Z'H_0$ fits the AMS-02 positron spectrum, while a 2 TeV dark matter particle would overshoot the measured flux.
The benchmark scenarios produce negligible antiproton flux and are marginally compatible with the extragalactic gamma-ray background, so the main tension lies with the CMB energy-deposition limit.
If confirmed, the framework ties together dark matter, radiative neutrino mass, a flavor anomaly, and a cosmic-ray excess using one new gauge symmetry and a handful of new states.

Reading between the lines

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

The positron half of the interpretation is directly testable by cosmic-ray and astrophysical observations without any collider input: a precise measurement of the local dark matter density near its nominal value of $0.4\text{ GeV cm}^{-3}$, rather than the upper end of the uncertainty, would push the required annihilation cross section above the CMB bound by a factor of roughly two to three.
If the $R_{K^{(*)}}$ anomaly is confirmed by later LHCb data, the model predicts vector-like quarks at the 10 TeV scale with Yukawa couplings near 0.1, making the heavy-quark sector a concrete target for future high-energy colliders; if the anomaly instead fades, the dark-matter and neutrino-mass parts of the model survive without the vector-like quark sector.
The two-zero texture of the neutrino mass matrix forces an inverted neutrino mass hierarchy, so future long-baseline neutrino oscillation experiments that determine the mass ordering could confirm or exclude this specific realization independently of any dark-matter or flavor measurement.
The light $H_0$ mediator in the 30 to 75 GeV range with the required Sommerfeld enhancement gives a velocity-dependent annihilation signal that could show up differently in dwarf-spheroidal gamma-ray searches versus the galactic center, a distinction not fully explored in the paper.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things you should know before reading this one. First, there is something real here: the authors push the gauged U(1)_{L_mu-L_tau} scotogenic model into the high-M_Z' region, add vector-like quark induced Z'bs couplings for R_K(*), and propose the NN -> Z'H0 channel as a new way to get the AMS-02 positron excess. The constraint compilation is thorough and mostly correct: neutrino trident, Bs mixing, Z -> 4mu, t -> cZ', direct detection, antiproton, EGRB, CMB. The Wilson coefficient derivation and the Sommerfeld enhancement setup are standard. If you work on U(1) extensions of scotogenic models, the first half of the paper is worth your time.

But the AMS-02 part does not hold up. The paper itself rejects NN -> Z'Z' ('is difficult to give desired BF through Sommerfeld enhancement', Sec. V A), leaving NN -> Z'H0 as the only channel. That channel fails on a simple cross-section estimate. With g' = 3e-3 and h_N ~ 0.8, the partial annihilation cross section into Z'H0 at freeze-out is roughly (g'^2 h_N^2)/(16 pi M_N^2), about 10^-31 cm^3/s for M_N = 1 TeV. Table IV quotes 0 ~ 10^-26 cm^3/s. That value is consistent with h_N^4/(16 pi M_N^2), i.e., NN -> H0H0, not NN -> Z'H0. Even a Sommerfeld enhancement of 10^3-10^4 leaves the local rate orders of magnitude below the required _BF ~ 7e-24 cm^3/s. So either the quoted cross section belongs to a different final state, or the positron flux was computed from a channel that is not the one actually dominating. The Table III benchmarks have the same disease: the paper admits SE != BF there and still treats them as valid. This is not a minor tuning issue; it is the load-bearing part of the simultaneous explanation.

The other weaknesses are softer. Yes, M_H0 is chosen so that SE numerically equals the fitted boost factor, and C9 is pinned to the global-fit value. That is benchmark-fitting rather than prediction. The CMB bound is only marginally evaded by appealing to the upper end of the local dark matter density. I wouldn't call those fatal in a model-building paper, but they are real limitations.

Who should read this? People building gauged U(1) models for flavor and dark matter, and anyone working on positron excess interpretations. The constraint scan and the vector-like quark mechanism are worth a look. The positron-excess conclusion should be dropped or reworked. As is, the central claim is not supported.

If I were an editor, I would send it to a serious referee: the model construction is substantial and the error is subtle enough that expert scrutiny is the right filter. But I would not accept it in anything close to its current form. The authors need to fix the annihilation cross-section calculation, redo the AMS-02 fit with the correct final state, or remove that section entirely.

Referee Report

2 major / 5 minor

Summary. This paper studies the gauged U(1)_{L_mu-L_tau} scotogenic model, augmented with vector-like quarks to generate an effective Z' bs coupling, and claims to explain simultaneously the R_K(*) anomaly and the AMS-02 positron excess while satisfying neutrino oscillation, relic density, direct detection, neutrino trident, B_s mixing, Z to 4 mu, antiproton, EGRB and CMB constraints. The R_K(*) explanation is obtained by fixing Y_Q/M_Q to reproduce the global-fit value C9^mu = -0.95. For DM, the paper performs a Monte Carlo scan of the parameter space and identifies NN -> Z'Z' and NN -> Z'H0 (with H0 -> Z'Z') as candidate channels for the positron excess. Benchmarks for these channels are given in Tables III and IV, with the Sommerfeld enhancement used to match the required boost factor. The paper concludes that the two anomalies can be explained simultaneously.

Significance. If correct, the paper would provide a very broad framework: radiative neutrino masses, a leptophilic DM candidate, an L_mu-L_tau gauge boson addressing B anomalies, and a simultaneous fit to cosmic-ray positron data. The paper has genuine strengths: it is implementation-heavy (FeynRules, micrOMEGAs, GALPROP), it considers a wide set of constraints, and it provides explicit benchmark points. The R_K(*) Wilson-coefficient derivation in Eqs. (25)-(27) is standard and the parameter choice is transparently documented. However, the central AMS-02 benchmark is numerically inconsistent: the NN -> Z'H0 cross section with g' = 3e-3 is many orders of magnitude too small to produce the quoted freeze-out cross section, so the paper's only claimed working channel does not actually work. This is a load-bearing error in the central claim, not a presentation issue.

major comments (2)

[Section V A, Table IV] The benchmark for the NN -> Z'H0 channel is numerically inconsistent. The amplitude contains one N-N-Z' vertex proportional to g' and one N-N-H0 vertex proportional to h_N, so the partial cross section scales as (g' h_N)^2/(16 pi M_N^2). With g' = 3e-3, h_N ~ 0.8 and M_N = 1 TeV, this gives <sigma v>_0 of order 1e-31 cm^3/s at freeze-out, not the 1e-26 cm^3/s quoted in Table IV. Even multiplying by the Sommerfeld factors shown in Fig. 5 (right), which reach at most about 1e4, the local annihilation cross section remains orders of magnitude below the required <sigma v>_BF ~ 7e-24 cm^3/s quoted in the table. If, instead, the quoted <sigma v>_0 is the total annihilation cross section, then it must be dominated by NN -> H0H0 (since g'^2 << h_N^2), in which case the positron flux has been computed from the wrong final state and the claim that NN -> Z'H0 is the source of the AMS-02 signal is unsupported. This invalidates the AMS-02 part of the simultaneous explanation.
[Section V B 3, Tables III and IV] For all benchmarks, the required annihilation cross section <sigma v>_BF exceeds the CMB-derived limit <sigma v>_CMB by factors of about two to three (for example, Table IV, M_N = 1 TeV: 7.35e-24 vs 3.25e-24 cm^3/s). The paper responds by appealing to a larger local DM density within observational uncertainty, which would reduce the required cross section by 'a factor of several times'. This is an unquantified assumption and not a constraint-satisfying result: at the nominal rho_sun = 0.4 GeV/cm^3 used elsewhere in the paper, the benchmarks are excluded. The conclusion that the model satisfies CMB constraints is therefore not supported by the presented benchmarks.

minor comments (5)

[Section IV, scan range] The scan range for M_H0 is written as [0, sqrt(4 pi M_Z'/g')], which is dimensionally inconsistent; the intended expression is probably sqrt(4 pi) M_Z'/g' or an equivalent dimensionless-corrected form.
[Section V A, text after Eq. (33)] 'For a given model parameters in Eq. (33)' is a cross-reference error: Eq. (33) defines the spin-independent direct detection cross section, not the model parameters of the benchmark.
[Abstract and Section V A] The abstract lists both NN -> Z'Z' and NN -> Z'H0 as channels that can interpret the AMS-02 excess, but Section V A states that NN -> Z'Z' 'is difficult to give desired BF through Sommerfeld enhancement'; the abstract should be made consistent with this conclusion.
[Equation (50)] The expression for f_eff^{Z'H0} in Eq. (50) has a bracket imbalance; it should presumably read [f_i(E_Z'/2) + 2(E_H0/E_Z') f_i(E_H0/4)] / [1 + 2(E_H0/E_Z')].
[Figures 1-4] The horizontal-axis labels for the Z' mass are inconsistent ('M'_Z' in some figures, 'M_Z'' in others); please standardize.

Circularity Check

1 steps flagged · score 6.0 of 10

AMS-02 'prediction' is a refit: MH0 is chosen so the Sommerfeld factor equals the AMS-fitted boost factor, so the positron-flux normalization is an input rather than a prediction; independent constraints remain genuine checks.

fitted input called prediction [Table IV caption and Sec. V A (AMS-02 positron flux fit)]
"The values of MH0 have been chosen such that the resulted Sommerfeld enhancement factors are match to fitted boost factors, i.e., SE≃BF."

In Eqs. (34)-(36), BF is introduced as a free parameter in the chi^2 fit to the AMS-02 positron data. The paper then chooses MH0 in Table IV so that the model's Sommerfeld enhancement equals that fitted BF. Since the predicted DM positron flux scales as BF times the freeze-out cross section times the spectrum, and since BF is fixed to the AMS-02 fit, the normalization of the 'predicted' flux in Fig. 6 is forced by the data by construction. The model does not independently predict the excess amplitude; it accommodates it by tuning MH0. The remaining nontrivial content is the spectral shape set by MN and the muon/tau final states, and the independent constraints (antiproton, EGRB, CMB) are genuine external checks, which prevents the whole paper from being fully circular.

full rationale

The R_K(*) part is an explicit fit rather than a disguised prediction: the paper fixes YQ=0.122 and MQ=10 TeV to reproduce the global-fit value C9=-0.95, so the 'explanation' of that anomaly is parameter accommodation, presented transparently. The same is true for the AMS-02 part: BF is fitted to the positron data and MH0 is then chosen so SE=BF, with the paper even stating this in the Table IV caption. Calling the resulting curve 'predicted' is therefore a fitted input called a prediction for the normalization, although the spectral shape and the external constraints (neutrino trident, Bs mixing, Z->4mu, antiproton, EGRB, CMB) are not circular. There is no load-bearing self-citation chain: the model setup uses prior work by other authors, and the Sommerfeld, EGRB, and CMB calculations are standard literature. Because the central claim of simultaneously explaining both anomalies reduces in part to fitting parameters to those anomalies, a partial-circularity score of 6 is appropriate rather than a higher score, since the consistency checks against independent data are genuine and the paper is explicit about its fitting choices.

Assumptions & free parameters 10 free parameters · 6 assumptions · 6 invented entities

The model introduces a Z' gauge boson, right-handed neutrinos, an inert doublet, a scalar singlet, and vector-like quarks. Most are inherited from Refs. [11] and [53], but all are unobserved. The benchmarks rely on fitting YQ/MQ, g', MZ', MH0, hN, and cosmic-ray background normalizations to the target observables.

free parameters (10)

YQ and MQ (vector-like quark Yukawa and mass) = YQ = 0.122, MQ = 10 TeV
Chosen to give C9 ~ -0.95 to match the R_K(*) global fit; no prediction.
g' (U(1)_{L_mu-L_tau} gauge coupling) = g' = 3e-3 for NN -> Z'H0 benchmarks; up to ~0.7 in scan
Gauge coupling of the new U(1); free parameter scanned in Eq. (32).
MZ' (Z' mass) = 10 to 12 GeV in AMS-02 benchmarks
Mass of the new gauge boson; free parameter determined by vS and g'.
MH0 (singlet-like scalar mass) = 29.6, 48.7, 74.7 GeV
Chosen so that Sommerfeld enhancement matches the BF fitted to AMS-02.
hN (effective DM-S coupling) = 0.77, 0.80, 0.91
Derived from RH neutrino mixing; chosen in benchmarks.
MN (dark matter mass) = 1, 1.5, 2 TeV
Dark matter mass in the positron fit benchmarks.
fe+ and f_pbar (background normalizations) = about 0.78 to 0.81 and 1.28
Free normalization factors for cosmic-ray backgrounds, varied in [0,5].
phi_e+ and phi_pbar (solar modulation potentials) = 600-620 MV and 1019 MV
Free parameters in the force-field solar modulation approximation.
Neutrino sector parameters (lambda5, M0, f_l) = not specified individually
Tuned to satisfy the neutrino oscillation condition |R| in [0.4,0.5] with theta_R = pi.
alpha (scalar mixing angle) = scanned in [0.01, 0.1]
Mixing angle between SM Higgs and singlet; constrained by direct detection.

assumptions (6)

domain assumption The U(1)_{L_mu-L_tau} symmetry is gauged and spontaneously broken by the singlet S; the Z2 symmetry stays unbroken.
Defines the model; from Section II.
domain assumption Only the inverted neutrino mass hierarchy can fit the two-zero texture of the one-loop neutrino mass matrix.
Stated in Section II B following Ref. [52], restricts parameter space.
ad hoc to paper The vector-like quark sector generates the effective Z'bs couplings with the texture in Eq. (24), and the CP-odd part mD is decoupled to set C9' = 0.
Assumed to simplify the flavor structure; quoted around Eq. (24).
standard math The Sommerfeld enhancement is computed with the semi-analytic formula from Refs. [88,89] for a Yukawa potential.
Used in Section V A; standard approximation.
domain assumption The Milky Way DM halo is NFW with local density 0.4 GeV/cm^3; propagation parameters are those of the DC case in Ref. [76]; minimal halo mass Mmin = 10^-6 Msun and Maccio concentration model are used.
Astrophysical inputs for positron, antiproton and EGRB calculations in Sections V A and V B 2.
ad hoc to paper The CMB constraint can be relaxed by a larger local DM density within observational uncertainty.
Invoked in Section V B 3 to keep benchmarks compatible with Planck; this is the paper's own caveat.

invented entities (6)

Z' gauge boson independent evidence
purpose: Mediates DM annihilation to muons/taus and, with vector-like quarks, provides Z'bs coupling to explain R_K and positron excess
Searchable in LHC dimuon and Z to 4 mu final states; the paper compares to ATLAS and CMS limits.
H0 singlet-like scalar independent evidence
purpose: Light mediator that produces the Sommerfeld enhancement for DM annihilation in the NN -> Z'H0 channel
Mixes with the SM Higgs; constrained by Higgs coupling measurements and direct detection.
Heavy vector-like quarks QL, UR, DR, etc. independent evidence
purpose: Generate the effective Z'bs coupling at loop level for the R_K anomaly
Induce B_s mixing and t -> c Z' decays; the paper uses those constraints.
Right-handed neutrinos N_e, N_mu, N_tau independent evidence
purpose: Generate neutrino masses at one loop and provide the dark matter particle N
Their Yukawa couplings are constrained by lepton flavor violation; the lightest one is the DM candidate.
Inert scalar doublet eta independent evidence
purpose: Z2-odd scalar in the neutrino mass loop and DM co-annihilation partner
Its charged component can be searched at colliders; it contributes to LFV.
Scalar singlet S independent evidence
purpose: Breaks U(1)_{L_mu-L_tau} and gives mass to Z' and the H0 scalar
Physical H0 state mixes with the SM Higgs and is testable via Higgs coupling deviations.

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Cite this review

Pith. "Pith review of Gauged $U(1)_{L_\mu-L_\tau}$ Scotogenic Model in light of $R_{K^{(*)}}$ Anomaly and AMS-02 Positron Excess." pith.science (2026). https://pith.science/paper/6SWTLVH3

@misc{pith2026190807192,
  author       = {Pith},
  title        = {Pith review of: Gauged $U(1)_L_\mu-L_\tau$ Scotogenic Model in light of $R_K^(*)$ Anomaly and AMS-02 Positron Excess},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6SWTLVH3}},
  note         = {Machine review of arXiv:1908.07192}
}

abstract

We study the gauged $U(1)_{L_\mu-L_\tau}$ scotogenic model with emphasis on latest measurement of LHCb $R_{K^{(*)}}$ anomaly and AMS-02 positron excess. In this model, neutrino masses are induced at one-loop level with $Z_2$-odd particles, i.e., right-handed neutrinos $N_\ell(\ell=e,\mu,\tau)$ and inert scalar doublet $\eta$ inside the loop. Meanwhile, the gauged $U(1)_{L_\mu-L_\tau}$ symmetry is broken spontaneously by the scalar singlet $S$, resulting to the massive gauge boson $Z'$. Provided certain couplings to quarks induced by heavy vector-like quarks, the gauge boson $Z'$ would contribute to the transition $b\to s \mu^+\mu^-$, hence explain the $R_{K^{(*)}}$ anomaly. As for the Majorana fermion DM $N$, the gauge boson $Z'$ and the singlet Higgs $H_0$ will generate various annihilation channels, among which the $NN\to Z'Z'$ and $NN\to Z'H_0(\to Z'Z')$ channel could be used to interpret the AMS-02 positron excess. We give a comprehensive analysis on model parameter space with consider various current constraints. The combined analysis shows that the $R_{K^{(*)}}$ anomaly and AMS-02 positron excess can be explained simultaneously.

Figures

Figures reproduced from arXiv: 1908.07192 by the authors.

**Figure 2.** FIG. 2. Same as figure. 1, but in the [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** FIG. 3. Survived samples in the [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: FIG. 4. The benchmarks in our model to fit AMS-02 positron data. Here cyan, orange and purple diamonds (red ,green [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]

**Figure 5.** Figure 5: FIG. 5. The Sommerfeld enhancement factor [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]

**Figure 6.** Figure 6: FIG. 6. The positron fluxes predicted by benchmarks of [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]

**Figure 7.** Figure 7: FIG. 7. The antiproton flux predicted by benchmarks in table III and IV with the AMS-02 data. [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

**Figure 8.** Figure 8: FIG. 8. Cosmological boost factor [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]

**Figure 9.** Figure 9: FIG. 9. Comparison of the EGRB flux produced by benchmarks in tables III and IV with the Fermi-LAT measure [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]

**Figure 10.** Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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As we mentioned in section V A, the relevant limits come from antiproton ﬂux, EGRB measure- ment and impact of energy deposition on CMB anisotropy

AMS-02 antiproton constraint Given the benchmarks to explain the positron excess, we now exam the constraints from other indirect detections. As we mentioned in section V A, the relevant limits come from antiproton ﬂux, EGRB measure- ment and impact of energy deposition on CMB anisotropy. From Eq. (22), the effective coupling ofZ′ ¯didj leads to antiproto...

2016

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For calculation of EGRB ﬂux, we follow the procedures in Ref

Fermi-LAT EGRB constraint The next important constraint we consider comes from the EGRB measured by Fermi-LAT collabora- tion [77]. For calculation of EGRB ﬂux, we follow the procedures in Ref. [90, 91]. The ﬂux of at redshiftz is given as dΦEGB dEγ = c(1 +z)2¯ρ2 DMBF⟨σv⟩0 8πM 2 N ∫ ∞ z dz′ (1 +z′)3B(z′,m min) H(z′) dN dE′γ e−τ(z,z′,E′ γ), (38) whereE′ γ ...

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Planck CMB constraint The last constraint necessarily need to consider is the effect of DM annihilation on CMB anisotropy. Annihilation of DM to SM particles between recombination and reionization epoch can inject and deposit energy into intergalactic medium (IGM) through produced electrons, positrons and photons via photoion- ization, Coulomb scattering,...

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