pith. sign in

arxiv: 2606.23317 · v1 · pith:HRXYUVNHnew · submitted 2026-06-22 · 🌌 astro-ph.HE

Galactic Cosmic Ray Transport in the Giant Circumgalactic Medium Halo

Chao-Ming Li , Andrew M. Taylor This is my paper

Pith reviewed 2026-06-26 07:31 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords cosmic ray transportcircumgalactic mediumgalactic halosecondary to primary ratioscosmic ray age distributioncosmic ray confinement
0
0 comments X

The pith

Cosmic rays in the Milky Way's giant circumgalactic halo form an extended 1/r tail and wider age spread while matching secondary-to-primary ratios.

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

The paper compares cosmic ray movement in a conventional small halo to the case of a giant halo whose size is fixed by the circumgalactic medium rather than chosen freely. Inside the source region the transport behaves similarly in both pictures, but outside it the giant-halo case produces a long 1/r density tail and a broader spread of particle ages. The giant-halo model still reproduces the observed ratios of secondary to primary cosmic rays, and the uncertainties coming from gas maps turn out to be comparable in size to those from nuclear cross sections. This supplies a physically motivated alternative confinement volume whose consequences reach diffuse gamma-ray and neutrino emission from the galactic surroundings.

Core claim

In the giant-halo scenario, CR transport within the source region remains similar to that in small-halo models, while substantial differences emerge at larger distances. In the giant-halo scenario, CRs develop an extended approximately 1/r spatial tail and exhibit a broader age distribution than the small-halo case. This model is shown to be consistent with current secondary-to-primary CR measurements. Uncertainties associated with Galactic gas distributions are comparable to those arising from nuclear spallation cross sections.

What carries the argument

The giant circumgalactic medium halo, whose height is fixed by the source-region extent rather than left free, which generates the extended 1/r cosmic-ray density tail outside that region.

If this is right

  • Transport inside the source region stays comparable to small-halo models.
  • An extended approximately 1/r spatial tail appears at larger distances.
  • Cosmic-ray ages show a broader distribution than in the small-halo case.
  • The setup remains consistent with observed secondary-to-primary ratios.
  • Uncertainties from gas distributions are comparable to those from spallation cross sections.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Predictions for diffuse gamma-ray and neutrino emission from the galactic environment would shift relative to small-halo expectations.
  • The total energy budget stored in cosmic rays throughout the halo could be revised upward.
  • Future mapping of cosmic-ray gradients at distances of tens to hundreds of kiloparsecs could directly test the tail.

Load-bearing premise

The halo height is set by the physical extent of the source region instead of being treated as a free parameter.

What would settle it

A measured cosmic-ray density profile lacking the 1/r tail beyond the galactic disk, or an age distribution narrower than the giant-halo prediction, would contradict the central claim.

Figures

Figures reproduced from arXiv: 2606.23317 by Andrew M. Taylor, Chao-Ming Li.

Figure 1
Figure 1. Figure 1: The comparison of the small-halo scenario and the giant-halo scenario. The red thin disk represents the CR injection source and Rd is the source radius. RH, zH are the radius of absorbing boundaries in R and z direction. virial radius, much larger than the source size, so CR transport is fully three-dimensional. The corresponding simplified 3D diffusion solution is given in Appendix B. 2.3. Differential eq… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of gas density models as a function of galactocentric radius in the Galactic plane. The left panel shows molecular gas, while the right panel shows atomic hydrogen. The CGM distribution is shown in both panels for comparison. 16O 15N 14N 13C 12C 11B 10B 10Be 9Be Projectile Cosmic Ray 7Be 9Be 10Be 10B 11B 12C 13C 14N 15N Fragment Cosmic Ray 10 mbarn Dragon2 Cross Section EPOS Cross Section [PITH… view at source ↗
Figure 3
Figure 3. Figure 3: The comparison of the spallation cross sections from DRAGON2 and EPOS model in CRMC software. The area of the circles represents the absolute value of the cross sections, and the reference value of 10 mbarn is shown below the legend. Channels dominating the production of boron and beryllium isotopes are highlighted by blue rectangles. 3.1.1. Cosmic ray spatial distribution [PITH_FULL_IMAGE:figures/full_fi… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of primary CR density distribution for small halo (left) and giant halo (right). The free escape boundary for small halo is zH = 10 kpc, RH = 20 kpc). For the giant halo, the free escape boundary is (RH = 250 kpc). Here we only plot the inner region up to 50 kpc to compare with the small halo. The colorbar is re-normalized to be close (not fit) to the typical CR density. 10 0 10 1 10 2 Distance … view at source ↗
Figure 5
Figure 5. Figure 5: Cosmic ray distribution due to diffusion for small￾halo and giant-halo scenario. The parameter settings are: Rd = 10 kpc for both cases; RH = 10 kpc , zH = 10 kpc for small-halo scenario and RH = 250 kpc for giant-halo scenario. 1028cm2 s −1 )(nH/10−4 cm−3 ) −1 (σ/237 mbarn)−1 , indi￾cating that the 1/r CR density profile can persist out to tens or even hundreds of kpcs, provided that the dif￾fusion timesc… view at source ↗
Figure 6
Figure 6. Figure 6: Particle age distribution at Earth from Monte Carlo simulation for both small halo (left panel) and giant halo (right panel) cases. Different colors of histograms represent different simulation time. The red curves show the fitting with analytical formulas. The exponential suppression at small τ reflects the fi￾nite travel time required for CRs to reach Earth, while at large τ the distribution approaches a… view at source ↗
Figure 7
Figure 7. Figure 7: Compare AMS data and small-halo model prediction, with different cross sections and gas templates. DRAGON2 (dg2) and EPOS-LHC (epos) cross sections are separated by blue and green colors. While Nakanishi2003/2006 (NSgas) and McMillan2017 (MCgas) gas models are separated by solid and dashed lines. The parameters are set to be: D0 = 1028.4 cm2 /s, δ = 0.6, zH = 8 kpc, Rd = 16 kpc. 10 20 40 60 80 100 Rigidity… view at source ↗
Figure 8
Figure 8. Figure 8: Similar to [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Predicted 10Be/ 9Be ratio for both small-halo(left) and giant-halo(right) scenarios with different cross section and gas template combinations. The parameters are set to be: D0 = 1028.4 cm2 /s, δ = 0.6, zH = 8.0 kpc, Rd = 16.0 kpc for the small-halo scenario and D0 = 1028.6 cm2 /s, δ = 0.5, Rd = 20.0 kpc for the giant-halo scenario. B. ANALYTICAL SOLUTION OF 3D DIFFUSION Analytical solution in very simple … view at source ↗
read the original abstract

Recent observations have revealed that the Milky Way is embedded in a massive circumgalactic medium (CGM) extending to several hundred kiloparsecs. Such an extended gaseous halo acts as both a reservoir of baryons and potentially as a confinement volume for Galactic cosmic rays (CRs). We investigate CR transport in this giant Galactic halo and compare its properties with those of conventional small-halo models. In the giant-halo scenario, the halo height is no longer a free parameter, but instead relates to the extent of the source region. We show that CR transport within the source region remains similar to that in small-halo models, while substantial differences emerge at larger distances. In the giant-halo scenario, CRs develop an extended approximately 1/r spatial tail and exhibit a broader age distribution than the small-halo case. This model is shown to be consistent with current secondary-to-primary CR measurements. We further find that uncertainties associated with Galactic gas distributions are comparable to those arising from nuclear spallation cross sections. These results suggest that the giant-halo model provides a physically motivated alternative to conventional small-halo models and may have important implications for diffuse gamma-ray and neutrino emission from the Galactic environment.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper investigates cosmic ray (CR) transport in a giant circumgalactic medium (CGM) halo extending to several hundred kpc, contrasting it with conventional small-halo models. It claims that halo height is no longer a free parameter but is instead set by the extent of the source region. Within the source region, transport properties remain similar to small-halo cases, while at larger radii the giant-halo model produces an extended ~1/r spatial tail and a broader CR age distribution. The model is reported to be consistent with existing secondary-to-primary CR measurements, with uncertainties from Galactic gas distributions comparable in magnitude to those from nuclear spallation cross sections. Implications for diffuse gamma-ray and neutrino emission are noted.

Significance. If the central results hold, the work supplies a physically motivated alternative to small-halo models in which the halo size is observationally anchored rather than tuned. The reported equivalence between gas-distribution and cross-section uncertainties is a useful quantitative statement that could guide future observational priorities. The extended 1/r tail and broader age distribution, if robustly derived, would affect predictions for high-energy emission from the Galactic environment.

minor comments (2)
  1. [Abstract] The abstract states that the model is 'consistent with current secondary-to-primary CR measurements' but does not identify the specific ratios or data sets used; a brief enumeration in the abstract or §1 would improve clarity.
  2. Notation for the halo height and source-region extent should be defined explicitly at first use (e.g., in §2) to avoid ambiguity when comparing giant- and small-halo cases.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending minor revision. The referee's summary accurately reflects the central claims regarding CR transport in the giant CGM halo, the physically motivated halo size, the 1/r tail, broader age distribution, and the comparison of uncertainties from gas distributions versus spallation cross sections. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The abstract and summary present a physically motivated giant-halo model in which halo height is tied to source-region extent, CR transport inside the source region is stated to remain similar to small-halo cases, and an extended 1/r tail plus broader age distribution emerge at large radii while remaining consistent with secondary-to-primary ratios. No equations, fitted parameters, or derivation steps are supplied that would allow any claimed prediction to be shown as identical to an input by construction. Gas-distribution uncertainties are compared to spallation uncertainties without any reduction to self-referential fitting. The derivation chain is therefore self-contained against external benchmarks and receives the default non-finding.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Review limited to abstract; the central modeling choice that halo size is tied to source extent is treated as an input assumption rather than derived. Gas-distribution uncertainties are highlighted but not quantified as free parameters in the text provided.

free parameters (1)
  • Galactic gas distributions
    Abstract states that uncertainties in these distributions are comparable to nuclear spallation cross-section uncertainties, implying they function as adjustable inputs.
axioms (1)
  • domain assumption The halo height relates to the extent of the source region rather than remaining an independent free parameter.
    Explicitly stated in the abstract as the defining difference from small-halo models.

pith-pipeline@v0.9.1-grok · 5741 in / 1344 out tokens · 41459 ms · 2026-06-26T07:31:28.720910+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

46 extracted references · 45 canonical work pages · 3 internal anchors

  1. [1]

    doi: 10.1016/j.physrep.2020.09.003

    Aguilar, M., Ali Cavasonza, L., Ambrosi, G., et al. 2021, Physics Reports, 894, 1, doi: https://doi.org/10.1016/j.physrep.2020.09.003

    work page doi:10.1016/j.physrep.2020.09.003 2021

  2. [2]

    2014, apj, 785, 63, doi: 10.1088/0004-637X/785/1/63

    Bhattacharjee, P., Chaudhury, S., & Kundu, S. 2014, apj, 785, 63, doi: 10.1088/0004-637X/785/1/63

    work page doi:10.1088/0004-637x/785/1/63 2014

  3. [3]

    2013, Nuclear Physics B Proceedings Supplements, 239, 140, doi: 10.1016/j.nuclphysbps.2013.05.023

    Blasi, P. 2013, Nuclear Physics B Proceedings Supplements, 239, 140, doi: 10.1016/j.nuclphysbps.2013.05.023

    work page doi:10.1016/j.nuclphysbps.2013.05.023 2013

  4. [4]

    2012 , Bdsk-Url-1 =

    Blasi, P., & Amato, E. 2012, jcap, 2012, 010, doi: 10.1088/1475-7516/2012/01/010

    work page doi:10.1088/1475-7516/2012/01/010 2012

  5. [5]

    2026, Astroparticle Physics, 176, 103203, doi: https://doi.org/10.1016/j.astropartphys.2025.103203

    Borchiellini, M., Maurin, D., & Vecchi, M. 2026, Astroparticle Physics, 176, 103203, doi: https://doi.org/10.1016/j.astropartphys.2025.103203

    work page doi:10.1016/j.astropartphys.2025.103203 2026

  6. [6]

    N., Hodges-Kluck, E., Qu, Z., et al

    Bregman, J. N., Hodges-Kluck, E., Qu, Z., et al. 2022, apj, 928, 14, doi: 10.3847/1538-4357/ac51de

    work page doi:10.3847/1538-4357/ac51de 2022

  7. [7]

    , keywords =

    Cao, Z., Aharonian, F., An, Q., et al. 2023, prl, 131, 151001, doi: 10.1103/PhysRevLett.131.151001

    work page doi:10.1103/physrevlett.131.151001 2023

  8. [8]

    , keywords =

    Cautun, M., Ben´ ıtez-Llambay, A., Deason, A. J., et al. 2020, mnras, 494, 4291, doi: 10.1093/mnras/staa1017 13

    work page doi:10.1093/mnras/staa1017 2020

  9. [9]

    Cox, D. P. 2005, araa, 43, 337, doi: 10.1146/annurev.astro.43.072103.150615 De La Torre Luque, P., Mazziotta, M., Loparco, F.,

    work page doi:10.1146/annurev.astro.43.072103.150615 2005

  10. [10]

    2021, jcap, 2021, 099, doi: 10.1088/1475-7516/2021/03/099

    Gargano, F., & Serini, D. 2021, jcap, 2021, 099, doi: 10.1088/1475-7516/2021/03/099

    work page doi:10.1088/1475-7516/2021/03/099 2021

  11. [11]

    2019, prd, 99, 103023, doi: 10.1103/PhysRevD.99.103023

    Evoli, C., Aloisio, R., & Blasi, P. 2019, prd, 99, 103023, doi: 10.1103/PhysRevD.99.103023

    work page doi:10.1103/physrevd.99.103023 2019

  12. [12]

    2017, jcap, 2017, 015, doi: 10.1088/1475-7516/2017/02/015

    Evoli, C., Gaggero, D., Vittino, A., et al. 2017, jcap, 2017, 015, doi: 10.1088/1475-7516/2017/02/015

    work page doi:10.1088/1475-7516/2017/02/015 2017

  13. [14]

    2018, jcap, 2018, 006, doi: 10.1088/1475-7516/2018/07/006

    Evoli, C., Gaggero, D., Vittino, A., et al. 2018, jcap, 2018, 006, doi: 10.1088/1475-7516/2018/07/006

    work page doi:10.1088/1475-7516/2018/07/006 2018

  14. [15]

    , keywords =

    Evoli, C., Morlino, G., Blasi, P., & Aloisio, R. 2020, prd, 101, 023013, doi: 10.1103/PhysRevD.101.023013

    work page doi:10.1103/physrevd.101.023013 2020

  15. [16]

    Faerman, Y., Sternberg, A., & McKee, C. F. 2017, apj, 835, 52, doi: 10.3847/1538-4357/835/1/52

    work page doi:10.3847/1538-4357/835/1/52 2017

  16. [17]

    A., Menon, M

    Fagundes, D. A., Menon, M. J., & Silva, P. V. R. G. 2012, Brazilian Journal of Physics, 42, 452, doi: 10.1007/s13538-012-0099-5 Ferri` ere, K., Gillard, W., & Jean, P. 2007, aap, 467, 611, doi: 10.1051/0004-6361:20066992

    work page doi:10.1007/s13538-012-0099-5 2012

  17. [18]

    Genolini, Y., Putze, A., Salati, P., & Serpico, P. D. 2015, aap, 580, A9, doi: 10.1051/0004-6361/201526344 G´ enolini, Y., Boudaud, M., Batista, P. I., et al. 2019, prd, 99, 123028, doi: 10.1103/PhysRevD.99.123028

    work page doi:10.1051/0004-6361/201526344 2015

  18. [19]

    , keywords =

    Heesen, V., O’Sullivan, S. P., Br¨ uggen, M., et al. 2023, aap, 670, L23, doi: 10.1051/0004-6361/202346008

    work page doi:10.1051/0004-6361/202346008 2023

  19. [20]

    F., Butsky, I

    Hopkins, P. F., Butsky, I. S., Panopoulou, G. V., et al. 2022, mnras, 516, 3470, doi: 10.1093/mnras/stac1791 IceCube Collaboration, Abbasi, R., Ackermann, M., et al. 2023, Science, 380, 1338, doi: 10.1126/science.adc9818

    work page doi:10.1093/mnras/stac1791 2022

  20. [21]

    2023, jcap, 2023, 053, doi: 10.1088/1475-7516/2023/03/053

    Kalashev, O., Martynenko, N., & Troitsky, S. 2023, jcap, 2023, 053, doi: 10.1088/1475-7516/2023/03/053

    work page doi:10.1088/1475-7516/2023/03/053 2023

  21. [22]

    Klypin, A., Zhao, H., & Somerville, R. S. 2002, apj, 573, 597, doi: 10.1086/340656

    work page doi:10.1086/340656 2002

  22. [23]

    2021, prd, 103, 103016, doi: 10.1103/PhysRevD.103.103016

    Korsmeier, M., & Cuoco, A. 2021, prd, 103, 103016, doi: 10.1103/PhysRevD.103.103016

    work page doi:10.1103/physrevd.103.103016 2021

  23. [24]

    1982, mnras, 201, 1041, doi: 10.1093/mnras/201.4.1041 Lhaaso Collaboration, Cao, Z., Aharonian, F., et al

    Lerche, I., & Schlickeiser, R. 1982, mnras, 201, 1041, doi: 10.1093/mnras/201.4.1041 Lhaaso Collaboration, Cao, Z., Aharonian, F., et al. 2025, National Science Review, 12, nwaf496, doi: 10.1093/nsr/nwaf496

    work page doi:10.1093/mnras/201.4.1041 1982

  24. [25]

    The lifetime of cosmic rays in the Milky Way

    Lipari, P. 2014, arXiv e-prints, arXiv:1407.5223, doi: 10.48550/arXiv.1407.5223 —. 2022, arXiv e-prints, arXiv:2204.13085, doi: 10.48550/arXiv.2204.13085

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1407.5223 2014

  25. [26]

    J., & Tout, C

    Maller, A. H., & Bullock, J. S. 2004, mnras, 355, 694, doi: 10.1111/j.1365-2966.2004.08349.x

    work page doi:10.1111/j.1365-2966.2004.08349.x 2004

  26. [27]

    McMillan, P. J. 2017, mnras, 465, 76, doi: 10.1093/mnras/stw2759

    work page internal anchor Pith review doi:10.1093/mnras/stw2759 2017

  27. [28]

    A., Spalding, J

    Mewaldt, R. A., Spalding, J. D., Stone, E. C., & Vogt, R. E. 1981, apjl, 251, L27, doi: 10.1086/183686

    work page doi:10.1086/183686 1981

  28. [29]

    C., Krause, M., Basu, A., et al

    Mora-Partiarroyo, S. C., Krause, M., Basu, A., et al. 2019, aap, 632, A10, doi: 10.1051/0004-6361/201834571

    work page doi:10.1051/0004-6361/201834571 2019

  29. [30]

    doi:10.1016/j.astropartphys.2009.03.004 , Eprint =

    Mori, M. 2009, Astroparticle Physics, 31, 341, doi: 10.1016/j.astropartphys.2009.03.004

    work page doi:10.1016/j.astropartphys.2009.03.004 2009

  30. [31]

    1954, Physical Review, 94, 440, doi: 10.1103/PhysRev.94.440

    Morrison, P., Olbert, S., & Rossi, B. 1954, Physical Review, 94, 440, doi: 10.1103/PhysRev.94.440

    work page doi:10.1103/physrev.94.440 1954

  31. [32]

    S., & Nizamov, B

    Pshirkov, M. S., & Nizamov, B. A. 2026, prl, 136, 081201, doi: 10.1103/kfld-35xl

    work page doi:10.1103/kfld-35xl 2026

  32. [33]

    2010, aap, 516, A66, doi: 10.1051/0004-6361/201014010

    Putze, A., Derome, L., & Maurin, D. 2010, aap, 516, A66, doi: 10.1051/0004-6361/201014010

    work page doi:10.1051/0004-6361/201014010 2010

  33. [34]

    Ramesh, D

    Ramesh, R., Nelson, D., Heesen, V., & Br¨ uggen, M. 2023, mnras, 526, 5483, doi: 10.1093/mnras/stad3104

    work page doi:10.1093/mnras/stad3104 2023

  34. [35]

    A., & Niro, V

    Recchia, S., Gabici, S., Aharonian, F. A., & Niro, V. 2021, apj, 914, 135, doi: 10.3847/1538-4357/abfda4

    work page doi:10.3847/1538-4357/abfda4 2021

  35. [36]

    2024, apj, 963, 111, doi: 10.3847/1538-4357/ad1ce8

    Silver, E., & Orlando, E. 2024, apj, 963, 111, doi: 10.3847/1538-4357/ad1ce8

    work page doi:10.3847/1538-4357/ad1ce8 2024

  36. [37]

    Annual Review of Nuclear and Particle Science , keywords =

    Strong, A. W., Moskalenko, I. V., & Ptuskin, V. S. 2007, Annual Review of Nuclear and Particle Science, 57, 285, doi: 10.1146/annurev.nucl.57.090506.123011

    work page doi:10.1146/annurev.nucl.57.090506.123011 2007

  37. [38]

    M., Gabici, S., & Aharonian, F

    Taylor, A. M., Gabici, S., & Aharonian, F. 2014, prd, 89, 103003, doi: 10.1103/PhysRevD.89.103003 Tepper-Garc´ ıa, T., Bland-Hawthorn, J., & Sutherland, R. S. 2015, apj, 813, 94, doi: 10.1088/0004-637X/813/2/94

    work page doi:10.1103/physrevd.89.103003 2014

  38. [39]

    2017, prd, 96, 103005, doi: 10.1103/PhysRevD.96.103005

    Tomassetti, N. 2017, prd, 96, 103005, doi: 10.1103/PhysRevD.96.103005

    work page doi:10.1103/physrevd.96.103005 2017

  39. [40]

    doi:10.1146/annurev-astro-091916-055240 , eprint =

    Tumlinson, J., Peeples, M. S., & Werk, J. K. 2017, araa, 55, 389, doi: 10.1146/annurev-astro-091916-055240

    work page internal anchor Pith review doi:10.1146/annurev-astro-091916-055240 2017

  40. [41]

    Cosmic Ray Monte Carlo Package, CRMC

    Ulrich, R., Pierog, T., & Baus, C. 2021, Cosmic Ray Monte Carlo Package, CRMC, 2.0.1, Zenodo, doi: 10.5281/zenodo.5270381

    work page doi:10.5281/zenodo.5270381 2021

  41. [42]

    J., & Williams, T

    Weiner, B. J., & Williams, T. B. 1996, aj, 111, 1156, doi: 10.1086/117860

    work page doi:10.1086/117860 1996

  42. [43]

    2020, A&A, 639, A131, doi: 10.1051/0004-6361/202037875

    Maurin, D. 2020, A&A, 639, A131, doi: 10.1051/0004-6361/202037875

    work page doi:10.1051/0004-6361/202037875 2020

  43. [44]

    Yiou, F., & Raisbeck, G. M. 1970, aplett, 7, 129

    1970

  44. [45]

    10.1051/0004-6361/202449412

    Zhang, Y., Comparat, J., Ponti, G., et al. 2024, aap, 690, A267, doi: 10.1051/0004-6361/202449412

    work page doi:10.1051/0004-6361/202449412 2024

  45. [46]

    2026, aap, 706, A102, doi: 10.1051/0004-6361/202556835

    Zhang, Y., Shreeram, S., Ponti, G., et al. 2026, aap, 706, A102, doi: 10.1051/0004-6361/202556835

    work page doi:10.1051/0004-6361/202556835 2026

  46. [47]

    2024, prd, 109, 083036, doi: 10.1103/PhysRevD.109.083036

    Zhao, M.-J., Bi, X.-J., Fang, K., & Yin, P.-F. 2024, prd, 109, 083036, doi: 10.1103/PhysRevD.109.083036

    work page doi:10.1103/physrevd.109.083036 2024