pith. sign in

arxiv: 2606.06773 · v1 · pith:IEUDTNOBnew · submitted 2026-06-04 · ✦ hep-ph · astro-ph.HE· hep-ex· nucl-th

Lepton interactions from GeV to EeV

Reinaldo Francener This is my paper

Pith reviewed 2026-06-28 00:04 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.HEhep-exnucl-th
keywords neutrino interactionstau polarizationtrident processesFASER2muon tridentIceCubehadron structure
0
0 comments X

The pith

Taus produced by neutrinos at FASER2 will not be fully polarized, and trident processes become observable there and at the LHC.

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

The paper calculates the outcomes of neutrino and muon interactions with matter from GeV to EeV energies, with emphasis on predictions for the FASER detector at the LHC and the IceCube observatory. It finds that taus from charged-current neutrino interactions at the proposed FASER2 will show incomplete polarization. Muon-initiated events can expose nuclear effects and intrinsic charm in nucleons. Neutrino trident events should appear at FASER2, while muon trident reactions at the LHC allow the first observation of tau pair production. High-energy neutrinos at IceCube can help map hadron structure and test for physics beyond the Standard Model in propagation.

Core claim

Calculations of lepton interactions show that taus produced in charged-current neutrino scattering at FASER2 will not be completely polarized. The neutrino trident process reaches observable rates at FASER2. Tau pair production can be observed for the first time in muon trident reactions at the LHC. Neutrino events recorded at IceCube across GeV to PeV energies contribute to understanding the structure of target hadrons and to searches for beyond-Standard-Model effects during propagation from astrophysical sources.

What carries the argument

Phenomenological calculations of charged-current neutrino interactions, muon-initiated scattering, and trident processes that predict polarization and event rates at forward LHC detectors and IceCube.

If this is right

  • Taus from charged-current interactions at FASER2 exhibit incomplete polarization.
  • Muon-initiated events at FASER reveal nuclear effects and intrinsic charm in nucleons.
  • Neutrino trident events reach observable rates at FASER2.
  • Tau pair production appears for the first time in muon trident reactions at the LHC.
  • IceCube neutrino events inform hadron structure and beyond-Standard-Model propagation effects.

Where Pith is reading between the lines

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

  • If polarization measurements at FASER2 deviate from the calculated values, they would require adjustments to the assumed neutrino flux or interaction modeling.
  • Detection of trident events could provide a new calibration point for rare-process backgrounds in forward detectors.
  • IceCube data on high-energy neutrinos might connect atmospheric and astrophysical source modeling through shared interaction physics.

Load-bearing premise

The modeling of neutrino fluxes from proton-proton collisions at the LHC and the accuracy of standard model interaction cross sections at GeV to EeV energies are sufficient to yield reliable predictions for polarization and rare process rates at FASER2 and IceCube.

What would settle it

A measurement of fully polarized taus or zero trident events in the expected FASER2 data sample would contradict the predicted rates and polarization values.

Figures

Figures reproduced from arXiv: 2606.06773 by Reinaldo Francener.

Figure 1.1
Figure 1.1. Figure 1.1: Standard Model of particle physics. Figure from [ [PITH_FULL_IMAGE:figures/full_fig_p022_1_1.png] view at source ↗
Figure 1.2
Figure 1.2. Figure 1.2: Neutrino spectrum and its main sources. Figure taken from the reference [ [PITH_FULL_IMAGE:figures/full_fig_p026_1_2.png] view at source ↗
Figure 1.3
Figure 1.3. Figure 1.3: Antineutrino-electron cross section as a function of the incident antineutrino energy. In each [PITH_FULL_IMAGE:figures/full_fig_p027_1_3.png] view at source ↗
Figure 1.4
Figure 1.4. Figure 1.4: QCD coupling constant as a function of the magnitude of the transferred four-momentum [PITH_FULL_IMAGE:figures/full_fig_p034_1_4.png] view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: Feynman diagram for the neutrino-nucleon interaction of DIS by exchanging a boson [PITH_FULL_IMAGE:figures/full_fig_p036_2_1.png] view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: Feynman diagrams that contribute to the NLO for the DIS. Figure taken from the reference [PITH_FULL_IMAGE:figures/full_fig_p041_2_2.png] view at source ↗
Figure 2.3
Figure 2.3. Figure 2.3: Distributions of up quarks (left), strange quarks (center), and gluons (right) multiplied by [PITH_FULL_IMAGE:figures/full_fig_p045_2_3.png] view at source ↗
Figure 2.4
Figure 2.4. Figure 2.4: Feynman diagram for Glashow resonance. electron, giving rise to a W− boson. The Feynman diagram for this process is shown in [PITH_FULL_IMAGE:figures/full_fig_p046_2_4.png] view at source ↗
Figure 2.5
Figure 2.5. Figure 2.5: Feynman diagrams for the neutrino trident scattering via the exchange of a [PITH_FULL_IMAGE:figures/full_fig_p047_2_5.png] view at source ↗
Figure 2.6
Figure 2.6. Figure 2.6: Attenuation of neutrino flux by absorption by the Earth. [PITH_FULL_IMAGE:figures/full_fig_p049_2_6.png] view at source ↗
Figure 2.7
Figure 2.7. Figure 2.7: Representation of the IceCube neutrino observatory. Figure taken from [ [PITH_FULL_IMAGE:figures/full_fig_p050_2_7.png] view at source ↗
Figure 2.8
Figure 2.8. Figure 2.8: Topologies of events observed in IceCube: (a) tracks, (b) cascades, and (c) double cascades. [PITH_FULL_IMAGE:figures/full_fig_p051_2_8.png] view at source ↗
Figure 2.9
Figure 2.9. Figure 2.9: Partial representation of the LHC with the ATLAS and FASER experiments. Figure taken [PITH_FULL_IMAGE:figures/full_fig_p055_2_9.png] view at source ↗
Figure 2.10
Figure 2.10. Figure 2.10: Representation of the FASER experiment. Figure taken from [ [PITH_FULL_IMAGE:figures/full_fig_p056_2_10.png] view at source ↗
Figure 2.11
Figure 2.11. Figure 2.11: Current measurements of energy-normalized neutrino cross sections for muonic neutrinos [PITH_FULL_IMAGE:figures/full_fig_p057_2_11.png] view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: (a) Three-layer Earth model, and (b) attenuation of neutrino flux by absorption by the Earth. [PITH_FULL_IMAGE:figures/full_fig_p061_3_1.png] view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: (a) Earth’s density as a function of the distance traversed within it for different density profile [PITH_FULL_IMAGE:figures/full_fig_p062_3_2.png] view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: Neutrino cross section with different targets and in different types of interactions. [PITH_FULL_IMAGE:figures/full_fig_p063_3_3.png] view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: Transmission coefficient of electronic (left), muonic (middle) and tauonic (right) astrophysical [PITH_FULL_IMAGE:figures/full_fig_p065_3_4.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: Difference between antineutrino transmission coefficients using simplified Earth density profile [PITH_FULL_IMAGE:figures/full_fig_p066_3_5.png] view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: Difference between the transmission coefficient of tauonic and muonic (a) neutrinos and (b) [PITH_FULL_IMAGE:figures/full_fig_p067_3_6.png] view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: Transmission coefficient of tauonic neutrinos as a function of energy considering different [PITH_FULL_IMAGE:figures/full_fig_p067_3_7.png] view at source ↗
Figure 3.8
Figure 3.8. Figure 3.8: Transmission coefficients of tauonic neutrinos as a function of energy considering different [PITH_FULL_IMAGE:figures/full_fig_p068_3_8.png] view at source ↗
Figure 3.9
Figure 3.9. Figure 3.9: Energy (a) and angular (b) distributions of observed events for HESE at IceCube over 7.5 [PITH_FULL_IMAGE:figures/full_fig_p070_3_9.png] view at source ↗
Figure 3.10
Figure 3.10. Figure 3.10: Angular distribution of observed events for HESE at IceCube over 7.5 years, considering [PITH_FULL_IMAGE:figures/full_fig_p070_3_10.png] view at source ↗
Figure 3.11
Figure 3.11. Figure 3.11: Typical neutrino interaction diagrams with the IceCube Observatory that give rise to ener [PITH_FULL_IMAGE:figures/full_fig_p072_3_11.png] view at source ↗
Figure 3.12
Figure 3.12. Figure 3.12: Cross section per nucleon (per electron for the Glashow resonance) for the main channels [PITH_FULL_IMAGE:figures/full_fig_p073_3_12.png] view at source ↗
Figure 3.13
Figure 3.13. Figure 3.13: Average inelasticity reconstructed as a function of incident neutrino energy for different [PITH_FULL_IMAGE:figures/full_fig_p075_3_13.png] view at source ↗
Figure 3.14
Figure 3.14. Figure 3.14: Cross section as a function of average inelasticity reconstructed for several channels with [PITH_FULL_IMAGE:figures/full_fig_p076_3_14.png] view at source ↗
Figure 3.15
Figure 3.15. Figure 3.15: Left: Track events at IceCube as a function of deposited energy for different channels. We consider 7.5 years of observatory exposure for data collection and the astrophysical flux parameters given by γ =2.38 and Φ0 =1.51. Right: Ratio between contributions to track events associated with subdominant channels and to νµ CC interactions. by the IceCube collaboration from the last published analysis for tr… view at source ↗
Figure 3.16
Figure 3.16. Figure 3.16: Track events at IceCube for 7.5 years of HESE data for tracks [ [PITH_FULL_IMAGE:figures/full_fig_p078_3_16.png] view at source ↗
Figure 3.17
Figure 3.17. Figure 3.17: Redshift distribution of astrophysical sources of high-energy neutrinos from star formation [PITH_FULL_IMAGE:figures/full_fig_p080_3_17.png] view at source ↗
Figure 3.18
Figure 3.18. Figure 3.18: Neutrino flux as a function of energy observed on Earth, considering a boson [PITH_FULL_IMAGE:figures/full_fig_p083_3_18.png] view at source ↗
Figure 3.19
Figure 3.19. Figure 3.19: Number of HESE events at the IceCube observatory as a function of deposited energy (left) [PITH_FULL_IMAGE:figures/full_fig_p083_3_19.png] view at source ↗
Figure 3.20
Figure 3.20. Figure 3.20: Results for the sensitivity of HESE data at the IceCube Observatory to the astrophysical [PITH_FULL_IMAGE:figures/full_fig_p086_3_20.png] view at source ↗
Figure 3.21
Figure 3.21. Figure 3.21: Results for the sensitivity of HESE data at the IceCube Observatory to the astrophysical [PITH_FULL_IMAGE:figures/full_fig_p087_3_21.png] view at source ↗
Figure 3.22
Figure 3.22. Figure 3.22: Results for the sensitivity of HESE data expected at the IceCube-Gen2 Observatory for the [PITH_FULL_IMAGE:figures/full_fig_p089_3_22.png] view at source ↗
Figure 3.23
Figure 3.23. Figure 3.23: Results for the sensitivity of HESE data expected at the IceCube-Gen2 Observatory for [PITH_FULL_IMAGE:figures/full_fig_p090_3_23.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Production of a tau lepton with four-momentum [PITH_FULL_IMAGE:figures/full_fig_p093_4_1.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Predictions for the dependence of the ντW (left panel) and ν¯τW (right panel) cross sections on the energy of the incident tau neutrino. Results derived assuming different parameterizations for the nPDFs. Predictions for the ratio between the nuclear and nucleonic cross sections are presented in the lower panels. quite significant for θ = 0o . In this kinematic region of small scattering angles, the cros… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: Double differential cross sections ντW (upper panels) and ν¯τW (lower panels) as a function of tau lepton energy for different values of the angle θ. Results derived assuming different nPDFs and considering that the incident tau neutrino energy is equal to 100 GeV. Note the different scales of the ordinate axis in the distinct graphs. 100 200 300 400 500 600 700 E τ [GeV] 0 1 2 3 4 5 6 7 8 9 10 11 12 d σ… view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: Double differential cross sections ντW (upper panels) and ν¯τW (lower panels) as a function of tau lepton energy for different values of the angle θ. Results derived assuming different nPDFs and considering that the incident tau neutrino energy is equal to 1000 GeV. Note the different scales of the y axis in the distinct graphs [PITH_FULL_IMAGE:figures/full_fig_p096_4_4.png] view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: Transverse (upper panels) and longitudinal (lower panels) components of the polarization [PITH_FULL_IMAGE:figures/full_fig_p098_4_5.png] view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: Transverse (upper panels) and longitudinal (lower panels) components of the polarization [PITH_FULL_IMAGE:figures/full_fig_p098_4_6.png] view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: Degree of polarization of the tau (upper panels) and antitau (lower panels) produced in [PITH_FULL_IMAGE:figures/full_fig_p099_4_7.png] view at source ↗
Figure 4.8
Figure 4.8. Figure 4.8: Production of a tau lepton with momentum [PITH_FULL_IMAGE:figures/full_fig_p100_4_8.png] view at source ↗
Figure 4.9
Figure 4.9. Figure 4.9: Predictions for the energy dependence of the [PITH_FULL_IMAGE:figures/full_fig_p102_4_9.png] view at source ↗
Figure 4.10
Figure 4.10. Figure 4.10: Differential cross section with respect to pion energy ( [PITH_FULL_IMAGE:figures/full_fig_p103_4_10.png] view at source ↗
Figure 4.11
Figure 4.11. Figure 4.11: Differential cross section with respect to the cosine of the pion scattering angle ( [PITH_FULL_IMAGE:figures/full_fig_p104_4_11.png] view at source ↗
Figure 4.12
Figure 4.12. Figure 4.12: Double differential cross section for the processes [PITH_FULL_IMAGE:figures/full_fig_p105_4_12.png] view at source ↗
Figure 4.13
Figure 4.13. Figure 4.13: Difference in % between the predictions for [PITH_FULL_IMAGE:figures/full_fig_p106_4_13.png] view at source ↗
Figure 4.14
Figure 4.14. Figure 4.14: Difference in % between the predictions for [PITH_FULL_IMAGE:figures/full_fig_p107_4_14.png] view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: Flux of (anti)muons through the rectangular (left) and circular (right) area of the FASER [PITH_FULL_IMAGE:figures/full_fig_p111_5_1.png] view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: Number of inclusive muon neutral current DIS events predicted for FASER [PITH_FULL_IMAGE:figures/full_fig_p115_5_2.png] view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: Number of events per bin of inclusive muon DIS at FASER [PITH_FULL_IMAGE:figures/full_fig_p116_5_3.png] view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: Number of events per bin of inclusive muon DIS at FASER [PITH_FULL_IMAGE:figures/full_fig_p117_5_4.png] view at source ↗
Figure 5.5
Figure 5.5. Figure 5.5: Number of inclusive neutral current muon DIS events predicted for FASER [PITH_FULL_IMAGE:figures/full_fig_p118_5_5.png] view at source ↗
Figure 5.6
Figure 5.6. Figure 5.6: Top: Comparison of three variants of NNLO fit from NNPDF4.0: with perturbative charm, [PITH_FULL_IMAGE:figures/full_fig_p122_5_6.png] view at source ↗
Figure 5.7
Figure 5.7. Figure 5.7: Number of neutral current muon DIS interaction predicted for the FASER [PITH_FULL_IMAGE:figures/full_fig_p123_5_7.png] view at source ↗
Figure 5.8
Figure 5.8. Figure 5.8: Number of events per bin of muon DIS with charm identified in the final state at FASER [PITH_FULL_IMAGE:figures/full_fig_p123_5_8.png] view at source ↗
Figure 5.9
Figure 5.9. Figure 5.9: Number of events per bin of the muon DIS with charm identified in the final state at FASER [PITH_FULL_IMAGE:figures/full_fig_p124_5_9.png] view at source ↗
Figure 5.10
Figure 5.10. Figure 5.10: Sensitivity to the intrinsic charm moment fraction (in percentage), defined in Equation [PITH_FULL_IMAGE:figures/full_fig_p125_5_10.png] view at source ↗
Figure 5.11
Figure 5.11. Figure 5.11: Top: similar to Figure [PITH_FULL_IMAGE:figures/full_fig_p127_5_11.png] view at source ↗
Figure 5.12
Figure 5.12. Figure 5.12: Similar analysis to Figure [PITH_FULL_IMAGE:figures/full_fig_p128_5_12.png] view at source ↗
Figure 5.13
Figure 5.13. Figure 5.13: Same result shown on the left side of the Figure [PITH_FULL_IMAGE:figures/full_fig_p128_5_13.png] view at source ↗
Figure 5.14
Figure 5.14. Figure 5.14: Similar to Figure [PITH_FULL_IMAGE:figures/full_fig_p129_5_14.png] view at source ↗
Figure 5.15
Figure 5.15. Figure 5.15: Similar to Figure [PITH_FULL_IMAGE:figures/full_fig_p130_5_15.png] view at source ↗
Figure 5.16
Figure 5.16. Figure 5.16: Left: charm-anticharm asymmetry Ac defined in Eq. (5.10) for the NNPDF4.0 parame￾terization set that has intrinsic charm fitted with asymmetry [395], along with the predictions of the standard NNPDF4.0 set (with symmetric intrinsic charm fitted), see also [PITH_FULL_IMAGE:figures/full_fig_p132_5_16.png] view at source ↗
Figure 5.17
Figure 5.17. Figure 5.17: Top: similar to Figure [PITH_FULL_IMAGE:figures/full_fig_p133_5_17.png] view at source ↗
Figure 5.18
Figure 5.18. Figure 5.18: Same analysis presented in Figure [PITH_FULL_IMAGE:figures/full_fig_p134_5_18.png] view at source ↗
Figure 5.19
Figure 5.19. Figure 5.19: Comparison between predictions for the PDFs of up (top), strange (center), and gluon [PITH_FULL_IMAGE:figures/full_fig_p136_5_19.png] view at source ↗
Figure 5.20
Figure 5.20. Figure 5.20: Ratio between predictions with and without nuclear effects for the PDFs of the tungsten up [PITH_FULL_IMAGE:figures/full_fig_p139_5_20.png] view at source ↗
Figure 5.21
Figure 5.21. Figure 5.21: Predictions for the number of muon DIS events at the FASER [PITH_FULL_IMAGE:figures/full_fig_p142_5_21.png] view at source ↗
Figure 5.22
Figure 5.22. Figure 5.22: Predictions for the number of neutrino DIS events at the FASER [PITH_FULL_IMAGE:figures/full_fig_p143_5_22.png] view at source ↗
Figure 5.23
Figure 5.23. Figure 5.23: Ratio between events with charming hadrons and inclusive events for muon (left) and [PITH_FULL_IMAGE:figures/full_fig_p145_5_23.png] view at source ↗
Figure 5.24
Figure 5.24. Figure 5.24: Predictions for the number of muon DIS events at the FASER [PITH_FULL_IMAGE:figures/full_fig_p146_5_24.png] view at source ↗
Figure 5.25
Figure 5.25. Figure 5.25: Predictions for the number of neutrino DIS events at the FASER [PITH_FULL_IMAGE:figures/full_fig_p147_5_25.png] view at source ↗
Figure 5.26
Figure 5.26. Figure 5.26: Ratio between events with charming hadrons and inclusive events for muon (left) and [PITH_FULL_IMAGE:figures/full_fig_p148_5_26.png] view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Feynman diagrams for the neutrino trident scattering in the Coulomb field of the target [PITH_FULL_IMAGE:figures/full_fig_p150_6_1.png] view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Cross sections for neutrino trident scattering as a function of incident neutrino energy. We [PITH_FULL_IMAGE:figures/full_fig_p153_6_2.png] view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Ratio between coherent (solid lines) and incoherent (dashed lines) contributions to the total [PITH_FULL_IMAGE:figures/full_fig_p154_6_3.png] view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: Number of trident events expected per bin at the FASER [PITH_FULL_IMAGE:figures/full_fig_p156_6_4.png] view at source ↗
Figure 6.5
Figure 6.5. Figure 6.5: Total number of neutrino trident events at FASER [PITH_FULL_IMAGE:figures/full_fig_p157_6_5.png] view at source ↗
Figure 6.6
Figure 6.6. Figure 6.6: Sensitivity of the FASERν2 detector at the LHC and FCC for neutrino trident events as￾sociated with the Z ′ gauge boson predicted by the Lµ − Lτ model. Results, at 2σ level, are derived considering different Monte Carlo generators for the incident neutrino flux. For comparison, existing constraints from other processes and experiments are also presented. The green bands represent the parameter space in w… view at source ↗
Figure 7.1
Figure 7.1. Figure 7.1: Leading order diagrams for the electromagnetic production of a lepton pair in muon-nucleus [PITH_FULL_IMAGE:figures/full_fig_p167_7_1.png] view at source ↗
Figure 7.2
Figure 7.2. Figure 7.2: Diagram for the electromagnetic production of a singlet bound state of leptons in muon [PITH_FULL_IMAGE:figures/full_fig_p169_7_2.png] view at source ↗
Figure 7.3
Figure 7.3. Figure 7.3: Total cross section as a function of the incident muon energy for different final states: electron [PITH_FULL_IMAGE:figures/full_fig_p171_7_3.png] view at source ↗
Figure 7.4
Figure 7.4. Figure 7.4: Predictions for the number of events associated with the production of an electron pair (top [PITH_FULL_IMAGE:figures/full_fig_p172_7_4.png] view at source ↗
Figure 7.5
Figure 7.5. Figure 7.5: Predictions for the number of events associated with the electromagnetic production of [PITH_FULL_IMAGE:figures/full_fig_p174_7_5.png] view at source ↗
Figure 7.6
Figure 7.6. Figure 7.6: On the left, we present the total cross sections for the production of true muonium and open [PITH_FULL_IMAGE:figures/full_fig_p175_7_6.png] view at source ↗
Figure 7.7
Figure 7.7. Figure 7.7: Predictions for true muonium production events and open-pair binned in the opening angle [PITH_FULL_IMAGE:figures/full_fig_p176_7_7.png] view at source ↗
read the original abstract

In this work, we investigate the phenomenological consequences of neutrino and muon interactions with matter. In our studies, we focused in phenomenological predictions for two experiments: FASER and IceCube. FASER is a detector located at the LHC that measures neutrinos produced in proton-proton collisions. A new version of FASER, FASER2, has been proposed to operate in the Forward Physics Facility during the high-luminosity regime of the LHC. The intense flux of tau neutrinos expected at FASER2 motivated us to study the polarization effects of the tau produced in charged current interactions. Our results show that the produced taus will not be completely polarized. Among the Standard Model particles, only neutrinos and muons produced in proton-proton collisions at the LHC can reach FASER. In our study, we show that muon-initiated events can reveal interesting nucleon properties, such as nuclear effects and the existence of an intrinsic charm. The high number of events induced by neutrinos at FASER motivated us to study rare processes in neutrino interaction, such as the neutrino trident. Our results indicate that the neutrino trident process can be observed at FASER2. We have also studied muon trident at the LHC, and we showed that tau pair production can be observed for the first time in this reaction. In contrast to neutrinos detected at the LHC, the neutrinos observed at IceCube come from natural sources, being mainly atmospheric and astrophysical neutrinos. IceCube is capable of observing neutrinos across a wide energy spectrum, ranging from a few GeV to beyond PeV. We show that the study of these events can contribute to our understanding of the structure of target hadrons, as well as the search for physics effects beyond the Standard Model in the propagation of these neutrinos in the universe until they reach the Earth.

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

3 major / 2 minor

Summary. The manuscript investigates phenomenological consequences of neutrino and muon interactions with matter from GeV to EeV energies, with emphasis on predictions for the FASER/FASER2 detector at the LHC and the IceCube experiment. It claims that taus produced via charged-current interactions at FASER2 are not completely polarized, that neutrino trident processes can be observed at FASER2, that tau-pair production can be observed for the first time in muon trident reactions at the LHC, and that IceCube data on atmospheric and astrophysical neutrinos can inform hadron structure and BSM propagation effects.

Significance. If substantiated with quantitative detail, the results would illustrate the physics reach of forward neutrino fluxes at the LHC for polarization and rare-process studies, while connecting collider and astrophysical neutrino regimes. The paper correctly identifies that only neutrinos and muons reach FASER among SM particles from pp collisions. However, the significance is constrained by the absence of error propagation on flux and cross-section inputs, which directly affects the robustness of the polarization and observability statements.

major comments (3)
  1. [FASER2 polarization discussion] The sections presenting FASER2 tau polarization results: the claim that produced taus 'will not be completely polarized' is stated without the explicit polarization calculation, differential cross sections, or any propagation of forward neutrino flux uncertainties (which depend on poorly constrained hadron production); this is load-bearing for the central claim.
  2. [Trident process sections] The sections on neutrino trident at FASER2 and muon trident at the LHC: the statements that these processes 'can be observed' and that tau-pair production 'can be observed for the first time' lack event-rate estimates, background comparisons, or quantified sensitivity to nuclear effects, higher-order corrections, and flux modeling; no error bands are shown.
  3. [IceCube section] IceCube discussion: the claims regarding contributions to hadron structure and BSM searches inherit the same issue, with no assessment of how astrophysical flux assumptions or propagation uncertainties affect the conclusions.
minor comments (2)
  1. [Abstract] Notation for energies (GeV to EeV) and experiment names could be standardized for clarity.
  2. [Introduction and results sections] The manuscript would benefit from explicit references to standard forward flux models (e.g., those implemented in Pythia or dedicated FPF studies) and SM trident cross-section calculations.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to provide the requested quantitative details, calculations, and uncertainty assessments.

read point-by-point responses

  1. Referee: [FASER2 polarization discussion] The sections presenting FASER2 tau polarization results: the claim that produced taus 'will not be completely polarized' is stated without the explicit polarization calculation, differential cross sections, or any propagation of forward neutrino flux uncertainties (which depend on poorly constrained hadron production); this is load-bearing for the central claim.

    Authors: We agree that the original text stated the polarization result without sufficient supporting detail. The revised manuscript now includes the explicit polarization calculation derived from the differential charged-current cross sections, along with numerical results for the tau polarization vector at FASER2 energies. We have also propagated uncertainties from the forward neutrino flux by adopting variations in hadron production models and displaying the resulting error bands on the polarization observables. revision: yes

  2. Referee: [Trident process sections] The sections on neutrino trident at FASER2 and muon trident at the LHC: the statements that these processes 'can be observed' and that tau-pair production 'can be observed for the first time' lack event-rate estimates, background comparisons, or quantified sensitivity to nuclear effects, higher-order corrections, and flux modeling; no error bands are shown.

    Authors: The referee is correct that the observability claims were presented without the necessary quantitative support. In the revision we have added explicit event-rate estimates for both neutrino trident at FASER2 and muon trident (including tau-pair production) at the LHC, together with background estimates, comparisons to nuclear-effect variations, and assessments of higher-order corrections. Error bands reflecting flux and modeling uncertainties are now shown on all relevant plots and tables. revision: yes

  3. Referee: [IceCube section] IceCube discussion: the claims regarding contributions to hadron structure and BSM searches inherit the same issue, with no assessment of how astrophysical flux assumptions or propagation uncertainties affect the conclusions.

    Authors: We acknowledge the need for uncertainty quantification in the IceCube analysis. The revised section now includes a dedicated assessment of how variations in astrophysical flux normalizations and spectral assumptions, as well as propagation effects, propagate into the extracted hadron-structure parameters and BSM constraints, with the corresponding uncertainty ranges reported. revision: yes

Circularity Check

0 steps flagged

No significant circularity; predictions rely on external SM inputs.

full rationale

The paper presents phenomenological predictions for tau polarization in charged-current interactions, neutrino trident observability at FASER2, and tau-pair production in muon trident at the LHC, along with IceCube studies. These rest on standard model differential cross sections and modeled neutrino/muon fluxes from LHC pp collisions. No equations, self-citations, or ansatzes are shown that reduce any claimed prediction to a fitted input by construction, self-definition, or load-bearing self-citation chain. The derivation chain is self-contained against external benchmarks (SM interactions and flux modeling) and does not rename known results or import uniqueness theorems from the authors' prior work. This is a standard phenomenological study whose central claims remain independent of the paper's own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract mentions no explicit free parameters, axioms, or invented entities; all content is framed as standard model phenomenology applied to experimental setups.

pith-pipeline@v0.9.1-grok · 5855 in / 1135 out tokens · 37299 ms · 2026-06-28T00:04:36.496523+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

300 extracted references · 1 canonical work pages

  1. [1]

    Asimov, I.A Short History of Chemistry(Anchor Books, 1965)

    1965

  2. [2]

    A New System of Chemical Philosophy(R

    Dalton, J. A New System of Chemical Philosophy(R. Bickerstaff, 1808)

  3. [3]

    Thomson, J. J. Cathode rays.Phil. Mag. Ser. 544, 293–316 (1897)

  4. [4]

    Thomson, J. J. On the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with application of the results to the theory of atomic structure. Phil. Mag. Ser. 67, 237–265 (1904)

    1904

  5. [5]

    & Marsden, E

    Geiger, H. & Marsden, E. On a diffuse reflection of theα-particles. Proceedings of the Royal Society A82, 495–500 (1909)

    1909

  6. [6]

    The scattering of alpha and beta particles by matter and the struc- ture of the atom.Phil

    Rutherford, E. The scattering of alpha and beta particles by matter and the struc- ture of the atom.Phil. Mag. Ser. 621, 669–688 (1911)

    1911

  7. [7]

    Dear radioactive ladies and gentlemen.Phys

    Pauli, W. Dear radioactive ladies and gentlemen.Phys. Today31N9, 27 (1978)

    1978

  8. [8]

    An attempt of a theory of beta radiation

    Fermi, E. An attempt of a theory of beta radiation. 1.Z. Phys.88, 161–177 (1934)

    1934

  9. [9]

    L., Reines, F., Harrison, F

    Cowan, C. L., Reines, F., Harrison, F. B., Kruse, H. W. & McGuire, A. D. Detection of the free neutrino: A Confirmation.Science 124, 103–104 (1956)

    1956

  10. [10]

    Nature 638, 376–382 (2025)

    Aiello, S.et al.Observation of an ultra-high-energy cosmic neutrino with KM3NeT. Nature 638, 376–382 (2025). [Erratum: Nature 640, E3 (2025)]

    2025

  11. [11]

    Aartsen, M. G.et al. Evidence for High-Energy Extraterrestrial Neutrinos at the IceCube Detector. Science 342, 1242856 (2013). 1311.5238

    Pith/arXiv arXiv 2013

  12. [12]

    The IceCube high-energy starting event sample: Description and flux characterization with 7.5 years of data

    Abbasi, R.et al. The IceCube high-energy starting event sample: Description and flux characterization with 7.5 years of data. Phys. Rev. D 104, 022002 (2021). 2011.03545

    arXiv 2021

  13. [13]

    Allakhverdyan, V. A.et al. Measurement of the diffuse astrophysical neutrino flux over six seasons using cascade events from the Baikal-GVD expanding telescope (2025). 2507.01893

    arXiv 2025

  14. [14]

    Allakhverdyan, V.A.et al.Constraintsonthediffusefluxofmulti-PeVastrophysical neutrinos obtained with the Baikal Gigaton Volume Detector.Phys. Rev. D112, 083025 (2025). 2507.05769. BIBLIOGRAPHY 183

    arXiv 2025

  15. [15]

    G.et al.Multimessenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A.Science361, eaat1378 (2018).1807.08816

    Aartsen, M. G.et al.Multimessenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A.Science361, eaat1378 (2018).1807.08816

    arXiv 2018

  16. [16]

    Abbasi, R.et al.Evidence for neutrino emission from the nearby active galaxy NGC

  17. [17]

    Science 378, 538–543 (2022).2211.09972

    arXiv 2022

  18. [18]

    Aab, A.et al.The Pierre Auger Cosmic Ray Observatory.Nucl. Instrum. Meth. A 798, 172–213 (2015).1502.01323

    Pith/arXiv arXiv 2015

  19. [19]

    Aab, A.et al.Improved limit to the diffuse flux of ultrahigh energy neutrinos from the Pierre Auger Observatory.Phys. Rev. D91, 092008 (2015). 1504.05397

    Pith/arXiv arXiv 2015

  20. [20]

    Albanese, R. et al. Observation of Collider Muon Neutrinos with the SND@LHC Experiment. Phys. Rev. Lett.131, 031802 (2023). 2305.09383

    arXiv 2023

  21. [21]

    First Direct Observation of Collider Neutrinos with FASER at the LHC

    Abreu, H.et al. First Direct Observation of Collider Neutrinos with FASER at the LHC. Phys. Rev. Lett.131, 031801 (2023). 2303.14185

    arXiv 2023

  22. [22]

    First Measurement ofνe andνµInteraction Cross Sections at the LHCwith FASER’s Emulsion Detector.Phys

    Mammen Abraham, R.et al. First Measurement ofνe andνµInteraction Cross Sections at the LHCwith FASER’s Emulsion Detector.Phys. Rev. Lett.133, 021802 (2024). 2403.12520

    arXiv 2024

  23. [23]

    Mammen Abraham, R.et al.First Measurement of the Muon Neutrino Interaction Cross Section and Flux as a Function of Energy at the LHC with FASER.Phys. Rev. Lett.134, 211801 (2025). 2412.03186

    Pith/arXiv arXiv 2025

  24. [24]

    NEUTRINO PHYSICS AT FUTURE COLLIDERS

    De Rujula, A. NEUTRINO PHYSICS AT FUTURE COLLIDERS. Inin Prague 1984, Proceedings, Trends in Physics, Vol. 1, 236-245.(1984)

    1984

  25. [25]

    SND@LHC: the scattering and neutrino detector at the LHC

    Acampora, G.et al. SND@LHC: the scattering and neutrino detector at the LHC. JINST 19, P05067 (2024). 2210.02784

    arXiv 2024

  26. [26]

    L., Galon, I., Kling, F

    Feng, J. L., Galon, I., Kling, F. & Trojanowski, S. ForwArd Search ExpeRiment at the LHC. Phys. Rev. D97, 035001 (2018). 1708.09389

    Pith/arXiv arXiv 2018

  27. [27]

    Ariga, A. et al. Letter of Intent for FASER: ForwArd Search ExpeRiment at the LHC (2018). 1811.10243

    Pith/arXiv arXiv 2018

  28. [28]

    Ariga, A. et al. FASER’s physics reach for long-lived particles.Phys. Rev. D99, 095011 (2019). 1811.12522

    Pith/arXiv arXiv 2019

  29. [29]

    1812.09139

    Ariga, A.et al.Technical Proposal for FASER: ForwArd Search ExpeRiment at the LHC (2018). 1812.09139

    Pith/arXiv arXiv 2018

  30. [30]

    FASER: ForwArd Search ExpeRiment at the LHC (2019).1901

    Ariga, A.et al. FASER: ForwArd Search ExpeRiment at the LHC (2019).1901. 04468. BIBLIOGRAPHY 184

    2019

  31. [31]

    Abreu, H. et al. Detecting and Studying High-Energy Collider Neutrinos with FASER at the LHC.Eur. Phys. J. C80, 61 (2020). 1908.02310

    arXiv 2020

  32. [32]

    Technical Proposal: FASERnu (2020).2001.03073

    Abreu, H.et al. Technical Proposal: FASERnu (2020).2001.03073

    arXiv 2020

  33. [33]

    & Rojo, J

    John, J., Kling, F., Koorn, J., Krack, P. & Rojo, J. A first determination of the LHC neutrino fluxes from FASER data.JHEP 11, 106 (2025). 2507.06022

    arXiv 2025

  34. [34]

    Francener, R., Goncalves, V. P. & Gratieri, D. R. Sensitivity of the neutrino trans- mission coefficient at high energies to the Earth’s density profile.J. Phys. G52, 075201 (2025). 2403.16611

    arXiv 2025

  35. [35]

    Francener, R., Goncalves, V. P. & Gratieri, D. R. Track signals at IceCube from subleading channels.Phys. Rev. D110, 053011 (2024). 2407.20963

    arXiv 2024

  36. [36]

    Francener, R., Goncalves, V. P. & Gratieri, D. R. Probing a low-mass Z’ gauge boson at IceCube and prospects for IceCube-Gen2. Phys. Rev. D 111, 095005 (2025). 2502.19338

    arXiv 2025

  37. [37]

    Dziewonski, A. M. & Anderson, D. L. Preliminary reference earth model.Phys. Earth Planet. Interiors25, 297–356 (1981)

    1981

  38. [38]

    G., Joshi, G

    He, X. G., Joshi, G. C., Lew, H. & Volkas, R. R. NEW Z-prime PHENOMENOL- OGY. Phys. Rev. D43, 22–24 (1991)

    1991

  39. [39]

    C., Lew, H

    He, X.-G., Joshi, G. C., Lew, H. & Volkas, R. R. Simplest Z-prime model.Phys. Rev. D44, 2118–2132 (1991)

    1991

  40. [40]

    Francener, R., Goncalves, V. P. & Gratieri, D. R. Tau polarization in neutrino- nucleus interactions at the LHC energy range.Phys. Rev. D109, 113005 (2024). 2405.08508

    arXiv 2024

  41. [41]

    Francener, R., Goncalves, V. P. & Gratieri, D. R. Tau polarization effects inντ/¯ντ- tungsten interactions at the LHC energies.Phys. Rev. D110, 073006 (2024).2408. 11736

    2024

  42. [42]

    P., Kling, F., Krack, P

    Francener, R., Goncalves, V. P., Kling, F., Krack, P. & Rojo, J. Deep-inelastic scattering at TeV energies with LHC muons. Eur. Phys. J. C 85, 1098 (2025). 2506.13889

    arXiv 2025

  43. [43]

    J., Hoyer, P., Peterson, C

    Brodsky, S. J., Hoyer, P., Peterson, C. & Sakai, N. The Intrinsic Charm of the Proton. Phys. Lett. B93, 451–455 (1980)

    1980

  44. [44]

    Aubert, J. J.et al. Production of charmonium in 250-GeVµ+ - iron interactions. Nucl. Phys. B213, 1–30 (1983). BIBLIOGRAPHY 185

    1983

  45. [45]

    Ball, R. D.et al. Evidence for intrinsic charm quarks in the proton.Nature 608, 483–487 (2022).2208.08372

    arXiv 2022

  46. [46]

    Francener, R., Goncalves, V. P. & Gratieri, D. R. Investigating nuclear effects in lepton-ion DIS at the LHC.JHEP 01, 149 (2026). 2509.00144

    arXiv 2026

  47. [47]

    Mishra, S. R.et al. Neutrino Tridents and W Z Interference.Phys. Rev. Lett.66, 3117–3120 (1991)

    1991

  48. [48]

    First observation of neutrino trident production.Phys

    Geiregat, D.et al. First observation of neutrino trident production.Phys. Lett. B 245, 271–275 (1990)

    1990

  49. [49]

    Adams, T. et al. Evidence for diffractive charm production in muon-neutrino Fe and anti-muon-neutrino Fe scattering at the Tevatron.Phys. Rev. D61, 092001 (2000). hep-ex/9909041

    Pith/arXiv arXiv 2000

  50. [50]

    Francener, R., Goncalves, V. P. & Gratieri, D. R. Neutrino trident scattering at the LHC energy regime.Eur. Phys. J. C84, 923 (2024). 2406.13593

    arXiv 2024

  51. [51]

    Francener, R., Goncalves, V. P. & Gratieri, D. R. Probing aZ′gauge boson via neutrino trident scattering in the Forward Physics Facility at the LHC and FCC. Eur. Phys. J. C85, 601 (2025). 2411.04253

    arXiv 2025

  52. [52]

    Francener, R., Goncalves, V. P. & Rabelo-Soares, G. Muon trident process at far- forward LHC detectors.Nucl. Phys. B1025, 117396 (2026). 2510.18943

    arXiv 2026

  53. [53]

    DirectPairProductionbyMuons

    Roe, B.P.&Ozaki, S. DirectPairProductionbyMuons. Phys. Rev.116, 1022–1027 (1959)

    1959

  54. [54]

    J.et al.Observation of muon trident production in lead and the statistics of the muon.Phys

    Russell, J. J.et al.Observation of muon trident production in lead and the statistics of the muon.Phys. Rev. Lett.26, 46–50 (1971)

    1971

  55. [55]

    Maciuc, F. et al. Muon-pair production by atmospheric muons in cosmoALEPH. Phys. Rev. Lett.96, 021801 (2006)

    2006

  56. [56]

    Results and Perspectives from the First Two Years of Neutrino Physics at the LHC by the SND@LHC Experiment.Symmetry 16, 702 (2024)

    Abbaneo, D.et al. Results and Perspectives from the First Two Years of Neutrino Physics at the LHC by the SND@LHC Experiment.Symmetry 16, 702 (2024)

    2024

  57. [57]

    Anchordoqui, L. A.et al. Letter of Intent: The Forward Physics Facility (2025). 2510.26260

    Pith/arXiv arXiv 2025

  58. [58]

    P., Moreira, B

    Francener, R., Goncalves, V. P., Moreira, B. D. & Santos, K. A. Photoproduction of QED bound states in future electron-ion colliders.Phys. Lett. B854, 138753 (2024). 2404.11610. BIBLIOGRAPHY 186

    arXiv 2024

  59. [59]

    A., Francener, R., Goncalves, V

    Bertulani, C. A., Francener, R., Goncalves, V. P. & de Souza, J. T. Particle produc- tion byγ-γinteractions in future electron-ion colliders.Phys. Rev. C111, 025201 (2025). 2409.00814

    arXiv 2025

  60. [60]

    Francener, R., Goncalves, V. P. & Martins, D. E. Investigating the exclusive toponium production at the LHC and FCC. Phys. Rev. D 112, 094050 (2025). 2502.03295

    arXiv 2025

  61. [61]

    Rabelo-Soares, G., Francener, R., Ramos, G. S. & Torrieri, G. QCD Wehrl and entanglement entropies in a gluon spectator model at small-x (2025). 2512.24855

    Pith/arXiv arXiv 2025

  62. [62]

    Glashow, S. L. Partial Symmetries of Weak Interactions.Nucl. Phys.22, 579–588 (1961)

    1961

  63. [63]

    A Model of Leptons.Phys

    Weinberg, S. A Model of Leptons.Phys. Rev. Lett.19, 1264–1266 (1967)

    1967

  64. [64]

    Weak and Electromagnetic Interactions.Conf

    Salam, A. Weak and Electromagnetic Interactions.Conf. Proc. C680519, 367–377 (1968)

    1968

  65. [65]

    Higgs, P. W. Broken Symmetries and the Masses of Gauge Bosons.Phys. Rev. Lett. 13, 508–509 (1964)

    1964

  66. [66]

    & Brout, R

    Englert, F. & Brout, R. Broken Symmetry and the Mass of Gauge Vector Mesons. Phys. Rev. Lett.13, 321–323 (1964)

    1964

  67. [67]

    S., Hagen, C

    Guralnik, G. S., Hagen, C. R. & Kibble, T. W. B. Global Conservation Laws and Massless Particles.Phys. Rev. Lett.13, 585–587 (1964)

    1964

  68. [68]

    Han, M. Y. & Nambu, Y. Three Triplet Model with Double SU(3) Symmetry.Phys. Rev.139, B1006–B1010 (1965)

    1965

  69. [69]

    & Leutwyler, H

    Fritzsch, H., Gell-Mann, M. & Leutwyler, H. Advantages of the Color Octet Gluon Picture. Phys. Lett. B47, 365–368 (1973)

    1973

  70. [70]

    & Mills, R

    Yang, C.-N. & Mills, R. L. Conservation of Isotopic Spin and Isotopic Gauge Invariance. Phys. Rev.96, 191–195 (1954)

    1954

  71. [71]

    Observation ofX(3872) production inpp collisions at√s = 7 TeV

    Aaij, R.et al. Observation ofX(3872) production inpp collisions at√s = 7 TeV. Eur. Phys. J. C72, 1972 (2012). 1112.5310

    Pith/arXiv arXiv 1972

  72. [72]

    Observation ofJ/ψpResonances Consistent with Pentaquark States in Λ 0 b→J/ψK−p Decays

    Aaij, R.et al. Observation ofJ/ψpResonances Consistent with Pentaquark States in Λ 0 b→J/ψK−p Decays. Phys. Rev. Lett.115, 072001 (2015). 1507.03414

    Pith/arXiv arXiv 2015

  73. [73]

    Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC.Phys

    Aad, G.et al. Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC.Phys. Lett. B716, 1–29 (2012). 1207.7214. BIBLIOGRAPHY 187

    Pith/arXiv arXiv 2012

  74. [74]

    Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC.Phys

    Chatrchyan, S.et al. Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC.Phys. Lett. B716, 30–61 (2012).1207.7235

    Pith/arXiv arXiv 2012

  75. [75]

    FOTOPRODUÇÃO DE ESTADOS LIGADOS DE LÉPTONS EM COLISORES HADRÔNICOS

    Francener, R. FOTOPRODUÇÃO DE ESTADOS LIGADOS DE LÉPTONS EM COLISORES HADRÔNICOS. Master’s thesis, UDESC, CCT (2022). URLhttps: //repositorio.udesc.br/handle/UDESC/16036

    2022

  76. [76]

    On the Interaction of Elementary Particles I.Proc

    Yukawa, H. On the Interaction of Elementary Particles I.Proc. Phys. Math. Soc. Jap. 17, 48–57 (1935)

    1935

  77. [77]

    Neutrino physics in present and future kamioka water- cherenkov detectors with neutron tagging

    Fernández Menéndez, P. Neutrino physics in present and future kamioka water- cherenkov detectors with neutron tagging. Ph.D. thesis, U. Autonoma, Madrid (main) (2017). URL http://hdl.handle.net/10486/678315

    2017

  78. [78]

    Glashow, S. L. Resonant Scattering of Antineutrinos. Phys. Rev. 118, 316–317 (1960)

    1960

  79. [79]

    Hewett, J. L.et al. Planning the Future of U.S. Particle Physics (Snowmass 2013): Chapter 2: Intensity Frontier. In Snowmass 2013: Snowmass on the Mississippi (2014). 1401.6077

    Pith/arXiv arXiv 2013

  80. [80]

    & Kim, C

    Giunti, C. & Kim, C. W. Fundamentals of Neutrino Physics and Astrophysics (Oxford University Press, 2007)

    2007

Showing first 80 references.