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REVIEW 2 major objections 5 minor 37 references

A new calculation of Earth-skimming very- and ultra-high energy tau neutrinos

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

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Pith's one-line read The paper calculates end-to-end how often Earth-skimming tau neutrinos yield detectable upward air showers for a POEMMA-like satellite, finding an effective aperture near 1 km² sr at $10^9$ GeV with 30–40% model uncertainty.

desk verdict A workmanlike proceedings calculation of POEMMA's tau-neutrino sensitivity that is genuinely new as a curve set, but the absolute aperture hangs on shower-detection modeling deferred to companion papers and excluded from the quoted uncertainty band. read the letter →

arxiv 1908.03603 v1 pith:RLQDWRQ4 submitted 2019-08-09 astro-ph.HE

Mary Hall Reno , Tonia M. Venters , John F. Krizmanic , Luis A. Anchordoqui , Claire Guepin , Angela V. Olinto (for the POEMMA Collaboration) This is my paper · ORCID
classification astro-ph.HE
keywords tauneutrinosEarth-skimmingultra-highenergyPOEMMAeffectiveaperturelossairCherenkovdetectiondiffuseneutrinoflux
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 sets out a new end-to-end calculation of the signal that would let a space-based telescope detect tau neutrinos by using the Earth as a neutrino converter: a tau neutrino charged-current interaction inside the Earth produces a tau, the tau escapes and decays in the atmosphere, and the resulting upward air shower emits Cherenkov light that the satellite sees. The paper's central quantitative claim is that for a diffuse flux, a POEMMA-like detector in full-sky-scanning mode reaches an effective aperture of roughly 1 km² sr at $10^9$ GeV, with a 30–40% spread coming from the high-energy extrapolations of the neutrino-nucleon cross section and the tau's electromagnetic energy loss. From that aperture, it derives five-year diffuse-flux sensitivities and transient-burst sensitivities, and shows which existing limits and which model fluxes those sensitivities beat. The calculation matters because it identifies the channel—upward tau air showers—as the one through which proposed space-based missions can realistically open the very- and ultra-high-energy neutrino sky.

What carries the argument

The load-bearing object is the observation-probability differential $dP_{\rm obs} = ds'\, P_{\rm exit}(E_{\nu_\tau},\theta_{\rm tr})\, p_{\rm decay}(s')\, P_{\rm det}(E_{\nu_\tau},\theta_v,\theta_{\rm tr},s')$, integrated over the visible surface patch and the trigger solid angle to give the effective aperture $\langle A\Omega\rangle(E_{\nu_\tau}) = \int dP_{\rm obs}\, \hat{r}\cdot\hat{n}\, dS\, d\Omega_{\rm tr}$. Here $P_{\rm exit}$ encodes the neutrino charged-current conversion and tau energy loss in the Earth, $p_{\rm decay}$ is the tau decay probability along the path, and $P_{\rm det}$ encodes the Cherenkov geometry and photoelectron count: the tau decay must fall within the effective Cherenkov cone, $\theta_{\rm Ch}^{\rm eff}\sim 1.5^\circ$, and the shower, whose energy is taken as half the tau energy, must produce at least 10 photoelectrons in POEMMA's 2.5 m² effective optical aperture. The uncertainty band in the result is generated by switching among the ALLM and BDHM parameterizations of tau electromagnetic energy loss and the associated high-energy neutrino cross-section extrapolations. This machinery is what turns an assumed neutrino flux into a predicted rate of upward air showers.

What would settle it

Compare the photon-density and effective-Cherenkov-angle model against calibrated measurements of Cherenkov light from air showers of known energy and geometry; on the observational side, a detected diffuse flux of Earth-skimming tau neutrinos whose inferred rate disagrees with the predicted effective aperture by more than the quoted uncertainty band would falsify the sensitivity calculation.

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Extended reading notes

Core claim

The paper's central claim is a new calculation of tau exit probabilities $P_{\rm exit}$ and detection probabilities $P_{\rm det}$ for Earth-skimming tau neutrinos, folded into an effective aperture and effective area for the POEMMA mission concept. With the standard charged-current neutrino interaction, tau propagation through the Earth with electromagnetic energy loss, tau decay in the atmosphere, and the Cherenkov photon density of the resulting extensive air shower, the effective aperture reaches around 1 km² sr at $E_{\nu_\tau}=10^9$ GeV for full 360° azimuthal coverage. Comparing the ALLM and BDHM tau energy-loss models and standard versus ALLM/BDHM-extrapolated neutrino cross sections gives a factor-of-two spread at the highest energies and a 30–40% uncertainty at the best energy; a top layer of water helps slightly at the highest energies, while rock gives more target nucleons at lower energies. Under five years of observation at 20% duty cycle, the full-coverage configuration is competitive with, and at the highest energies exceeds, the current IceCube/Auger/ANITA limits and the projected sensitivities of ground- and ice-based instruments, while the 30°-coverage configuration is not competitive for diffuse fluxes but remains the relevant mode for transient sources.

Load-bearing premise

The calculation leans on numerical models deferred to two companion papers: the air-shower Cherenkov photon density as a function of altitude and angle, the effective Cherenkov angle's dependence on shower parameters, and the approximation that the air-shower energy is half the tau energy; if those are inaccurate, the absolute sensitivity shifts outside the stated 30–40% band.

Editorial extensions

If this is right

  • With full 360° azimuthal coverage and five years of observation, POEMMA's diffuse all-flavor sensitivity reaches below the current IceCube, Auger, and ANITA limits around $10^9$ GeV, so a null detection would begin to disfavor the higher cosmogenic flux models.
  • With only 30° coverage, POEMMA would not compete in diffuse mode; the mission's case for diffuse neutrinos depends on expanding to full azimuthal coverage.
  • For transient sources, the effective-area calculation gives concrete reach: long blazar flares modeled by RFGBW out to roughly 43 Mpc, tidal disruption events out to about 100 Mpc, and the extended-emission short gamma-ray burst model of KMMK out to about 117 Mpc for a single event.
  • At the highest energies, the choice between ALLM and BDHM tau energy-loss models changes the expected rate by up to a factor of two, so the calculation identifies tau photonuclear energy loss as the input that most needs pinning down.

Reading between the lines

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

  • The same $P_{\rm exit}\otimes P_{\rm det}$ machinery is detector-agnostic: if the air-shower and Cherenkov models are validated, any future satellite or high-altitude balloon can reuse the aperture integral with only its altitude, orbit, collection area, and threshold changed.
  • Because the exit probability is directly proportional to the charged-current cross section at energies where attenuation is small, an observed rate of Earth-skimming tau showers could be inverted to constrain neutrino-nucleon cross sections around $10^8$–$10^{10}$ GeV, beyond direct accelerator reach.
  • The paper's 30–40% uncertainty band is dominated by energy-loss and cross-section extrapolations, not by detector parameters, which suggests that improving those particle-physics inputs is currently more valuable than increasing the telescope's collection area.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This paper presents a calculation of the acceptance of POEMMA to very- and ultra-high-energy Earth-skimming tau neutrinos. The authors write the diffuse effective aperture in Eq. (2.1) as an integral over the Earth's surface and tau emergence angles of the observation probability, which factorizes in Eq. (2.2) into tau exit probability, tau decay probability, and detection probability. They show the resulting effective aperture for POEMMA at 525 km altitude (Fig. 1), tau exit fluxes for several elevation angles (Fig. 2, left), diffuse all-flavor sensitivity curves (Fig. 2, right), and transient-source fluence sensitivities (Fig. 3). The main quantitative results are an effective aperture of order 1 km^2 sr near 10^9 GeV and a stated +/-30-40% sensitivity variation from neutrino cross-section and tau energy-loss model choices.

Significance. If the calculation is correct, this is a useful public quantification of POEMMA's tau-neutrino sensitivity, with an explicit breakdown of the dominant model uncertainties from neutrino cross sections and tau electromagnetic energy loss. The authors should be credited for a transparent formulation, for stating their approximations (theta_v approximately equal to theta_tr, E_shower = E_tau/2, theta_Ch^eff approximately 1.5 degrees), and for comparing against Auger, IceCube, ANITA, ARIANNA, ARA-37 and GRAND10k sensitivity estimates. The paper's principal value is as an independent cross-check of the POEMMA concept-study sensitivity; however, the absolute normalization rests on details of the air-shower detection model that are deferred to companion papers and are not yet validated at the level required by the quoted uncertainty band.

major comments (2)
  1. [Section 2, Eq. (2.3)] Eq. (2.3) as written is not consistent with the definition of dPobs in Eq. (2.2). In Eq. (2.2), dPobs is a differential probability in the decay path s' (dimensionless after integration), while in Eq. (2.3) it is multiplied by the disk area pi (v-s)^2 (theta_Ch^eff)^2 to obtain an effective area. Since the text states that Pdet already includes whether the detector lies within the Cherenkov cone, multiplying by the disk area appears to double-count the Cherenkov acceptance; if dPobs is meant to denote a different (e.g., per-unit-area) quantity in Eq. (2.3), that needs to be stated explicitly. Figure 3 and all transient-source fluence sensitivities are based on Eq. (2.3), so the authors should provide a derivation of the point-source effective area from Eq. (2.1) or otherwise clarify the formula.
  2. [Section 2 (Pdet paragraph) and final paragraph] The absolute value of the effective aperture and of the transient sensitivities depends on the air-shower detection model, which is not developed in this paper. The paragraph after Eq. (2.2) states that Pdet depends on the photon density as a function of altitude, theta_tr and shower energy; that the effective Cherenkov angle is 'on the order of 1.5 degrees, though its exact value depends on the altitude of the decay, theta_tr, and the shower energy [19]'; and that 'we have assumed that the shower energy is half of the tau energy.' These inputs enter multiplicatively through Pdet in Eq. (2.2), so a modest error in the photon-density model or in the shower-energy normalization would shift the central sensitivity outside the +/-30-40% band quoted for E_nu = 10^9 GeV, a band that covers only neutrino cross-section and tau energy-loss variations. The final paragraph's statement that 'Modeling of air showers, the impact of cloud cover and other variables are being reviewed and improved [37]' explicitly flags this part of the calculation as unfinished. The authors should either fold these systematics into the quoted uncertainty or validate the air-shower model (e.g., against full EAS simulations) before the absolute sensitivity curves are presented as quantitative predictions.
minor comments (5)
  1. [Section 3, second paragraph] The word 'intstrument' should be 'instrument'.
  2. [Author affiliations] The affiliation 'CRNS' should be 'CNRS'.
  3. [Eq. (2.1) and Eq. (2.2)] The notation dPobs is used as a differential in s' in Eq. (2.2), but Eq. (2.1) integrates it over dS and dOmega_tr; for clarity, define the observation probability density explicitly or indicate the integration variables in the definition of dPobs.
  4. [Fig. 1 (right)] The solid and dot-dashed curves are described in the text, but the figure itself has no legend; adding a legend or directly labeling the curves would improve readability.
  5. [Fig. 3 caption] The caption uses 'left figure' and 'right figure'; 'left panel' and 'right panel' would be clearer.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the sensitivity curves are computed outputs, not fitted inputs.

full rationale

The paper's derivation chain is a convolution of independently sourced physics inputs. Eq. (2.2) defines dPobs from P_exit (neutrino cross section and tau energy loss, with ALLM/BDHM and SM/ALLM/BDHM cross-section variants imported from external references), p_decay (standard tau decay kinematics), and P_det (POEMMA optical response parameters from Ref. [19]). The effective aperture in Eq. (2.1) and effective area in Eq. (2.3) are integrals over these inputs; they are outputs, not quantities used to set the inputs. The paper is transparent about the assumptions entering P_det: 'The effective Cherenkov angle theta_Ch^eff is on the order of 1.5 deg, though its exact value depends on the altitude of the decay, theta_tr, and the shower energy [19]' and 'In our evaluations below, we have assumed that the shower energy is half of the tau energy.' These are model inputs, possibly uncertain, but not circular: no target quantity is defined in terms of itself, and no fitted parameter is renamed as a prediction. The closing caveat ('Modeling of air showers, the impact of cloud cover and other variables are being reviewed and improved [37]') is a limitation statement, not a circularity. The quoted +/-30-40% uncertainty refers to cross-section and energy-loss variations; it does not indicate that the sensitivity was derived from itself. Refs. [19] and [22] are self-citations for technical details, but they are not used as an external uniqueness theorem or to forbid alternative choices, and the central claim remains an independent convolution of these inputs. Therefore no circularity step can be exhibited.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central sensitivity numbers rest on standard but unverified-in-this-paper model inputs: neutrino cross sections, tau energy-loss parameterizations, Earth density profile, and POEMMA detector parameters. None are fitted to the target result, and the two energy-loss models are used to bracket uncertainty rather than to force agreement.

free parameters (2)
  • Shower energy fraction = 0.5 (E_shower = 0.5 * E_tau)
    The paper assumes the air shower energy is half the tau energy (Section 2). This factor is chosen by hand and directly affects the predicted photon density and hence the detection probability.
  • Effective Cherenkov angle (theta_eff_Ch) = ~1.5 degrees
    The paper uses an effective Cherenkov angle on the order of 1.5 degrees (Section 2), treating it as approximately constant though it notes the exact value depends on altitude, theta_tr, and shower energy. This parameter controls the viewable area in Eq. (2.3).
assumptions (5)
  • domain assumption Neutrino-nucleon charged-current cross sections (sigma_SM from PDFs, plus sigma_ALLM and sigma_BDHM extrapolations) are correct at PeV-EeV energies.
    Used throughout Section 2 for the exit probability P_exit; based on literature, extrapolated far above energies where they are experimentally tested.
  • domain assumption Tau electromagnetic energy loss is described by the ALLM or BDHM structure-function parameterizations.
    Used in Section 2 to compute tau exit probability and exit energy; the two models bracket the uncertainty.
  • domain assumption The Earth density profile is modeled with a 3 km water outer layer over rock of mass density 2.65 g/cm^3.
    Used in Section 2 for tau propagation and neutrino conversion; the paper compares to an all-rock model.
  • domain assumption The tau decay length follows the standard gamma c tau = 5 km * E_tau / 10^8 GeV.
    Standard relativity formula used in Section 2 for decay probability.
  • domain assumption POEMMA detector response parameters (2.5 m^2 optical area, 0.2 quantum efficiency, 10 photoelectron threshold) represent the concept study design.
    Used to convert photon density to detection probability in Section 2; from the POEMMA concept study, not independently verified here.

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Cite this review

Pith. "Pith review of A new calculation of Earth-skimming very- and ultra-high energy tau neutrinos." pith.science (2026). https://pith.science/paper/RLQDWRQ4

@misc{pith2026190803603,
  author       = {Pith},
  title        = {Pith review of: A new calculation of Earth-skimming very- and ultra-high energy tau neutrinos},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RLQDWRQ4}},
  note         = {Machine review of arXiv:1908.03603}
}
read the original abstract

Cosmic neutrinos above a PeV are produced either within astrophysical sources or when ultra-high energy cosmic rays interact in transit through the cosmic background radiation. Detection of these neutrinos will be essential for understanding cosmic ray acceleration, composition and source evolution. By using the Earth as a tau neutrino converter for upward-going extensive air showers from tau decays, balloon-borne and space-based instruments can take advantage of a large volume and mass of the terrestrial neutrino target. The theoretical inputs and uncertainties in determining the tau lepton exit probabilities and their translation to detection acceptance will be discussed in the context of a new calculation we have performed. We quantify the experimental detection capability based on our calculation, including using the Probe of Extreme Multi-Messenger Astrophysics (POEMMA) concept study response parameters for optical air Cherenkov detection. These case studies are used to illustrate the features and uncertainties in upward tau air shower detection.

Figures

Figures reproduced from arXiv: 1908.03603 by the authors.

Figure 1
Figure 1. (left) shows our definition of angles and distances relevant for a detector an altitude h above the surface of the Earth. The angle θv is the angle relative to the local normal ˆn of the line of sight from tau emergence point to the detector, while θtr is the angle the exiting tau trajectory makes with respect to the same local normal. The detector is a distance v from the exit point. The tau decays a distance s fro… view at source ↗
Figure 2
Figure 2. Left: The flux of tau neutrinos exiting the Earth, scaled by energy, Eτ for four elevation angles βtr ≡ 90◦ −θtr with different approximations for the cross section and energy loss. Right: The sensitivity for POEMMA with ∆φ = 360◦ (dashed) and 30◦ to the all-flavor diffuse neutrino flux scaled by energy-squared, assuming 5 years of observing with a 20% duty cycle. A band of cosmogenic flux predictions by Kotera et a… view at source ↗
Figure 3
Figure 3. All-flavor sensitivity scaled by E 2 ν , as a function of Eν . The dark blue band shows the sensitivity for a large portion of the sky at a given time, while the lighter blue region shows other viewing locations. The left figure is for long bursts, averaged over 380 days, including the effects of the Sun and Moon. The right figure shows the best all-flavor sensitivity to short bursts (103 s). Models by Fang and Metz… view at source ↗

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