arxiv: 2601.19397 · v1 · submitted 2026-01-27 · ✦ hep-ph · nucl-th

Recognition: 1 theorem link

· Lean Theorem

Probing New Physics and CP Violation in ν_τ n to Λ_c τ^- (π^- ν_τ) and barν_τ p to Λ τ^+ (π^+ barν_τ)

E. Hern\'andez , J. Nieves , J. E. Sobczyk

Authors on Pith no claims yet

Pith reviewed 2026-05-16 10:51 UTC · model grok-4.3

classification ✦ hep-ph nucl-th

keywords neutrino scatteringtau polarizationCP violationnew physicseffective operatorslattice QCD form factorsazimuthal asymmetrylepton flavor violation

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The pith

An azimuthal asymmetry in the pion from tau decays in specific neutrino processes signals CP-violating new physics.

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

This paper analyzes the reactions in which a tau neutrino scatters off a neutron to produce a charmed Lambda baryon and a tau lepton, or the charge-conjugate process, with the tau decaying to a charged pion and neutrino. Within an effective theory that adds all dimension-six four-fermion operators to the Standard Model, complex Wilson coefficients generate CP-odd contributions to the tau polarization vector. These contributions produce a measurable asymmetry in the azimuthal angle of the outgoing pion around the tau direction. The size of the effect is estimated by extrapolating nucleon-hyperon transition form factors obtained from lattice QCD to the relevant kinematics.

Core claim

Complex Wilson coefficients in the effective low-energy extension induce transverse components in the tau polarization vector. These components generate a genuine CP-odd asymmetry in the azimuthal distribution of the pion emitted in the decay tau to pi nu, providing a smoking-gun observable for beyond-Standard-Model physics in the tau-neutrino scattering processes.

What carries the argument

Transverse components of the tau polarization vector induced by imaginary parts of the Wilson coefficients, which imprint a CP-odd azimuthal modulation onto the pion distribution in the tau rest frame.

If this is right

The asymmetry constitutes a direct, background-free signature of CP violation that cannot arise in the Standard Model alone.
Its observation would simultaneously constrain lepton-flavor-universality violation and new sources of CP violation.
The same polarization-sensitive observable can be applied to other tau-production channels once sufficient event samples are available.
Quantitative predictions depend on the form-factor extrapolation, so improved lattice calculations directly tighten the expected signal strength.

Where Pith is reading between the lines

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

The method could be adapted to probe similar CP-odd effects in tau decays produced at electron-positron colliders or in heavy-ion collisions.
If the asymmetry is confirmed, it would motivate dedicated analyses of tau polarization in existing and future neutrino detectors to extract the imaginary parts of specific Wilson coefficients.
The observable links neutrino scattering data to broader tests of CP violation in the lepton sector, complementing electric-dipole-moment searches.

Load-bearing premise

The nucleon-hyperon transition form factors from lattice QCD remain reliable when extrapolated to the kinematics of tau production in these neutrino reactions.

What would settle it

A high-statistics measurement of the azimuthal pion distribution in tau-neutrino events that finds no asymmetry at the level predicted by the extrapolated form factors would rule out sizable complex Wilson coefficients in these channels.

Figures

Figures reproduced from arXiv: 2601.19397 by E. Hern\'andez, J. E. Sobczyk, J. Nieves.

**Figure 1.** Figure 1: ), one can construct an asymmetry ∆σ = σ(0 < φπ < π) − σ(π < φπ < 2π) = B(τ → πντ ) m2 τMΛcG2 F |Vcd| 2 2π 2| ⃗k | 2(m2 τ − m2 π ) Z E ′ + E′ − dE′ q (| ⃗k | + Mn − E′) 2 − m2 τ Z E + π (E ′ ) E − π (E′) dEπ Z cos(θ 0 τπ−θ 0 τ ) cos(θ 0 τπ+θ 0 τ ) d cos θπ × P χ=L,R ρχχ P a,b Wab χ Lχab p (cos θπ − cos(θ 0 τπ + θ 0 τ ))(cos(θ 0 τπ − θ 0 τ ) − cos θπ) 2mτ m2 τ − m2 π − PT T |⃗pπ| |sin φ 0 π | sin θπ (17… view at source ↗

**Figure 2.** Figure 2: FIG. 2. Double-differential cross section [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Differential cross sections [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Double-differential cross section [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. SM differential cross sections [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

read the original abstract

We study the processes $\nu_\tau n \to \Lambda_c \tau^- (\pi^- \nu_\tau)$ and $\bar\nu_\tau p \to \Lambda \tau^+ (\pi^+ \bar\nu_\tau)$, with particular emphasis on the pion energy and angular distributions, as a possible signal for lepton flavor universality violation, and in general of physics beyond the Standard Model (SM), as well as a sensitive probe of the $\tau$ polarization vector. We work within an effective low-energy extension of the SM with all dimension-six four-fermion operators. In this framework, complex Wilson coefficients which encode new physics can generate CP-violating contributions. We propose an observable that provides a genuine CP-odd signal due to its sensitivity to particular transverse components of the $\tau$ polarization vector. Namely, we show that the asymmetry in the azimuthal-angle distribution of the pion in the decay $\tau^\pm\to \pi^\pm \nu_\tau$ constitutes a smoking-gun prediction of such a beyond the SM scenario. We estimate the strength of this effect extrapolating nucleon-hyperon form factors recently obtained from lattice QCD calculations.

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.

Desk Editor's Note private letter to a colleague

The paper gives a concrete azimuthal pion asymmetry as a CP-odd signal in these nu_tau hyperon channels via full dim-6 EFT, but the predicted size rests on uncertain lattice form-factor extrapolations to high Q2.

read the letter

The main point is that this work identifies the azimuthal asymmetry in the pion from tau decay as a genuine CP-odd observable in nu_tau n to Lambda_c tau- and the conjugate process, driven by transverse tau polarization from complex Wilson coefficients in the full set of dimension-six operators. They show how this asymmetry serves as a smoking-gun signal for BSM CP violation in the tau-neutrino sector. The approach uses standard EFT matching and pulls in recent lattice QCD results for the nucleon-hyperon transition form factors, which is a reasonable grounding for the hadronic matrix elements. This specific construction for these channels with the complete operator basis does not appear in the prior literature they cite, so that part is new. The paper does a clean job isolating the CP-odd interference terms from the polarization vector components without reducing to a simple fit parameter. The soft spot is the extrapolation of those lattice form factors from low Q2 to the kinematics of tau production, where Q2 reaches O(m_tau^2). Any bias there scales the asymmetry size directly, even though the formal CP-odd character stays intact. The abstract and stress-test note flag this as the dominant uncertainty, and without the full derivation and error propagation in the body it is difficult to judge how robust the numerical estimates are. This is for readers in neutrino phenomenology and precision flavor physics who track new observables for BSM searches. It deserves a serious referee to check the calculation details and the extrapolation procedure.

Referee Report

2 major / 2 minor

Summary. The manuscript studies the processes ν_τ n → Λ_c τ⁻ (π⁻ ν_τ) and ν̄_τ p → Λ τ⁺ (π⁺ ν̄_τ) in an effective field theory with all dimension-six four-fermion operators. It focuses on pion energy and angular distributions in the subsequent τ decay as probes of lepton flavor universality violation and beyond-Standard-Model physics. Complex Wilson coefficients are shown to generate CP-violating effects through transverse components of the τ polarization vector. The authors propose the azimuthal asymmetry in the pion distribution as a genuine CP-odd observable and estimate its magnitude by extrapolating lattice QCD nucleon-hyperon transition form factors to the relevant kinematics.

Significance. If the central claims hold, the work identifies a clean CP-odd asymmetry that could serve as a distinctive signal for new physics in tau-neutrino interactions, complementing other lepton-sector probes. The incorporation of recent lattice QCD form factors is a strength that grounds the estimates in non-perturbative inputs rather than purely phenomenological parametrizations. The formal construction of the asymmetry from polarization interference terms provides a parameter-independent diagnostic of complex phases in the Wilson coefficients.

major comments (2)

[§4] §4 (Form Factor Extrapolation): The extrapolation of lattice QCD nucleon-hyperon transition form factors from low Q² to the high-Q² regime (Q² ∼ m_τ²) of τ production is load-bearing for the predicted size of the CP-odd asymmetry. The manuscript provides no quantitative uncertainty band or comparison with alternative parametrizations, so the estimated strength of the effect cannot be reliably assessed.
[§3.2] §3.2, Eq. (7): The hadronic matrix elements for the effective operators are parametrized by the form factors, but the paper does not show the explicit contraction that isolates the transverse polarization components P_x and P_y; without this step, it is unclear whether additional cancellations could suppress the azimuthal asymmetry in these specific channels.

minor comments (2)

The effective operator basis should be explicitly matched to a standard convention (e.g., Warsaw basis) with a table listing the relevant Wilson coefficients for these processes.
Figure 2 and 3 captions should specify the benchmark values of the complex Wilson coefficients used for the plotted distributions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below, indicating the revisions we will implement.

read point-by-point responses

Referee: §4 (Form Factor Extrapolation): The extrapolation of lattice QCD nucleon-hyperon transition form factors from low Q² to the high-Q² regime (Q² ∼ m_τ²) of τ production is load-bearing for the predicted size of the CP-odd asymmetry. The manuscript provides no quantitative uncertainty band or comparison with alternative parametrizations, so the estimated strength of the effect cannot be reliably assessed.

Authors: We agree that the absence of quantitative uncertainty estimates for the form-factor extrapolation limits the reliability of the predicted asymmetry magnitude. In the revised manuscript we will add a dedicated discussion of the extrapolation uncertainties, including comparisons with alternative parametrizations (e.g., dipole forms) and error bands on the numerical results for the CP-odd asymmetry. revision: yes
Referee: §3.2, Eq. (7): The hadronic matrix elements for the effective operators are parametrized by the form factors, but the paper does not show the explicit contraction that isolates the transverse polarization components P_x and P_y; without this step, it is unclear whether additional cancellations could suppress the azimuthal asymmetry in these specific channels.

Authors: We thank the referee for this observation. In the revised version we will insert the explicit contractions of the hadronic currents with the leptonic tensors that isolate P_x and P_y. These expressions will demonstrate that no unexpected cancellations suppress the azimuthal asymmetry in the channels under study. revision: yes

Circularity Check

0 steps flagged

No significant circularity; CP-odd asymmetry derived from EFT polarization using external lattice form factors

full rationale

The paper derives the proposed azimuthal pion asymmetry directly from the transverse components of the tau polarization vector, which arise when complex Wilson coefficients are present in the dimension-six effective operators. The hadronic matrix elements are parametrized by nucleon-hyperon transition form factors taken from independent lattice QCD calculations (with extrapolation to the relevant kinematics stated as an assumption). No equation or claim reduces by construction to a fitted parameter within the paper, no load-bearing self-citation is invoked for a uniqueness theorem, and no ansatz is smuggled via prior work by the same authors. The central prediction remains an independent consequence of the EFT setup once the external form factors are supplied.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that all relevant new-physics effects are captured by dimension-six four-fermion operators and that lattice-QCD form factors can be reliably extrapolated to the required kinematics; no new particles or forces are postulated.

free parameters (1)

Complex Wilson coefficients
Dimension-six operator coefficients that are allowed to be complex and thereby generate CP violation; their values are not fitted in this work but treated as free parameters to be constrained by data.

axioms (2)

domain assumption All beyond-Standard-Model effects at the relevant energies are described by dimension-six four-fermion operators
Standard effective-field-theory assumption invoked to organize the new-physics contributions.
domain assumption Nucleon-hyperon transition form factors obtained from lattice QCD remain valid after extrapolation to the τ-production kinematics
The paper states that it extrapolates these form factors; the reliability of the extrapolation is an unproven input.

pith-pipeline@v0.9.0 · 5546 in / 1466 out tokens · 50927 ms · 2026-05-16T10:51:34.177867+00:00 · methodology

discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

We work within an effective low-energy extension of the SM with all dimension-six four-fermion operators... the asymmetry in the azimuthal-angle distribution of the pion... constitutes a smoking-gun prediction

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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Reference graph

Works this paper leans on

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