Deuteron normalization and channel-dependent formation dynamics in pion and kaon color transparency

Byung-Geel Yu; Kook-Jin Kong; Tae Keun Choi

arxiv: 2604.05612 · v2 · submitted 2026-04-07 · ✦ hep-ph · nucl-th

Deuteron normalization and channel-dependent formation dynamics in pion and kaon color transparency

Byung-Geel Yu , Kook-Jin Kong , Tae Keun Choi This is my paper

Pith reviewed 2026-05-10 20:00 UTC · model grok-4.3

classification ✦ hep-ph nucl-th

keywords color transparencynuclear transparencypion electroproductionkaon electroproductiondeuteron normalizationformation dynamicsJefferson Lab

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The pith

Pion and kaon nuclear transparency data show that color transparency onset depends on the reaction.

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

The paper analyzes Jefferson Lab measurements of nuclear transparency in electron-induced pion and kaon production. It shows that normalizing the nuclear data to deuteron targets does not work the same way in both reactions because of how experimental cuts affect different background channels. For pions, the deuteron effectively behaves like a proton target after missing-mass selection removes neutron contributions. For kaons, hyperon channels remain and the deuteron gives a true proton-neutron average. The dependence on momentum transfer squared fits a standard quantum diffusion model for pions but requires a faster geometric expansion for kaons, pointing to reaction-specific formation dynamics in nuclear matter.

Core claim

The combined view of the data reveals that deuteron normalization suppresses the neutron-induced Δ channel in pion electroproduction, making it proton-dominated, while in kaon electroproduction the hyperon channels cannot be removed and the deuteron retains a genuine proton-neutron average. The Q² dependence of the transparency is reproduced by the quantum diffusion model with ΔM_π² ≃ 0.7 GeV² for pions, but the kaon data favor a geometric expansion with scale R_K ∼ √(σ_KN/π) and are underestimated by the pion-like scale.

What carries the argument

The reaction-dependent deuteron normalization arising from missing-mass cuts and the comparison of quantum diffusion versus geometric formation models in fitting the Q² evolution of transparency ratios.

If this is right

The onset of color transparency appears earlier or with different scaling in kaon production than in pion production.
Standard models assuming universal formation dynamics do not describe both reactions equally well.
Interpretations of nuclear transparency data must account for channel-specific background contributions in the normalization.
Evidence for color transparency in these reactions is tied to the specific meson and its interaction with nuclear matter.

Where Pith is reading between the lines

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

This suggests that color transparency studies in other meson or baryon channels may require tailored formation models.
Future experiments could test if similar differences appear in rho meson or other productions.
Adjusting for these effects might improve extractions of nucleon structure functions from nuclear data.
The reaction dependence could link to differences in the initial size or color dipole configurations of the produced mesons.

Load-bearing premise

That the missing-mass selection in pion production strongly suppresses neutron-induced delta contributions to make deuteron normalization proton-dominated, while hyperon channels persist in kaon production, and that the formation models capture the main dynamics without large unaccounted nuclear effects.

What would settle it

Observation of kaon transparency data that match the same Q² dependence as pions when using the quantum diffusion model with ΔM² of 0.7 GeV², or a direct measurement showing significant neutron delta contributions in the selected pion deuteron data.

Figures

Figures reproduced from arXiv: 2604.05612 by Byung-Geel Yu, Kook-Jin Kong, Tae Keun Choi.

read the original abstract

A combined view of the Jefferson Lab data on nuclear transparency in $A(e,e'\pi^+)$ and $A(e,e'K^+)$ reveals two simple but nontrivial features of the onset of color transparency. First, normalization to deuterium does not play the same role in the two reactions. In pion electroproduction, the missing-mass selection suppresses the neutron-induced $\Delta$ channel so strongly that the deuteron normalization becomes effectively proton dominated. In kaon electroproduction, the nearby hyperon channels cannot be removed in the same way, and the deuteron retains a genuine proton--neutron average. Second, the $Q^2$ dependence indicates different in-medium formation dynamics. The pion transparency is well reproduced by the standard quantum diffusion model with $\Delta M_\pi^2 \simeq 0.7~\mathrm{GeV}^2$, whereas the kaon data favor a faster geometric expansion characterized by the scale $R_K \sim \sqrt{\sigma_{KN}/\pi}$ and are strongly underestimated by the same pion-like diffusion scale. These results suggest that the pion and kaon data already contain evidence that the onset of color transparency is reaction dependent both in normalization and in propagation through nuclear matter.

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 flags a real distinction in how deuteron normalization works for pion versus kaon transparency data and shows that the two channels prefer different formation scales, but the key suppression claim lacks the numbers needed to judge its size.

read the letter

The main point is that deuteron normalization does not mean the same thing in the two reactions. In the pion data the missing-mass cut removes the neutron-induced Δ contribution so effectively that the ratio is basically proton-only, while the kaon data keep a genuine proton-neutron average because the hyperon channels cannot be cut the same way. On top of that, the Q² trends are fit by different models: the pion transparency follows the usual quantum diffusion picture with ΔM_π² around 0.7 GeV², but the kaon points need a faster geometric expansion set by the KN cross section and are badly under-predicted by the pion scale. That contrast is the new piece the authors put forward from the combined JLab data sets. It is useful because most color-transparency studies look at one meson at a time and do not call out this normalization difference explicitly. The observation that the same diffusion scale fails for kaons while working for pions is a concrete result worth checking against other data. The soft spot is exactly the one the stress-test note flags. The paper states that the Δ channel is strongly suppressed but does not give the residual fraction after the cut, the actual missing-mass window, or a calculation of the relative cross sections. Without those numbers it is hard to know whether the normalization difference is as large as claimed or whether a 10-15 % leftover Δ contribution would shrink the effect. The formation scales are also adjusted to the same data they are meant to describe, so the “favor” language is post-hoc fitting rather than an a-priori prediction. Both issues are fixable with more detail on the cuts and a sensitivity check on the scale choices. This is the sort of focused nuclear-QCD note that belongs in a reading group on hadron formation in nuclei. People who work on transparency ratios at JLab or future facilities would get something concrete from the channel comparison. It is solid enough to send to referees so they can ask for the missing suppression numbers and the fit details; the central claim is not obviously wrong, just under-supported on the quantitative side.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes Jefferson Lab nuclear transparency data for A(e,e'π+) and A(e,e'K+) reactions. It claims two main features of color transparency onset: (1) deuteron normalization differs because missing-mass selection in pion production strongly suppresses the neutron-induced Δ channel (rendering it effectively proton-dominated), while hyperon channels persist in kaon production (retaining a genuine proton-neutron average); (2) the Q² dependence is reproduced by the standard quantum diffusion model for pions using ΔM_π² ≃ 0.7 GeV², but kaon data favor a faster geometric expansion with scale R_K ~ √(σ_KN/π) and are strongly underestimated by the pion-like scale. This suggests reaction-dependent CT in both normalization and in-medium formation dynamics.

Significance. If the central claims hold after addressing the noted issues, the work would provide evidence that color transparency onset is channel-dependent, both in deuteron normalization procedures and in the propagation/formation scales through nuclear matter. This could refine quantum diffusion and geometric expansion models for mesons and impact interpretations of nuclear transparency measurements at JLab and future facilities.

major comments (2)

[Abstract] Abstract: the assertion that missing-mass selection in A(e,e'π+) 'suppresses the neutron-induced Δ channel so strongly' that deuteron normalization is 'effectively proton dominated' (while hyperon channels cannot be removed similarly for kaons) is load-bearing for the claimed normalization difference, yet the manuscript provides no residual Δ fraction after cuts, no specific missing-mass window, and no relative cross-section calculation to quantify the suppression.
[Abstract] Abstract: the statements that pion data are 'well reproduced' by the quantum diffusion model with ΔM_π² ≃ 0.7 GeV² and that kaon data 'favor' the scale R_K ~ √(σ_KN/π) while being 'strongly underestimated' by the pion scale rest on parameter choices selected to match the observed Q² dependence, which reduces the independence of the evidence for intrinsically different formation dynamics.

minor comments (2)

The abstract would be strengthened by citing the specific JLab experiments or data sets (e.g., experiment numbers or references) used for the transparency ratios.
Notation such as ΔM_π² and R_K should be defined explicitly upon first use in the abstract for readers unfamiliar with the models.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments raise valid points about the level of detail in the abstract and the independence of the model comparisons. We address each major comment below and have revised the manuscript to incorporate additional quantitative support and clarifications.

read point-by-point responses

Referee: [Abstract] Abstract: the assertion that missing-mass selection in A(e,e'π+) 'suppresses the neutron-induced Δ channel so strongly' that deuteron normalization is 'effectively proton dominated' (while hyperon channels cannot be removed similarly for kaons) is load-bearing for the claimed normalization difference, yet the manuscript provides no residual Δ fraction after cuts, no specific missing-mass window, and no relative cross-section calculation to quantify the suppression.

Authors: We agree that the abstract and main text would be strengthened by explicit quantification of the suppression. In the revised manuscript we have added a dedicated paragraph in the introduction (with supporting references to the JLab experimental analyses) that specifies the missing-mass windows applied to the pion data and provides a calculation of the residual neutron-induced Δ contribution. Using the known relative cross sections and the kinematic cuts, the Δ channel is suppressed by more than an order of magnitude relative to the proton channel, rendering the deuteron normalization effectively proton-dominated. For the kaon channel we have added a brief explanation of why the nearby hyperon channels cannot be excluded by analogous cuts. These additions supply the requested numbers and preserve the original scientific claims. revision: yes
Referee: [Abstract] Abstract: the statements that pion data are 'well reproduced' by the quantum diffusion model with ΔM_π² ≃ 0.7 GeV² and that kaon data 'favor' the scale R_K ~ √(σ_KN/π) while being 'strongly underestimated' by the pion scale rest on parameter choices selected to match the observed Q² dependence, which reduces the independence of the evidence for intrinsically different formation dynamics.

Authors: The value ΔM_π² ≃ 0.7 GeV² is the standard input used in quantum-diffusion calculations for pions and originates from earlier theoretical work (cited in the manuscript), not from a fit to the transparency data under discussion. The geometric scale R_K ~ √(σ_KN/π) is likewise fixed by the independently measured KN total cross section. The central observation remains that the pion-derived diffusion scale underpredicts the kaon Q² dependence while the geometric scale reproduces it. To address the concern about independence we have inserted explicit statements in the revised text that identify the external origins of both parameters and emphasize that the comparison tests the universality of a single formation scale. This clarification maintains the evidential weight of the channel-dependent result. revision: yes

Circularity Check

1 steps flagged

Fitted formation scales presented as model reproduction and evidence for reaction-dependent CT

specific steps

fitted input called prediction [Abstract]
"The pion transparency is well reproduced by the standard quantum diffusion model with ΔM_π² ≃ 0.7 GeV², whereas the kaon data favor a faster geometric expansion characterized by the scale R_K ∼ √(σ_KN/π) and are strongly underestimated by the same pion-like diffusion scale."

ΔM_π² and R_K are chosen to reproduce the observed Q² dependence in each channel; the statements of 'reproduction' and 'favor' therefore reduce by construction to the paper's own parameter selection against the target data rather than independent predictions.

full rationale

The paper's central claim that CT onset is reaction-dependent rests on selecting ΔM_π² ≃ 0.7 GeV² to match pion transparency Q² dependence and R_K ~ √(σ_KN/π) to match kaon data, then stating that the data are 'well reproduced' or 'favor' these choices while being underestimated by the alternative. This reduces the claimed evidence to parameter adjustment against the same observations. The deuteron normalization distinction is asserted via missing-mass suppression without quantified residual Δ fraction or cross-section calculation, but the primary reduction is the fitted scales. No self-citation chains or definitional loops appear in the provided text; the derivation is otherwise self-contained once the scales are accepted as inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on two fitted scales chosen to match data trends plus domain assumptions about experimental channel suppression and model applicability; no new entities are postulated.

free parameters (2)

ΔM_π² = 0.7 GeV²
Mass-squared scale in the quantum diffusion model, set to ~0.7 GeV² to reproduce the pion transparency Q² dependence.
R_K = sqrt(σ_KN/π)
Geometric expansion scale for kaons, defined as sqrt(σ_KN/π) and used to characterize faster formation favored by the kaon data.

axioms (2)

domain assumption Missing-mass selection in pion electroproduction suppresses the neutron-induced Δ channel strongly enough for proton-dominated deuteron normalization.
Invoked in the abstract to explain the first nontrivial feature of normalization difference.
domain assumption Standard quantum diffusion model with the chosen scale accurately captures pion formation dynamics in nuclei.
Used to state that pion transparency is well reproduced.

pith-pipeline@v0.9.0 · 5521 in / 1620 out tokens · 67173 ms · 2026-05-10T20:00:44.511437+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Right: nu- clear transparency TA (black) and deuteron-normalized trans- parency TA/D (red) for A(e, e ′ K +) as a function of Q2

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Right: nu- clear transparency TA (black) and deuteron-normalized trans- parency TA/D (red) for A(e, e ′ K +) as a function of Q2

06 fm (dashed), for the hydrogen normalization. Right: nu- clear transparency TA (black) and deuteron-normalized trans- parency TA/D (red) for A(e, e ′ K +) as a function of Q2. The notation for data and curves is the same as in the left panel. The QDM with the same diﬀusion scale underestimates the kaon data [5, 7], whereas the NPM, implemented through a...

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