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arxiv: 2508.06579 · v3 · submitted 2025-08-07 · ✦ hep-ph · nucl-th

Inclusion of the Longitudinal Momentum-Transfer Component and Kinematic Factors in a diffraction approach for H(d,p)X Reactions

Ya. D. Krivenko-Emetov , B. I. Sidorenko This is my paper

Pith reviewed 2026-05-19 00:04 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords deuteron breakupGlauber-Sitenko approximationlongitudinal momentum transfertransverse momentumdifferential cross sectionquark effectswave function parametrization
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The pith

Including the longitudinal momentum component in the diffraction model for deuteron breakup decreases the cross section with rising transverse momentum and shifts its maximum slightly.

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

The paper analyzes the differential cross section for the H(d,p)X reaction in the Glauber-Sitenko approximation using several deuteron wave function parametrizations. It incorporates small longitudinal momentum transfers Qz below 0.5 GeV/c together with transverse momenta p_perp below 0.5 GeV/c in the anti-laboratory frame. The calculations show that adding the longitudinal component causes the cross section to fall as transverse momentum grows and produces a modest shift plus growth at the peak position. This adjustment matters for comparing model results to data in the p3 range of 0.25 to 0.5 GeV/c, where quark effects could appear. The work tests how well the chosen wave functions capture the reaction kinematics at these low momentum values.

Core claim

Within the Glauber-Sitenko approximation and with deuteron wave functions that include single-Gaussian, multi-Gaussian K2, and forms derived from the Av18 and NijmI nucleon-nucleon potentials, the inclusion of the longitudinal momentum-transfer component Qz and associated kinematic factors produces a decrease in the differential cross section as transverse momentum p_perp increases, together with a relatively small shift and growth of the cross-section maximum.

What carries the argument

The Glauber-Sitenko multiple-scattering approximation extended to include the longitudinal momentum transfer Qz and full kinematic factors when evaluating the differential cross section for deuteron breakup.

Load-bearing premise

The Glauber-Sitenko approximation stays valid and the selected deuteron wave-function parametrizations correctly describe the kinematics for Qz below 0.5 GeV/c and p_perp below 0.5 GeV/c.

What would settle it

A set of measurements that shows the cross section increasing rather than decreasing with transverse momentum, or that exhibits a large unaccounted shift in the peak position, would contradict the predicted effect of adding the longitudinal component.

Figures

Figures reproduced from arXiv: 2508.06579 by B. I. Sidorenko, Ya. D. Krivenko-Emetov.

Figure 1
Figure 1. Figure 1: Dependence of Ep d 3σ/d3k on kz, calculated using the single-Gaussian "Tartakovsky parametrization" [32], for px = 0.00001 GeV/c and Qz = 0.00001 GeV/c. The point represents the experimental data approximation; the continuous curve corresponds to the calculation based on the Glauber–Sitenko multiple scattering diffraction theory (MSDT). 13 [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Dependence of Ep d 3σ d 3k on k, calculated using the single-Gaussian "Tartakovsky parametrization" [32], for px = 0.5 GeV/c and Qz = 0.00001 GeV/c [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Dependence of Ep d 3σ d 3k on kz, calculated using the single-Gaussian "Tartakovsky parametrization" [32], for px = 0.00001 GeV/c and Qz = 0.5 GeV/c. λ− > √ .267, σN − > 40., ρN − > 0.1, pd− > 9.1, βN − > √ 0.96, Ns− > 1.0, mp− > 938.272/1000, M d− > 1875.6/1000, kx− > 0.01, Qz− > 0.07 14 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Within the framework of the Glauber–Sitenko model using wave functions based on [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Dependence of Ep d 3σ/d3k on kz, obtained using the wave function of the multi-Gaussian "K2 parametrization" at px = 0.000015 GeV/c, Qz = −0.015 GeV/c 15 [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Dependence of Ep d 3σ/d3k on kz, obtained using the wave function of the multi-Gaussian "K2 parametrization" at px = 0.000015 GeV/c, Qz = 0.05 GeV/c [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Dependence of Ep d 3σ/d3k on kz, obtained using the wave function of the multi-Gaussian "K2 parametrization" at px = 0.05 GeV/c, Qz = −0.015 GeV/c 16 [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Within the framework of the Glauber–Sitenko model using wave functions based on [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Dependence of Epd 3σ/d3k on kz, obtained using the multi-Gaussian wave function of the ”Av18 parametrization’ at px = 0.00001 GeV/c, Qz = −0.5 GeV/c 17 [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Dependence of Epd 3σ/d3k on kz, obtained using the multi-Gaussian wave function of the ”Av18 parametrization’ at px = 0.00001 GeV/c, Qz = 0.00001 GeV/c [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Dependence of Epd 3σ/d3k on kz, obtained using the multi-Gaussian wave function of the ”Av18 parametrization’ at px = 0.05 GeV/c, Qz = 0.5 GeV/c 18 [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Dependence of Epd 3σ/d3k on kz, obtained using the multi-Gaussian wave function of the ”Av18 parametrization’ at px = 0.00001 GeV/c, Qz = 0.5 GeV/c [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Dependence of Epd 3σ/d3k on kz, obtained using the multi-Gaussian wave function of the ”Av18 parametrization’ at px = 0.12 GeV/c, Qz = 0.00001 GeV/c 19 [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Within the framework of the Glauber-Sitenko model using wave functions constructed [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Dependence of Epd 3σ/d3k on kz, obtained using the multi-Gaussian wave function of the ”Nijm-I parametrization” at px = 0.145 GeV/c, Qz = −0.01 GeV/c 20 [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Within the Glauber–Sitenko model using wave functions based on the NijmI potential, [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗
read the original abstract

In this work, within the framework of the Glauber-Sitenko approximation, an analysis of the differential cross section for deuteron breakup into a proton in the reaction H(d,p)X is presented. The study is carried out using various parameterizations of the deuteron wave function, including the single-Gaussian parametrization, the multi-Gaussian K2 parametrization, and models based on the Av18 and NijmI nucleon-nucleon potentials. Special attention is given to the effects of small longitudinal components of the transferred momentum (Qz < 0.5 GeV/c) and the transverse momentum of the proton-neutron pair (p_perp < 0.5 GeV/c) in the anti-laboratory reference frame. The results are compared with experimental data, particularly in the region of longitudinal momenta p\_3 = 0.25-0.5 GeV/c, where quark effects are expected to manifest. Preliminary estimates show a decrease in the cross section with increasing transverse momentum, as well as a relatively small shift (and growth) of the cross-section maximum due to the inclusion of the longitudinal component Qz.

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

2 major / 2 minor

Summary. The manuscript analyzes the differential cross section for the H(d,p)X deuteron-breakup reaction in the Glauber-Sitenko diffraction approximation. It incorporates the longitudinal momentum-transfer component Qz (< 0.5 GeV/c) together with transverse momentum p_perp (< 0.5 GeV/c) in the anti-laboratory frame, employing four deuteron wave-function models (single-Gaussian, K2 multi-Gaussian, Av18, NijmI). Preliminary estimates are reported of a decrease in cross section with rising p_perp and a modest shift plus growth of the maximum when Qz is restored; results are compared with data in the p3 = 0.25–0.5 GeV/c interval where quark effects are anticipated.

Significance. If the quantitative trends survive a full error analysis and explicit validation of the eikonal assumptions, the work would supply a concrete test of the diffraction framework at intermediate momenta and help quantify the kinematic window in which quark-gluon degrees of freedom might become visible. The systematic comparison across several wave-function parametrizations is a clear strength that allows model dependence to be assessed.

major comments (2)
  1. [Abstract and §4 (Results)] Abstract and §4 (Results): the central claims of a decrease in cross section with p_perp and a small shift/growth of the maximum are stated only as “preliminary estimates” with no numerical values, error bars, or explicit comparison tables shown; without these the magnitude and statistical significance of the reported effects cannot be verified.
  2. [§2 (Formalism) and §3 (Kinematics)] §2 (Formalism) and §3 (Kinematics): the Glauber-Sitenko eikonal series is applied for Qz < 0.5 GeV/c and p_perp < 0.5 GeV/c without any explicit check that the high-energy, small-angle, and negligible-off-shell assumptions remain valid; this kinematic window precisely overlaps the short-distance region (p3 = 0.25–0.5 GeV/c) where the paper expects quark effects to appear, rendering the approximation’s applicability load-bearing for the claimed trends.
minor comments (2)
  1. [§1 (Introduction)] Define the anti-laboratory frame and the relation between p3, Qz and p_perp explicitly at first use to improve readability.
  2. [§2 (Wave functions)] Add a short table summarizing the parameters of each deuteron wave function (rms radius, D-state probability, etc.) for direct comparison.

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 and indicate the revisions planned for the updated version.

read point-by-point responses

  1. Referee: [Abstract and §4 (Results)] Abstract and §4 (Results): the central claims of a decrease in cross section with p_perp and a small shift/growth of the maximum are stated only as “preliminary estimates” with no numerical values, error bars, or explicit comparison tables shown; without these the magnitude and statistical significance of the reported effects cannot be verified.

    Authors: We agree that the presentation would benefit from more quantitative detail. In the revised manuscript we will update the abstract and §4 to quote explicit numerical examples of the cross-section reduction with rising p_perp and the magnitude of the peak shift and growth when Qz is restored. A compact table comparing results obtained with and without the longitudinal component for the four wave-function models will also be added. A complete statistical error analysis lies beyond the scope of this initial exploration and is reserved for subsequent work. revision: partial

  2. Referee: [§2 (Formalism) and §3 (Kinematics)] §2 (Formalism) and §3 (Kinematics): the Glauber-Sitenko eikonal series is applied for Qz < 0.5 GeV/c and p_perp < 0.5 GeV/c without any explicit check that the high-energy, small-angle, and negligible-off-shell assumptions remain valid; this kinematic window precisely overlaps the short-distance region (p3 = 0.25–0.5 GeV/c) where the paper expects quark effects to appear, rendering the approximation’s applicability load-bearing for the claimed trends.

    Authors: We acknowledge the importance of this point. The revised §2 will contain an explicit paragraph discussing the range of validity of the Glauber-Sitenko eikonal approximation at the momenta considered, supported by references to earlier applications of the same framework to deuteron-breakup reactions at comparable energies. We will also state the kinematic conditions under which the high-energy and small-angle assumptions are expected to hold and note the proximity of the chosen window to the region where quark effects may appear. revision: yes

Circularity Check

0 steps flagged

No significant circularity; kinematic inclusion is independent of inputs

full rationale

The paper computes the differential cross section for H(d,p)X within the Glauber-Sitenko eikonal framework by adding the longitudinal momentum transfer Qz < 0.5 GeV/c and transverse p_perp < 0.5 GeV/c to the standard kinematic factors. It employs four external deuteron wave-function inputs (single-Gaussian parametrization, K2 multi-Gaussian, Av18 and NijmI potentials) taken from prior NN literature and performs direct numerical integration to obtain the reported decrease in cross section with p_perp and the small shift/growth of the maximum. These outcomes are explicit consequences of the added Qz term in the amplitude and are compared against experimental data; they do not reduce to the wave-function parameters or the Glauber-Sitenko ansatz by algebraic identity or by renaming a fit. No self-citation chain, uniqueness theorem, or fitted-input-as-prediction pattern appears in the derivation. The calculation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard Glauber-Sitenko multiple-scattering approximation and on pre-existing deuteron wave-function models whose parameters are taken from the literature or fitted to nucleon-nucleon data; no new particles or forces are postulated.

free parameters (1)
  • deuteron wave-function parameters
    Single-Gaussian and K2 multi-Gaussian parametrizations, as well as those derived from Av18 and NijmI potentials, contain adjustable parameters that are chosen or fitted to reproduce deuteron properties or scattering data.
axioms (1)
  • domain assumption Glauber-Sitenko approximation is applicable for the small-momentum kinematics considered
    The entire analysis of the differential cross section is performed inside this high-energy diffraction framework without additional justification for the low-momentum regime.

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