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arxiv: 1906.10912 · v1 · pith:7TRRAHQRnew · submitted 2019-06-26 · ✦ hep-ph · nucl-th

Coarse graining hadronic scattering

Enrique Ruiz Arriola , Jacobo Ruiz de Elvira This is my paper

Pith reviewed 2026-05-25 15:47 UTC · model grok-4.3

classification ✦ hep-ph nucl-th
keywords coarse grainingchiral dynamicshadronic scatteringpi pi scatteringpi N scatteringcutoff radiuspartial wave analysis
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The pith

Coarse graining hadronic scattering reduces short-distance unknowns to a finite number of parameters fixed by cutoff radius.

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

The paper proposes that coarse graining can be applied to hadronic reactions such as ππ and πN scattering, extending prior work on nucleon-nucleon cases. When chiral dynamics fixes the interaction for distances larger than a cutoff r_c, the unknown short-distance region requires only a finite number of parameters given by N_Par = N_S × N_I × (p r_c)^2 / 2. This count determines the degrees of freedom ν = N_Dat − N_Par in χ² fits to data below a given center-of-mass energy, allowing standard statistical confidence levels. The method is discussed with a view toward systematic data selection and testing chiral symmetry.

Core claim

If the interaction is taken to be given by chiral dynamics at long distances above a given value r > r_c larger than the elementary radii of the interaction hadrons, the unknown short distance region r < r_c is characterized by a finite number of fitting parameters. This number of independent parameters needed for a presumably complete description of scattering data for a CM energy below √s has been found to be given by N_Par = N_S × N_I × (p r_c)^2 / 2 with N_S and N_I the number of spin and isospin channels, and p the CM momentum respectively.

What carries the argument

The cutoff radius r_c that divides chiral long-distance dynamics from a short-distance region described by a finite set of fit parameters scaling with momentum squared.

If this is right

  • The number of needed parameters grows quadratically with center-of-mass momentum.
  • Standard χ² per degree of freedom can be used directly to assign confidence levels to fits.
  • The same counting applies to any set of experiments on ππ or πN scattering.
  • Consistency between the long-distance chiral part and data can be checked once short-distance parameters are fixed.

Where Pith is reading between the lines

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

  • The counting formula could be tested by refitting published partial-wave analyses with the predicted parameter limit.
  • Extending the method to higher energies would require raising r_c or accepting more parameters.
  • The approach might help identify which data points are most sensitive to short-distance physics.

Load-bearing premise

The long-distance interaction above the cutoff radius r_c is completely given by chiral dynamics.

What would settle it

A fit to scattering data below a chosen energy that requires substantially more than N_Par = N_S × N_I × (p r_c)^2 / 2 free parameters to reach acceptable χ² values.

Figures

Figures reproduced from arXiv: 1906.10912 by Enrique Ruiz Arriola, Jacobo Ruiz de Elvira.

Figure 1
Figure 1. Figure 1: Colour online: The p-value as a function of the reduced χ 2 for different number of degrees of freedom ν = 100,1000,10000. model has been found to provide the largest mutually 3σ self-consistent Granada-2013 database at about pion production threshold [5]. One important consequence of this database is that paves the road for theoretical tests such as ChPT [6]. In fact, it has recently been shown [7] that C… view at source ↗
Figure 2
Figure 2. Figure 2: Colour online: (left panel) The CM energy as a function of the CM momentum for ππ (solid,red) , πN (solid,black) and NN (solid,blue). We also plot the corresponding thresholds at KK¯, π∆ and N∆ where the inelastic cross (right panel) section increases substantially (we take π 0π 0 , π + p and pp respectively. In [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Colour online: Electromagnetic potentials for pointlike charge one particles (Solid,Black) and finite size particles , π +π + (Red,dashed) , π + p (Brown, dotted-dashed) and pp (Blue,dotted) as a function of the distance. As we see by looking at [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Colour online: The impact parameter as a function of the CM momentum for different partial waves with angular momenta L = 0,1,2,3 (solid,blue). The (black,dotted) line indicates the critical radius marking the range of the interaction. For instance, if we have pCM ≤ 300MeV only S- and P-waves probe the interaction region 3 . For a given partial wave the idea of coarse graining is illustrated in [PITH_FULL… view at source ↗
Figure 5
Figure 5. Figure 5: Colour online: An illustration of the coarse graining idea for a maximal CM momentum pmax = 400MeV which corresponds to a wavelength λmin = 3 and hence ∆r = 0.5 fm 5.3 The number of parameters Once we fix maximum CM momentum pCM,max and the cut-off radius rc the number of pa￾rameters NPar can be easily calculated as follows. For a central potential U(r) one has a tower of angular momentum states L = 0,1,2,… view at source ↗
Figure 6
Figure 6. Figure 6: Colour online: (Left panel) Allowed independent parameters (shaded area) based on coarse grain￾ing the interaction below rc = 1.5 rm. (Right panel) The estimated number of independent parameters as a function of the CM momentum for ππ (dashed,blue) , πN (dotted,black) and NN (solid,red) scattering. If we take the L = 0 state, we have the grid points ∆r = h¯/pCM,max → rn = n∆r. (5.7) The idea is to useUn ≡U… view at source ↗
read the original abstract

We show that it makes sense to coarse grain hadronic interactions such as $\pi\pi$ and $\pi N$ reactions following previous work on NN scattering. Moreover, if the interaction is taken to be given by chiral dynamics at long distances above a given value $r > r_c$ larger than the elementary radii of the interaction hadrons the unknown short distance region $r< r_c$ is characterized by a {\it finite} number of fitting parameters. This number of independent parameters needed for a presumably complete description of scattering data for a CM energy below $\sqrt{s}$ has been found to be given by $N_{\rm Par} = N_S \times N_I \times (p r_c )^2 /2 $ with $N_S$ and $N_I$ the number of spin and isospin channels, and $p$ the CM momentum respectively. Therefore, for an experiment (or sets of experiments) with a total number of data $N_{\rm Dat}$ the number of degrees of freedom involved in a $\chi^2$-fit is given by $\nu = N_{\rm Dat}-N_{\rm Par}$ and confidence levels can be obtained accordingly by standard means. Namely a $1 \sigma$ confidence level corresponds to $\chi_{\rm min}^2/\nu \in (1- \sqrt{2/\nu},1+\sqrt{2/\nu})$. We discuss the approach for $\pi\pi$ and $\pi N$ with an eye put on a data selection program and the eventual validation of chiral symmetry.

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 / 0 minor

Summary. The manuscript proposes coarse-graining hadronic scattering (ππ, πN) by fixing the long-range interaction (r > r_c) to chiral dynamics and parameterizing the short-distance region (r < r_c) with a finite number of parameters N_Par = N_S × N_I × (p r_c)^2 / 2. This count is asserted to enable standard χ² fits with ν = N_Dat − N_Par degrees of freedom and conventional confidence intervals, extending prior NN work toward data-driven validation of chiral symmetry.

Significance. If the separation is valid and the counting formula is rigorously derived, the result would supply a concrete, energy-dependent estimate of short-range parameters in chiral EFTs for meson-baryon scattering, allowing statistically controlled fits and clearer tests of chiral symmetry. The approach inherits the practical utility demonstrated in NN coarse-graining and could guide data-selection programs.

major comments (2)
  1. [Abstract] Abstract, paragraph 2: the formula N_Par = N_S × N_I × (p r_c)^2 / 2 is stated as 'found to be' without an explicit construction of the short-range operator basis, its dimension (p r_c)^2 / 2 per channel, or a proof of completeness once the long-range chiral piece is fixed; the central claim that the short-distance region is thereby fully characterized therefore rests on an unshown argument.
  2. [Abstract] Abstract, paragraph 2: the load-bearing assumption that chiral dynamics holds exactly for all r > r_c (with no residual long-range contributions near the cutoff) is not accompanied by error estimates or a quantitative justification; any non-chiral tails would be absorbed into the short-distance parameterization, changing the effective N_Par and undermining the separation into an energy-dependent but otherwise independent finite set.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful report and the recommendation for major revision. We address the two major comments point by point below, indicating where the manuscript will be revised for clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract] Abstract, paragraph 2: the formula N_Par = N_S × N_I × (p r_c)^2 / 2 is stated as 'found to be' without an explicit construction of the short-range operator basis, its dimension (p r_c)^2 / 2 per channel, or a proof of completeness once the long-range chiral piece is fixed; the central claim that the short-distance region is thereby fully characterized therefore rests on an unshown argument.

    Authors: The counting formula follows from the partial-wave decomposition of a short-range interaction confined to r < r_c. For a given CM momentum p the maximum relevant angular momentum satisfies l_max ≈ p r_c, so the number of independent partial waves per spin-isospin channel scales as ∑(2l+1) ≈ (p r_c)^2/2. Any short-range potential (or equivalent operator basis) can therefore be parameterized by a finite set of coefficients whose dimension is exactly N_S × N_I × (p r_c)^2/2; higher partial waves are kinematically suppressed and absorbed into the long-range chiral piece. This counting was derived and validated numerically in our earlier NN coarse-graining papers and is applied here without modification. To make the argument self-contained we will add a concise derivation (including the operator-basis dimension) as a new subsection in the revised manuscript. revision: yes

  2. Referee: [Abstract] Abstract, paragraph 2: the load-bearing assumption that chiral dynamics holds exactly for all r > r_c (with no residual long-range contributions near the cutoff) is not accompanied by error estimates or a quantitative justification; any non-chiral tails would be absorbed into the short-distance parameterization, changing the effective N_Par and undermining the separation into an energy-dependent but otherwise independent finite set.

    Authors: The separation assumes that, once r_c is chosen larger than the elementary hadron radii, all long-range dynamics are captured by the known chiral two-pion and one-pion exchange potentials. Residual non-chiral contributions (e.g., from heavier-meson exchange) are suppressed by the chiral power counting and fall exponentially beyond r_c. We acknowledge that an explicit error budget would strengthen the presentation. In the revision we will insert a paragraph that (i) recalls the chiral suppression factors, (ii) quotes the size of neglected terms from the NN literature where the same cutoff choice was used, and (iii) estimates the induced shift in N_Par to be at most one additional parameter per channel at the energies considered. revision: yes

Circularity Check

0 steps flagged

No circularity; parameter counting follows from independent partial-wave phase space once long-range chiral piece is assumed

full rationale

The central formula N_Par = N_S × N_I × (p r_c)^2 / 2 is presented as following from phase-space or partial-wave considerations for the short-distance region once the interaction for r > r_c is fixed to chiral dynamics. This counting is not obtained by fitting to the data it later analyzes, nor is it defined in terms of the target observables; it functions as an a priori estimate of the number of short-range parameters needed for a complete description below a given √s. The paper explicitly states the long-range chiral assumption as an input (abstract, paragraph 2) rather than deriving it from the short-range fit. No load-bearing step reduces by construction to a self-citation, a fitted input renamed as prediction, or an ansatz smuggled via prior work; the approach is self-contained against external benchmarks once the separation scale r_c is chosen.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on the premise that chiral dynamics fully governs the long-range tail once r_c is chosen larger than hadron sizes, plus the assumption that short-distance physics admits a finite parameterization whose dimension is given by the supplied counting rule.

free parameters (1)
  • r_c
    Cutoff radius separating long- and short-distance regimes; must be chosen larger than elementary hadron radii but is otherwise a free modeling choice.
axioms (1)
  • domain assumption Chiral dynamics governs the interaction at long distances r > r_c
    Stated directly in the abstract as the condition that allows the short-distance region to be treated with a finite set of parameters.

pith-pipeline@v0.9.0 · 5809 in / 1365 out tokens · 38204 ms · 2026-05-25T15:47:47.777187+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Uncertainty quantification and falsification of Chiral Nuclear Potentials

    nucl-th 2019-07 unverdicted novelty 5.0

    Chiral nuclear potentials exhibit systematic discrepancies with experimental NN scattering data in regimes where the theory is expected to perform best.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages · cited by 1 Pith paper · 16 internal anchors

  1. [1]

    Weinberg, Phenomenological Lagrangians, Physica A96 (1979) 327–340

    S. Weinberg, Phenomenological Lagrangians, Physica A96 (1979) 327–340

    work page 1979

  2. [2]

    Weinberg, Effective field theory, past and future, Int

    S. Weinberg, Effective field theory, past and future, Int. J. Mod. Phys. A31 (2016) 1630007

    work page 2016

  3. [3]

    Fitting and selecting scattering data

    E. Ruiz Arriola, J. E. Amaro and R. Navarro Pérez, Fitting and selecting scattering data, PoS Hadron2017 (2018) 134, [1711.11338]. 4Of course, this is only valid around the threshold region. Going to the resonance region is another story, as although many proposals implementing unitarity have been made, there is no uniquely and accepted method. 9 Coarse g...

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  4. [4]

    Self-consistent statistical error analysis of $\pi\pi$ scattering

    R. Navarro Pérez, E. Ruiz Arriola and J. Ruiz de Elvira, Self-consistent statistical error analysis of ππ scattering, Phys. Rev. D91 (2015) 074014, [1502.03361]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  5. [5]

    Coarse grained Potential analysis of neutron-proton and proton-proton scattering below pion production threshold

    R. Navarro Pérez, J. E. Amaro and E. Ruiz Arriola, Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold, Phys. Rev. C88 (2013) 064002, [1310.2536]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  6. [6]

    The falsification of Chiral Nuclear Forces

    E. Ruiz Arriola, J. E. Amaro and R. Navarro Pérez, The falsification of Chiral Nuclear Forces, EPJ Web Conf. 137 (2017) 09006, [1611.02607]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  7. [7]

    Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order

    P. Reinert, H. Krebs and E. Epelbaum, Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order, Eur. Phys. J.A54 (2018) 86, [1711.08821]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  8. [8]

    D. R. Entem, R. Machleidt and Y . Nosyk, High-quality two-nucleon potentials up to fifth order of the chiral expansion, Phys. Rev. C96 (2017) 024004, [1703.05454]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  9. [9]

    E. E. Salpeter and H. A. Bethe, A Relativistic equation for bound state problems, Phys. Rev. 84 (1951) 1232–1242

    work page 1951

  10. [10]

    Explicitly Covariant Light-Front Dynamics and Relativistic Few-Body Systems

    J. Carbonell, B. Desplanques, V . A. Karmanov and J. F. Mathiot,Explicitly covariant light front dynamics and relativistic few body systems, Phys. Rept. 300 (1998) 215–347, [nucl-th/9804029]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  11. [11]

    Nieves and E

    J. Nieves and E. Ruiz Arriola, Bethe-Salpeter approach for unitarized chiral perturbation theory, Nucl. Phys. A679

    work page

  12. [12]

    Some Three-body force cancellations in Chiral Lagrangians

    E. Ruiz Arriola, Some Three-body force cancellations in Chiral Lagrangians, 1606.07535

    work page internal anchor Pith review Pith/arXiv arXiv

  13. [13]

    Namyslowski, Relativistic, 3-dimensional, 2-body integral equations

    J. Namyslowski, Relativistic, 3-dimensional, 2-body integral equations. on-shell and off-shell formalisms, Physical Review 160 (1967) 1522

    work page 1967

  14. [14]

    M. F. M. Lutz, E. E. Kolomeitsev and C. L. Korpa, Spectral representation for u- and t-channel exchange processes in a partial-wave decomposition, Phys. Rev. D92 (2015) 016003, [1506.02375]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  15. [15]

    T. W. Allen, G. L. Payne and W. N. Polyzou, Comparison of relativistic nucleon-nucleon interactions, Phys. Rev. C62 (2000) 054002, [nucl-th/0005062]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  16. [16]

    I. R. Simo, J. E. Amaro, E. Ruiz Arriola and R. Navarro Perez, Low energy peripheral scaling in nucleon-nucleon scattering and uncertainty quantification, J. Phys. G45 (2018) 035107, [1705.06522]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  17. [17]

    Coarse graining of NN inelastic interactions up to 3 GeV:Repulsive vs Structural core

    P. Fernandez-Soler and E. Ruiz Arriola, Coarse graining of NN inelastic interactions up to 3 GeV: Repulsive versus structural core, Phys. Rev. C96 (2017) 014004, [1705.06093]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  18. [18]

    Partial Wave Analysis of Chiral NN Interactions

    R. Navarro Perez, J. E. Amaro and E. Ruiz Arriola, Partial Wave Analysis of Chiral NN Interactions, Few Body Syst. 55 (2014) 983–987, [1310.8167]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  19. [19]

    Coarse graining $\pi\pi$ scattering

    J. Ruiz de Elvira and E. Ruiz Arriola, Coarse graining ππ scattering, Eur. Phys. J.C78 (2018) 878, [1807.10837]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  20. [20]

    J. M. Alarcón, J. Ruiz de Elvira and E. Ruiz Arriola, Coarse graining πN scattering, In preparation

    work page

  21. [21]

    Coarse grained NN potential with Chiral Two Pion Exchange

    R. Navarro Pérez, J. E. Amaro and E. Ruiz Arriola, Coarse grained NN potential with Chiral Two Pion Exchange, Phys. Rev. C89 (2014) 024004, [1310.6972]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  22. [22]

    Low energy chiral two pion exchange potential with statistical uncertainties

    R. Navarro Pérez, J. E. Amaro and E. Ruiz Arriola, Low energy chiral two pion exchange potential with statistical uncertainties, Phys. Rev. C91 (2015) 054002, [1411.1212]. 10

    work page internal anchor Pith review Pith/arXiv arXiv 2015