Pith. sign in

REVIEW 4 major objections 6 minor 75 references

Models for differential cross section in proton-proton scattering and their implications at ISR and LHC energies

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Seven composite exponential models fitted to proton-proton elastic scattering claim to reproduce the dip-bump structure and forward-peak shrinkage from 23 GeV to 28 TeV, and to yield elastic, total, and inelastic cross sections across…

desk verdict Seven-parameter exponential fits to pp elastic dσ/dt across ISR-LHC; the dip-bump curves look plausible, but the σtot and σinel headline numbers for two models come from a post-fit modification, and the validation is circular. read the letter →

arxiv 2506.05532 v2 pith:N3I3TMII submitted 2025-06-05 hep-ph

Muhammad Saad Ashraf , Nosheen Akbar , Sarwat Zahra This is my paper
classification hep-ph
keywords elasticscatteringdifferentialcrosssectionproton-protondip-bumpstructuretotalopticaltheoremcompositeexponentialmodelsISRandLHCenergies
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

The paper proposes seven composite exponential parametrizations for the elastic proton-proton differential cross section and fits them to data spanning center-of-mass energies from 23 GeV to 28 TeV, including extrapolated predictions. It claims the fits reproduce the forward exponential peak, its energy-dependent shrinkage, and the dip-bump structure, with the dip position shifting to smaller momentum transfer as energy grows. From the fitted curves the authors compute elastic, total, and inelastic cross sections, comparing them with measured reference values. A sympathetic reader would care because a compact, few-parameter description of the full elastic shape could connect nonperturbative proton structure to collider observables.

What carries the argument

The load-bearing object is a family of composite exponential ansatze of the form $(s/s_0)^\eta$ times sums of terms $A_i e^{-B_i (s/s_0)^\mu t}$, with optional multiplicative factors such as $(1-\alpha t/t_0)^2$, $(1-t/t_0)^p$, $\log(1+\alpha t/t_0)$, or $e^{-\gamma(t/t_0)^m}(1+t/t_0)^{-n}$. The energy-scaling factors and the free coefficients are fixed by nonlinear least-squares fits to data at each energy; the same fitted curve is then numerically integrated to obtain $\sigma_{el}$ and evaluated at $t=0$ with the optical theorem to obtain $\sigma_{tot}$.

What would settle it

Measure the $pp$ elastic differential cross section down to $|t|$ around $0.001\,\text{GeV}^2$ at 13 TeV with luminosity-independent methods and compare the extrapolated $t=0$ value with $\sigma_{tot}^2(1+\rho^2)/(16\pi(\hbar c)^2)$; if the model curves miss the measured forward point by more than the quoted errors, the reported $\sigma_{tot}$ and $\sigma_{inel}$ are not physical. Also, a single precise measurement of $\sigma_{el}$ by integrating down to very small $|t|$ would test the 0-12 GeV$^2$ integration used here.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that a sum of four energy-scaled exponential terms, optionally decorated with quadratic zeros, saturation-like factors, logarithms, or stretched-exponential/power-law damping, is enough to describe $d\sigma/d|t|$ for $pp$ elastic scattering across the whole measured and extrapolated range. The fits are claimed to track the steep forward cone, the dip and subsequent bump, and the hard tail at large momentum transfer, and the extracted $\sigma_{el}$, $\sigma_{tot}$, and $\sigma_{inel}$ agree with reference values for most models, with the stretched-exponential variant judged most consistent. If true, this would show that the energy dependence of the elastic amplitude can be captured by a small number of effective parameters rather than by a detailed Regge or QCD input.

Load-bearing premise

The argument assumes that each fitted curve can be trusted outside the $|t|$ range where data exist, especially at $t=0$ where the optical theorem is applied, even though some datasets begin only at $|t|=0.38\,\text{GeV}^2$ and for two models a divergent power-law factor is simply dropped to make $t=0$ finite.

Editorial extensions

If this is right

  • Elastic, total, and inelastic $pp$ cross sections can be extracted from one fitted expression at each energy, without separate models for the forward region and the dip.
  • The dip position moving to smaller $|t|$ with energy and the rising slope parameter are built into the fits, so the same parameters encode proton opacity and size growth.
  • Model 7, if the comparison is right, gives the most reliable total and inelastic cross sections among the seven, including at extrapolated energies of 14, 15, and 28 TeV.
  • The fitted expressions provide $B(t)$ and $C(t)$, the local logarithmic slope and curvature, which can be compared with Odderon-sensitive $pp$ versus $p\bar p$ measurements.
  • Few-parameter fits are more stable to extrapolation, so the same models can be confronted with future higher-energy collider data.

Reading between the lines

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

  • If the paper is right, the same multi-exponential structure could be used as a prior for machine-learning fits, since the parameter space is small and the physical features are pre-built.
  • A direct test the authors do not run: use their $B(t)$ and $C(t)$ formulas to compare $pp$ and $p\bar p$ slope differences at 1.96 TeV, which would sharpen the Odderon link.
  • The extrapolation to 28 TeV could be checked before any collider runs by demanding that $\sigma_{el}/\sigma_{tot}$ follow $(\log s)^{-1}$ with a single $n$ across all energies; the paper already sees this for model 7 at LHC energies.
  • Fitting the same models to separate low-$|t|$ and dip-region data subsets would reveal whether the $t=0$ extrapolation is stable, addressing the weakest assumption.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes seven composite exponential parametrizations of the proton-proton elastic differential cross section $d\sigma/d|t|$ as functions of $s$ and $t$, with energy-dependent prefactors $(s/s_0)^\eta$ and $(s/s_0)^\mu$. Each model is fitted at ISR energies (23--62.5 GeV), LHC energies (2.76--13 TeV), and at energies where the comparison data are themselves extrapolated model outputs (200, 800 GeV; 14, 15, 28 TeV; 27.43 GeV). From the fits the authors compute $\sigma_{\rm el}$ by numerical integration, $\sigma_{\rm tot}$ from the optical theorem using the fitted value at $t=0$, and $\sigma_{\rm inel}$ by subtraction. The paper claims reproduction of the dip-bump structure, dip position, and shrinkage of the forward peak, and reports $\sigma_{\rm el}$, $\sigma_{\rm tot}$, and $\sigma_{\rm inel}$ at all energies.

Significance. If the central claims were established, a compact set of analytic expressions describing $pp$ elastic scattering from 23 GeV to 28 TeV would be a practically useful phenomenological input for collider, cosmic-ray, and Monte Carlo studies. The paper does not provide reproducible code, machine-checked derivations, or parameter uncertainties, and its quantitative claims are not supported by a standard goodness-of-fit statistic. The validation procedure is partly circular, because several of the fitted 'data' sets are the outputs of the same models later cited as confirmation. The $\sigma_{\rm tot}$ and $\sigma_{\rm inel}$ results for Models 5 and 6 are obtained only after a post-fit modification of divergent fitted functions. For these reasons the significance of the paper, as it stands, is not established.

major comments (4)
  1. [III, Eq. (23)] The quantity defined in Eq. (23) is not a chi-square per degree of freedom, despite the text describing it as such. The formula is a sum of squared residuals divided by the sum of squared data values; it contains no experimental uncertainties, no number of data points, and no subtraction of the number of fitted parameters. Consequently the very small values reported in Tables I--VII (e.g., $\chi^2=0.00029$ for Model 1 at 13 TeV) cannot be interpreted as evidence of good or superior fits, and the statement that Model 2 is 'best with respect to least value of $\chi^2$' is not supported.
  2. [III C, Eq. (26), Tables V, VI, X] The computation of $\sigma_{\rm tot}$ for Models 5 and 6 is not a prediction of the fitted models. Equations (16) and (19) contain terms proportional to $t^{-m}$ and $t^{-n}$ with $m=n=0.1$ in Tables V and VI, so the fitted differential cross sections diverge as $t\to 0$ and cannot be evaluated in Eq. (26). The paper itself states in Sec. III C that the extrapolated values of $(d\sigma/dt)_{t=0}$ are 'drastically lowered' and that the tabulated $\sigma_{\rm tot}$ values were obtained by neglecting this factor after fitting. Therefore the $\sigma_{\rm tot}$ and $\sigma_{\rm inel}$ entries for Models 5 and 6 in Tables X and XI are evaluations of a modified, unfitted function, not results of the models that were fit to data.
  3. [III A and II] The validation of the models is partly circular. The fits at 200 GeV and 800 GeV use predicted differential cross sections of the impact-picture model of Ref. [62], the 27.43 GeV fit uses the FMO model of Ref. [63], and the 14, 15, and 28 TeV fits use the extended Bialas-Bzdak model of Ref. [47]. Section III A then cites agreement with those same models as confirmation of the 'physical relevance' of the proposed parametrizations. Agreement with inputs that were fitted is not an independent test, and the comparison of $\sigma_{\rm tot}$ with Ref. [47] in Table X is similarly circular.
  4. [III C and Tables I--VII] The paper concedes in Sec. III C that the non-linear fitting has no known initial values, that 'many solutions' exist, and that oversimplified $t$-dependence affected the extrapolation to $t=0$. With 9--13 free parameters per energy, no parameter uncertainties reported, and many parameters pinned at identical values across all energies (e.g., $A_3=-0.06$, $A_4=0.04$, $B_3=3.00$, $B_4=2.754$ in Tables I--VII), the fitted parameter sets and the derived cross sections lack demonstrated robustness. This is a load-bearing issue because the claimed energy dependences, including shrinkage, are inferred from these parameter values.
minor comments (6)
  1. [Abstract] The abstract mislabels the observables: it reads 'inelastic cross section ($\sigma_{\rm tot}$), and total cross section ($\sigma_{\rm tot}$)', where the first should be $\sigma_{\rm inel}$.
  2. [II A 7, Eq. (21)] Equation (21) contains a stray '$\mu t$' in the fourth exponential term, presumably a typographical artifact.
  3. [III, Eq. (23)] The quantity in Eq. (23) should be renamed a normalized residual measure rather than $\chi^2$; the tables should also report the number of data points $N$ used in each fit.
  4. [III C, Table X] The $\rho$ values used in Eq. (26) are listed without references or uncertainties; since $\sigma_{\rm tot}$ depends on $\rho$ through $1+\rho^2$, the sources and errors of the $\rho$ values should be documented.
  5. [III C, Figure 8] Figure 8 constructs reference curves by joining reference points at a subset of energies; the statement that all calculated $\sigma_{\rm el}$ values 'lie on the reference curve' should be quantified, since an interpolated polygonal curve is not a measured prediction.
  6. [Throughout] There are many minor language and typographical errors, including 'the the', 'helds', and inconsistent spelling of 'Bialas-Bzdak'; a careful editing pass is needed.

Circularity Check

2 steps flagged · score 6.0 of 10

Partial circularity: the extrapolated-energy agreement is a fit to the same model curves, and the sigma_tot values for Models 5 and 6 come from a post-fit modification rather than from the fitted expressions.

  1. fitted input called prediction [Section II (Methodology) and Section III A (Comparison with Other Models)]
    "At the extrapolated energies of sqrt(s) = 14, 15, and 28 TeV which is beyond the capabilities of LHC, the results of fitting of our models shows good agreement with the differential cross sections fits calculated by extended Bialas-Bzdak (BB) model of ref. [47]."

    Section II states that the models 'are also fitted to extrapolated results at future LHC energies of 14, 15 and 28 TeV of ref. [47]' and that predicted results at 200/800 GeV and 27.43 GeV from refs. [62] and [63] are also fitted. The BB, impact-picture, and FMO curves are thus the training targets for those energies. Citing agreement with the same curves in Section III A as evidence that the models 'encapsulate the key physical mechanisms' is circular: the parameters were chosen to minimize discrepancy to those very predictions, so the agreement is a property of the fit, not an independent confirmation.

  2. fitted input called prediction [Section III C (Eq. 26 and Table 10), with Eqs. (16) and (19) and Tables V and VI]
    "The model 5 and 6 contained the power law factor in the first exponential term due to which the extrapolated values of the (d sigma /dt)t=0 are drastically lowered and resulted in very lower values of total cross section sigma_tot. When this factor is neglected in these models then sigma_tot values increased while keeping other parameters same. The sigma_tot results of model 5 and 6 have been shown after doing this modification in Table 10."

    The fitted functions for Models 5 and 6 include terms proportional to t^{-m} with m=0.1 (Tables V and VI). As t->0 these terms diverge, so the fitted expressions have no value at t=0 and Eq. (26) cannot be evaluated. The paper reports Table 10 for these models after 'neglecting' the power-law factor, i.e. after evaluating a different function than the one fitted to the data. The sigma_tot (and the sigma_inel obtained from Eq. (27)) are therefore not predictions of the fitted models; they are outputs of a post-fit modification presented as model results.

full rationale

The real-data part of the paper (fits to ISR and TOTEM d sigma/dt, integration for sigma_el, and comparison with experimental sigma_el) is self-contained and does not reduce to its inputs by construction. However, two load-bearing steps are circular. First, the model parameters at the extrapolated energies 14/15/28 TeV, 200/800 GeV, and 27.43 GeV are fitted to curves generated by the BB, impact-picture, and FMO models, and the paper then treats agreement with those same curves as validation of its models. Second, the sigma_tot results for Models 5 and 6 are not obtained from the fitted expressions, which diverge at t=0; the paper explicitly says the power-law factor was neglected after fitting. Presenting those post-fit values as 'results ... by extrapolation of our models at t=0' means the quoted sigma_tot and sigma_inel for Models 5 and 6 are not consequences of the fitted model. These issues affect part of the central quantitative output, but the main d sigma/dt fits to real collider data are not themselves circular, so the overall circularity is partial rather than total. No load-bearing self-citation chain is present.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claim rests on roughly 10-14 fitted parameters per model per energy (amplitudes, slopes, exponents) and on five modeling assumptions: the exponential-sum ansatz, the (s/s0) scaling form, the optical theorem extrapolation, the validity of integrating and extrapolating beyond the fitted range, and the use of other models' outputs as data. No new physical entities are introduced.

free parameters (7)
  • A1, A2, A3, A4 (per model, per energy) = e.g., A1 ~ 20-700 mb/GeV^2; A3 often -0.06 or -9.06
    Amplitudes of the exponential terms in Eqs. (4), (7), (10), (13), (16), (19), (22); fitted to data at each energy.
  • B1, B2, B3, B4 (per model, per energy) = e.g., B1 ~ 8-16.5 GeV^-2; B3 often fixed at 3.00 or 7.207
    Slopes of the exponentials; fitted per energy and show the energy-dependent shrinkage.
  • eta and mu (per energy) = e.g., eta ~ 0.02-0.25; mu ~ 10^-5-0.08
    Exponents in the scaling factors (s/s0)^eta and (s/s0)^mu; fitted per energy, so they do not provide a global energy dependence.
  • alpha (models 2, 3, 4, 6) = 0.1, 0.18, 0.2, 2.7
    Modulation strength in the (1 - alpha t/t0)^2, (1 + alpha e^{-C1 t}), or log(1 + alpha t/t0) factors; fitted per energy.
  • beta (model 4) = 0.02-0.2
    Second modulation strength in the (1 - beta t/t0)^2 factor.
  • t0 (models 3-7) = 1.0, 10, or 20 GeV^2
    Reference momentum scale chosen by hand, not fitted, and it changes value between energy rows (e.g., 10 at GeV energies, 20 at TeV energies in Model 5).
  • m, n, p, gamma (models 2, 3, 5, 6, 7) = m=0.1-1, n=0.01-1.34, p=0.1-0.3, gamma=0.001
    Power-law, saturation, and stretched-exponential exponents fitted per energy.
assumptions (6)
  • ad hoc to paper The differential cross section for pp elastic scattering can be represented as a finite sum of exponential terms multiplied by polynomial, logarithmic, or power-law correction factors.
    All seven models in Sec. II A assume this functional form without derivation; it is an empirical ansatz.
  • domain assumption The energy dependence of each term is fully captured by the scale factors (s/s0)^eta and (s/s0)^mu, with s0 = 1 GeV^2.
    Introduced in Sec. II A as 'reminiscent' of Regge/pomeron forms; no derivation from Regge theory is given, and eta and mu are refitted per energy.
  • standard math The optical theorem, sigma_tot^2 = 16 pi (hbar c)^2 / (1 + rho^2) (dsigma/dt) at t=0, with rho taken from the literature, applies to the extrapolated model value.
    Eq. (26); the theorem itself is standard, but its application here assumes the fitted dsigma/dt can be extrapolated to t=0.
  • domain assumption Fitting the model to data over a limited |t| range allows reliable extrapolation to t=0 and to |t| values up to 12 GeV^2 for integration.
    Used in Sec. III B/C; violated for models 5 and 6 where the t=0 limit diverges unless the fitted term is removed.
  • domain assumption The 'data' at 27.43 GeV, 200 GeV, 800 GeV, 14 TeV, 15 TeV, and 28 TeV are the model outputs of refs. [47], [62], [63], treated as valid fitting targets.
    Sec. II states the models are fitted to 'extrapolated results at future LHC energies' and predictions of other models; no experimental data at those energies are used.
  • ad hoc to paper The normalized chi^2 of Eq. (23), which ignores experimental uncertainties and the number of degrees of freedom, is an adequate measure of fit quality.
    Eq. (23) divides by the sum of data^2 rather than using experimental errors; the paper calls it 'chi-square per degree of freedom' without subtracting the number of parameters.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Models for differential cross section in proton-proton scattering and their implications at ISR and LHC energies." pith.science (2026). https://pith.science/paper/N3I3TMII

@misc{pith2026250605532,
  author       = {Pith},
  title        = {Pith review of: Models for differential cross section in proton-proton scattering and their implications at ISR and LHC energies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N3I3TMII}},
  note         = {Machine review of arXiv:2506.05532}
}
abstract

Few composite exponential models for the differential cross section are proposed to analyse the proton-proton ($pp$) elastic scattering at several energies. These proposed models are fitted to the data for $pp$ elastic differential cross section reported at CERN-ISR, LHC, and extrapolated energies of other models. These models have produced important features including dip-bump structure and shrinkage of the forward peak. Position of the dip is also well produced by our models for all the data across a broad energy range of $\sqrt{s}$ = 23 GeV, 23.5 GeV, 27.23 GeV, 30.7 GeV, 44.7 GeV, 52.8 GeV, 62.5 GeV, 200 GeV, 800 GeV, 2.76 TeV, 7 TeV, 8 TeV, 13 TeV, 14 TeV, 15 TeV, and 28 TeV. Employing these proposed models, elastic cross section, inelastic cross section, and total cross section are calculated at all the energies. Calculated results are compared with experimental data and theoretical results of other models. Implications of these results (obtained by models) related to the structure and dynamics of proton are discussed. The findings of this study emphasize the significance of combining theoretical and phenomenological approaches to accurately describe $pp$ elastic scattering at high energies and provide significant information to future LHC experiments for the investigation of differential cross section.

Figures

Figures reproduced from arXiv: 2506.05532 by the authors.

Figure 1
Figure 1. FIG. 1: (a) Model 1 fits on the [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (a) Same legend as in Fig.1 with Model 2. (b) Same legend as in Fig.1 with Model 2. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: (a) Same legend as in Fig.1 with Model 3. (b) Same legend as in Fig.1 with Model 3. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4: (a) Same legend as in Fig.1 with Model 4. (b) Same legend as in Fig.1 with Model 4. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: (a) Same legend as in Fig.1 with Model 5. (b) Same legend as in Fig.1 with Model 5. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: (a) Same legend as in Fig.1 with Model 6. (b) Same legend as in Fig.1 with Model 6. [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: (a) Same legend as in Fig.1 with Model 7. (b) Same legend as in Fig.1 with Model 7. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Graphical comparison of total, elastic, and inelastic cross-section calculation results by our models presented [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

75 extracted references · 73 canonical work pages

  1. [62]

    and Soffer, Jacques and Wu, Tai Tsun, (1979), ”A New Impact Picture for Low and High-Energy Proton Proton Elastic Scattering”, Phys

    Bourrely, C. and Soffer, Jacques and Wu, Tai Tsun, (1979), ”A New Impact Picture for Low and High-Energy Proton Proton Elastic Scattering”, Phys. Rev. D, 19, 3249

    work page 1979

  2. [63]

    Froissaron and Maximal Odderon with spin-flip in $pp$ and $\bar pp$ high energy elastic scattering

    Bence, N. et al., (2020), ”Froissaron and Maximal Odderon with spin-flip in pp and ¯pp high energy elastic scattering”, arXiv:2010.11987 [hep-ph]

    work page Pith review arXiv 2020

  3. [47]

    Nemes, F. and C. org, T. and Csanad, M., (2015), ”Excitation function of elastic pp scattering from a unitarily extended Bialas-Bzdak model”, Int. J. Mod. Phys. A, 30, 1550076

    work page 2015

  4. [1]

    Donnachie and P.V

    A. Donnachie and P.V . Landshoff, (1992) ”Total cross sections”, Phy. Lett. B296, 227-232. 21

    work page 1992

  5. [2]

    Block, M. M. and Halzen, F., (2011) ”Forward hadronic scattering at 7 TeV: An update on predictions for the LHC”, Phys. Rev. D 83

    work page 2011

  6. [3]

    Donnachie and P.V

    A. Donnachie and P.V . Landshoff, (2013) ”pp and ¯pp total cross sections and elastic scattering”, Phys. Lett. B 727, 500-505

    work page 2013

  7. [4]

    and Dosch, G

    Donnachie, S. and Dosch, G. and Landshoff, P. and Nachtmann, O., (2002) ”Pomeron Physics and QCD”, Cambridge Univer- sity Press

    work page 2002

  8. [5]

    and Ross, D.A., (1997) ”Quantum Chromodynamics and the Pomeron”, Cambridge University Press

    Forshaw, J.R. and Ross, D.A., (1997) ”Quantum Chromodynamics and the Pomeron”, Cambridge University Press

    work page 1997

Show all 75 references
  1. [6]

    Nagy et al., (1979) ”Measurements of elastic proton-proton scattering at large momentum transfer at the CERN intersecting storage rings”, Nucl

    E. Nagy et al., (1979) ”Measurements of elastic proton-proton scattering at large momentum transfer at the CERN intersecting storage rings”, Nucl. Phys. B 150, 221-267

    1979

  2. [7]

    et al., (2020) ”Elastic differential cross-section dσ /dt at √s = 2.76 TeV and implications on the existence of a colourless C-odd three-gluon compound state”, Eur

    Antchev, G. et al., (2020) ”Elastic differential cross-section dσ /dt at √s = 2.76 TeV and implications on the existence of a colourless C-odd three-gluon compound state”, Eur. Phys. J. C 80, CERN-EP-2018-341, TOTEM-2018-002

    2020

  3. [8]

    et al., (2013) ”Measurement of proton-proton inelastic scattering cross-section at√s=7 TeV”, Europhysics Letters 101, 21003

    Antchev, G. et al., (2013) ”Measurement of proton-proton inelastic scattering cross-section at√s=7 TeV”, Europhysics Letters 101, 21003

    2013

  4. [9]

    et al., (2011) ”Proton-proton elastic scattering at the LHC energy of 7 TeV”, Europhysics Letters 95, 41001

    The TOTEM Collaboration and Antchev, G. et al., (2011) ”Proton-proton elastic scattering at the LHC energy of 7 TeV”, Europhysics Letters 95, 41001

    2011

  5. [10]

    et al., (2022) ”Characterisation of the dip-bump structure observed in proton- proton elastic scattering at √s = 8 TeV”, Eur

    The TOTEM Collaboration and Antchev, G. et al., (2022) ”Characterisation of the dip-bump structure observed in proton- proton elastic scattering at √s = 8 TeV”, Eur. Phys. J. C 82, 263

    2022

  6. [11]

    et al., (2019) ”Elastic differential cross-section measurement at √s=13 TeV by TOTEM”, Eur

    Antchev, G. et al., (2019) ”Elastic differential cross-section measurement at √s=13 TeV by TOTEM”, Eur. Phys. J. C79, 861

    2019

  7. [12]

    Abazov, V . M. et al., (2021) ”Odderon Exchange from Elastic Scattering Differences between pp and ¯pp Data at 1.96 TeV and from pp Forward Scattering Measurements”, Phys. Rev. Lett. 127, 062003

    2021

  8. [13]

    Marco Bozzo et al., (1984) ”Low momentum transfer elastic scattering at the CERN proton-antiproton collider”, Phys. Lett. B 147, 385-391

    1984

  9. [14]

    UA4 Collaboration, (1985) ”Elastic Scattering at the CERN SPS Collider Up to a Four Momentum Transfer of 1.55 GeV 2”, Phys. Lett. B 155, 197

    1985

  10. [15]

    CDF Collaboration, (1994) ”Measurement of small angle ¯pp elastic scattering at √s = 546 GeV and 1800 GeV”, Phys. Rev. D, 50, 5518

    1994

  11. [16]

    E710 Collaboration, (1988) ”Measurement of b, the Nuclear Slope Parameter of the ¯ pp Elastic Scattering Distribution at√s = 1800 GeV”, Phys. Rev. Lett., 61, 525

    1988

  12. [17]

    E710 Collaboration, (1989) ”Measurement of the ¯pp Total Cross-Section at √s = 1.8 TeV”, Phys. Rev. Lett.,63, 2784

    1989

  13. [18]

    E710 Collaboration, (1992) ”Measurement of ρ, the ratio of the real to imaginary part of the ¯ pp forward elastic scattering amplitude, at √s = 1.8 TeV”, Phys. Rev. Lett.,68, 2433

    1992

  14. [19]

    and et al., (2016) ”Measurement of the total cross section from elastic scattering in pp collisions at √s = 8 TeV with the ATLAS detector”, Phys

    Aaboud, M. and et al., (2016) ”Measurement of the total cross section from elastic scattering in pp collisions at √s = 8 TeV with the ATLAS detector”, Phys. Rev. Lett.,117, 182002

    2016

  15. [20]

    and et al, (2016) ”Single spin asymmetry AN in polarized proton–proton elastic scattering at √s = 200 GeV at RHIC”, Phys

    Adamczyk, L. and et al, (2016) ”Single spin asymmetry AN in polarized proton–proton elastic scattering at √s = 200 GeV at RHIC”, Phys. Rev. Lett., 719, 62-69

    2016

  16. [21]

    Froissart, (1961) ”Asymptotic behavior and subtractions in the Mandelstam representation”, Phys

    M. Froissart, (1961) ”Asymptotic behavior and subtractions in the Mandelstam representation”, Phys. Rev., 123, 1053

    1961

  17. [22]

    Gauron, L

    P. Gauron, L. Lukaszuk and B. Nicolescu, (1992) ”Consistency of the maximal odderon approach with the QFT constraints”, Phys. Lett. B, 294, 298

    1992

  18. [23]

    M. M. Block et al., (1994) ”The High-energy behavior of the forward scattering parameters σtotal, ρ and B”, arXiv:hep- ph/9412306, 73-78

    1994

  19. [24]

    J. R. Cudell et al, (2002) ”Hadronic scattering amplitudes: Medium-energy constraints on asymptotic behavior”, Phys. Rev. D, 65, 074024

    2002

  20. [25]

    COMPETE Collaboration, (2002) ”Benchmarks for the forward observables at RHIC, the Tevatron Run II and the LHC”, Phys. Rev. D, 89, 201801

    2002

  21. [26]

    TOTEM Collaboration, (2018) ”First determination of theρ parameter at √s = 13 TeV — probing the existence of a colourless three-gluon bound state”, arXiv:1812.04732 [hep-ex]

    2018 arXiv

  22. [27]

    M. M. Islam, (2018) ”https://slac.stanford.edu/econf/C111215/papers/islam.pdf”

    2018

  23. [28]

    Dremin and V .A

    I.M. Dremin and V .A. Nechitailo, (2013) ”Proton periphery activated by multiparticle dynamics”, Nuc. Phys. A,916, 241-248

    2013

  24. [29]

    L., (2023) ” pp elastic scattering at ISR and LHC energies”, Phys

    Nekrasov, M. L., (2023) ” pp elastic scattering at ISR and LHC energies”, Phys. Rev. D, 108, 034028

    2023

  25. [30]

    et al., (2010) ”The Color Glass Condensate”, Ann

    Gelis, F. et al., (2010) ”The Color Glass Condensate”, Ann. Rev. Nucl. Part. Sci., 60, 463-489

    2010

  26. [31]

    and Fazal-e-Aleem, (1980),”Dipole Pomeron and Proton-Proton Elastic Scattering at High Energies”, Austr

    Saleem, M. and Fazal-e-Aleem, (1980),”Dipole Pomeron and Proton-Proton Elastic Scattering at High Energies”, Austr. Jour. Phys., 33, 481

    1980

  27. [32]

    R. N. Cahn, (1982),”Coulomb-Hadronic Interference in an Eikonal Model”, Z. Phys. C., 15, 253-260

    1982

  28. [33]

    D. A. Fagundes, M. J. Menon, (2012),”Total Hadronic Cross Section and Elastic Slope: An Almost Model-Independent Connection”, Nucl. Phys. A, 880, 1-15

    2012

  29. [34]

    Kundr´at and M

    V . Kundr´at and M. Lokaj ´ıˇcek, (1992),”High-energy elastic hadron scattering in Coulomb and hadronic regions”, Phys. Rev. D, 46, 4087–4090

    1992

  30. [35]

    et al., (2015),”Evidence for non-exponential elastic proton–proton differential cross-section at low | t | and √s = 8 TeV by TOTEM”, Nucl

    Antchev G. et al., (2015),”Evidence for non-exponential elastic proton–proton differential cross-section at low | t | and √s = 8 TeV by TOTEM”, Nucl. Phys. B, 899, 527-546

    2015

  31. [36]

    and others (TOTEM Collaboration), (2019),”Elastic Differential Cross-Section Measurement at 13 TeV by TOTEM”, Eur

    Antchev, G. and others (TOTEM Collaboration), (2019),”Elastic Differential Cross-Section Measurement at 13 TeV by TOTEM”, Eur. Phys. J. C, 79, 103. 22

    2019

  32. [37]

    Kohara, A. K. and Ferreira, E. and Kodama, T., (2017), ”Amplitudes for High-Energy Proton-Proton Elastic Scattering”, Eur. Phys. J. C, 77, 877

    2017

  33. [38]

    Jenkovszky, L’aszl’o and Szanyi, Istv’an, (2018), ”Elastic and inelastic diffraction at the LHC”, EPJ Web Conf., 172, 06004

    2018

  34. [39]

    Martynov, (2018), ”Did TOTEM experiment discover the Odderon?”, Phys

    E. Martynov, (2018), ”Did TOTEM experiment discover the Odderon?”, Phys. Lett. B, 778, 414-418

    2018

  35. [40]

    Selyugin, (2015), ”Nucleon structure and the high energy interactions”, Phys

    O.V . Selyugin, (2015), ”Nucleon structure and the high energy interactions”, Phys. Rev. D,91, 113003

    2015

  36. [41]

    Selyugin, (2012), ”GPDs of the nucleons and elastic scattering at high energies”, Eur

    O.V . Selyugin, (2012), ”GPDs of the nucleons and elastic scattering at high energies”, Eur. Phys. J. C,72, 2073

    2012

  37. [42]

    Selyugin, (2019), ”New feature in the differential cross sections at 13 TeV measured at the LHC”, Phys

    O.V . Selyugin, (2019), ”New feature in the differential cross sections at 13 TeV measured at the LHC”, Phys. Lett. B, 797, 134870

    2019

  38. [43]

    Selyugin, (2024), ”New properties of elastic pp and p ¯p scattering at high energies”, Eur

    O.V . Selyugin, (2024), ”New properties of elastic pp and p ¯p scattering at high energies”, Eur. Phys. J. C, 84, 649

    2024

  39. [44]

    Wei,Watanabe

    Xie. Wei,Watanabe. Akira, Huang. Mei, (2019), ”Elastic proton-proton scattering at LHC energies in holographic QCD”, J. of High Energy Phys., 2019, 53

    2019

  40. [45]

    Phillips and V

    R.J.N. Phillips and V . Barger, (1973), ”Model independent analysis of the structure in pp scattering”, Phys. Lett. B, 46, 412-414

    1973

  41. [46]

    Gonc ¸alves, V .P., Silva, P.V .R.G., (2015), ”The Phillips–Barger model for the elastic cross section and the Odderon”, Eur. Phys. J. C, 79, 237

    2015

  42. [48]

    Cs ¨org˝o, Tam ´as and Hegyi, Sandor and Szanyi, Istv ´an, (2023), ”L ´evy α-Stable Model for the Non-Exponential Low- | t | Proton–Proton Differential Cross-Section”, Universe, 9, 361

    2023

  43. [49]

    et al., (2025), ”Scaling of the elastic proton-proton cross-section”, arXiv.2501.08398[hep-ph]

    Praszalowicz, M. et al., (2025), ”Scaling of the elastic proton-proton cross-section”, arXiv.2501.08398[hep-ph]

    2025 arXiv

  44. [50]

    et al., (2024), ”Scaling laws of elastic proton-proton scattering differential cross sections”, Phys

    Baldenegro, C. et al., (2024), ”Scaling laws of elastic proton-proton scattering differential cross sections”, Phys. Lett. B. 856, 138960

    2024

  45. [51]

    M. M. Block and F. Halzen, (2011), ”New fit to high-energy pp and p ¯p scattering data”, Phys. Rev. D, 83, 077901

    2011

  46. [52]

    V . V . Anisovich et al., (2014), ”Impact parameter analysis of pp andp ¯p scattering”, Phys. Rev. D, 90, 074005

    2014

  47. [53]

    Dulat et al., (2016), ”New Parton Distribution Functions from the CT14 Global Analysis”, Phys

    S. Dulat et al., (2016), ”New Parton Distribution Functions from the CT14 Global Analysis”, Phys. Rev. D, 93, 033006

    2016

  48. [54]

    TOTEM Collaboration, (2013), ”Luminosity-independent measurement of the total proton-proton cross-section at √s = 8 TeV”, Phys. Rev. Lett.,111, 012001

    2013

  49. [55]

    Pierre Auger Collaboration, (2016), ”Testing Hadronic Interactions at Ultra-High Energies”, Phys. Rev. Lett., 117, 192001

    2016

  50. [56]

    Ostapchenko, (2019), ”QGSJET-II: physics, recent improvements, and results for air showers”, EPJ Web Conf.,208, 11002

    S. Ostapchenko, (2019), ”QGSJET-II: physics, recent improvements, and results for air showers”, EPJ Web Conf.,208, 11002

    2019

  51. [57]

    et al., (2019), ”The elastic differential pp cross-section at 13 TeV: an empirical model analysis”, EPJ Web Conf., 206, 06003

    Grau, A. et al., (2019), ”The elastic differential pp cross-section at 13 TeV: an empirical model analysis”, EPJ Web Conf., 206, 06003

    2019

  52. [58]

    M., (2013), ”Elastic pp scattering from the optical point to past the dip: An empirical model analysis”, Phys

    Dremin, I. M., (2013), ”Elastic pp scattering from the optical point to past the dip: An empirical model analysis”, Phys. Lett. B, 720, 83-86

    2013

  53. [59]

    et al., (2019), ”FCC Physics Opportunities”, Eur

    Abada, A. et al., (2019), ”FCC Physics Opportunities”, Eur. Phys. J. C, 79, 474

    2019

  54. [60]

    et al., (2019), ”Machine Learning for High-Energy Physics Applications”, arXiv:1807.02876 [physics.comp- ph]

    Albertsson K. et al., (2019), ”Machine Learning for High-Energy Physics Applications”, arXiv:1807.02876 [physics.comp- ph]

    2019 arXiv

  55. [61]

    Amaldi et al., (1980), ”Impact parameter interpretation of proton-proton scattering from a critical review of all ISR data”, Nuc

    U. Amaldi et al., (1980), ”Impact parameter interpretation of proton-proton scattering from a critical review of all ISR data”, Nuc. Phys. B, 166, 301-320

    1980

  56. [64]

    Brodsky and Glennys R

    Stanley J. Brodsky and Glennys R. Farrar, (1973), ”Scaling Laws at Large Transverse Momentum”, Phys. Rev. Lett., 31, 1153-1156

    1973

  57. [65]

    Collins, P. D. B., (1977), ”An Introduction to Regge Theory and High Energy Physics”, Cambridge University Press

    1977

  58. [66]

    Jenkovszky, L ´aszl´o and Schicker, Rainer and Szanyi, Istv´an,(2022) ”Regge Models of Proton Diffractive Dissociation Based on Factorisation and Structure Functions”, Entropy, 24, 7

    2022

  59. [67]

    Adamczyk et al

    L. Adamczyk et al. (STAR Collaboration), (2013) ”Single spin asymmetry AN in polarized proton-proton elastic scattering at√s = 200 GeV”, Phys. Lett. B, 719, 62-69

    2013

  60. [68]

    Adamczyk, Leszek., (2015) ”Measurement of the Total Cross Section in Proton Proton Collisions at√s=7 TeV with the ALFA Sub-Detector of ATLAS”, Phys. Lett. B, DIS2015, 61

    2015

  61. [69]

    Antchev, G. et al. (TOTEM collaboration), (2013) ”Luminosity-independent measurements of total, elastic and inelastic cross- sections at √s = 7 TeV”, EPL, 101, 2, 21004

    2013

  62. [70]

    et al., (2021) ”Evidence of Odderon-exchange from scaling properties of elastic scattering at TeV energies”, Eur

    Csorgo T. et al., (2021) ”Evidence of Odderon-exchange from scaling properties of elastic scattering at TeV energies”, Eur. Phys. J. C, 81, 180

    2021

  63. [71]

    et al., (2019) ”First measurement of elastic, inelastic and total cross-section at TeV by TOTEM and overview of cross-section data at LHC energies”, Eur

    Anchtev G. et al., (2019) ”First measurement of elastic, inelastic and total cross-section at TeV by TOTEM and overview of cross-section data at LHC energies”, Eur. Phys. J. C, 79

    2019

  64. [72]

    et al., (2013) ”Measurement of proton-proton elastic scattering and total cross-section at √s = 7 TeV”, EPL, 101, 21002

    Anchtev G. et al., (2013) ”Measurement of proton-proton elastic scattering and total cross-section at √s = 7 TeV”, EPL, 101, 21002

    2013

  65. [73]

    et al., (2013) ”Luminosity-Independent Measurement of the Proton-Proton Total Cross Section at √s = 8 TeV”, EPL, 111, 012001

    Antchev, G. et al., (2013) ”Luminosity-Independent Measurement of the Proton-Proton Total Cross Section at √s = 8 TeV”, EPL, 111, 012001. 23

    2013

  66. [74]

    et al., (1978) ”Measurement of the Proton Proton Total Cross-Section and Small Angle Elastic Scattering at ISR Energies”, Nucl

    Baksay, L. et al., (1978) ”Measurement of the Proton Proton Total Cross-Section and Small Angle Elastic Scattering at ISR Energies”, Nucl. Phys. B, 141, 1-28

    1978

  67. [75]

    Cafagna, Francesco S., (2021) ”Latest results for Proton-Proton Cross Section Measurements with the TOTEM experiment at LHC”, PoS, ICRC2019, 207

    2021

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.