Semihard interactions at high energies

E. G. S. Luna; T. V. Iser

REVIEW 3 major objections 5 minor 1 cited by

Semihard interactions at high energies

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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

Pith's one-line read A QCD minijet eikonal model finds that describing the measured ratio of real to imaginary forward amplitude at 13 TeV requires an odd semihard component, independent of the TOTEM/ATLAS normalization choice.

desk verdict Solid fits, but the advertised odd semihard component is never actually fitted — the conclusion outruns the calculation. read the letter →

arxiv 2502.03168 v1 pith:YV46YNP4 submitted 2025-02-05 hep-ph hep-exhep-th

T. V. Iser , E. G. S. Luna This is my paper · ORCID

classification hep-phhep-exhep-th

keywords minijetmodelsemihardinteractionstotalcrosssectionrhoparametereikonalnext-to-leading-orderQCDTOTEMATLAS/ALFA

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

This paper is about what actually controls the forward proton-antiproton amplitude at LHC energies. The authors run a QCD eikonal minijet model—where the growth of the total cross section comes from semihard gluon-dominated jet production—against the world's $pp$ and $\bar{p}p$ data at $\sqrt{s} \ge 10$ GeV, fitting the TOTEM and ATLAS/ALFA normalizations separately. Both fits reproduce the total cross section well, but both miss the measured value of $\rho$ at 13 TeV, the ratio of the real to imaginary parts of the forward amplitude. Because dispersion relations tie $\rho$ tightly to the energy growth of the total cross section, the authors read this residual as evidence that the semihard amplitude itself must carry an odd (particle-antiparticle antisymmetric) component that does not vanish at high energies. If they are right, the standard even-only semihard picture is incomplete, and the real part of the high-energy amplitude is shaped by semihard dynamics, not just soft physics.

What carries the argument

The load-bearing object is the semihard eikonal pair. The even piece is $\chi^+_{\rm SH}(s,b) = \frac{N}{2}\tilde{\sigma}(s)\,W_{\rm SH}(b;\nu_{\rm SH})$, with $\tilde{\sigma}(s)$ the NLO QCD jet cross section (CT18 PDFs, $p_{T\min}=1.1$ GeV), $N$ a phenomenological factor absorbing the K-factor and cutoff uncertainty, and $W_{\rm SH}(b) = \frac{\nu_{\rm SH}^2}{96\pi}(\nu_{\rm SH}b)^3 K_3(\nu_{\rm SH}b)$ a dipole overlap density. The model sets the odd semihard eikonal to zero, leaving the soft eikonal as the only source of crossing-odd behavior. The forward observables $\sigma_{\rm tot}(s)$ and $\rho(s)$ are computed from the full eikonal via standard integrals, and dispersion relations tie $\rho$ to the energy growth of $\sigma_{\rm tot}$; that tie is what converts the 13 TeV $\rho$ mismatch into evidence for an omitted odd semihard amplitude.

What would settle it

A global fit that keeps the semihard eikonal purely even but lets $\gamma$ and $\mu^-_{\rm soft}$ float, or that changes the soft dipole form factor, would falsify the central claim if it then reproduces the 13 TeV $\rho$ values from both TOTEM and ATLAS/ALFA within uncertainties.

Watch

Extended reading notes

Core claim

The central claim is that a purely even semihard amplitude cannot describe the forward $pp$ amplitude at 13 TeV. In the model, the eikonal is the sum of a soft piece (with an odd term) and a semihard piece driven by the NLO QCD cross section for jet production, and the forward observables $\sigma_{\rm tot}(s)$ and $\rho(s)$ follow from the eikonal through standard integrals. Global fits using CT18 PDFs and $p_{T\min}=1.1$ GeV give $\chi^2/\nu \simeq 1.18$ (TOTEM-based) and $1.10$ (ATLAS-based), so the total cross section over a wide energy range is described; the failure is concentrated in the 13 TeV $\rho$ point. The authors conclude that, independent of which collaboration's normalization is correct, a satisfactory description of $\rho$ requires adding an odd component to the semihard amplitude that persists asymptotically. They explicitly leave the implementation of that odd semihard term to a future study.

Load-bearing premise

The paper's conclusion assumes that the 13 TeV $\rho$ mismatch reflects missing physics in the semihard amplitude rather than the fixed values of the soft-eikonal parameters $\gamma$ and $\mu^-_{\rm soft}$ or other modeling choices.

Editorial extensions

If this is right

A purely even semihard amplitude cannot describe the forward proton amplitude at 13 TeV; an odd semihard term that persists at high energies must be added.
The requirement holds for both TOTEM and ATLAS/ALFA normalizations, so it does not depend on which collaboration's absolute scale is correct.
The extension should fix the 13 TeV rho point while leaving the already good description of the total cross section largely unchanged.
The paper explicitly plans to implement the odd semihard component and to test the sensitivity of the results to the choice of parton distribution functions.

Reading between the lines

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

A testable extension: if the odd semihard term persists asymptotically, it predicts a non-vanishing and possibly growing difference between proton-proton and proton-antiproton total cross sections at LHC energies.
The paper's inference rests on the fixed soft parameters $\gamma = 0.7$ and $\mu^-_{\rm soft} = 0.5$ GeV; a fit that lets these parameters float while keeping the semihard sector even would show whether the 13 TeV $\rho$ residual can be absorbed without new odd physics.
The proposed odd term would most naturally be generated by C-odd (three-gluon) exchange in the semihard regime, giving the model a concrete partonic interpretation to test.
A targeted check is the energy slope of $\rho$: a persistent odd semihard amplitude should leave a distinctive imprint in $\rho(s)$ between 7 and 14 TeV that differs from the even-only prediction.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

Two things to know. First, this is a short proceedings paper that re-fits the authors' eikonal minijet model to forward pp and pbarp data using CT18 PDFs, splitting TOTEM and ATLAS/ALFA into two ensembles. The fits are respectable (chi2/nu 1.18 and 1.10). Second, the advertised conclusion—that both datasets require a crossing-odd semihard component at high energies—is not derived anywhere in the paper. No model containing an odd semihard term is fitted, no delta-chi2 is reported, and the only evidence is that the 13 TeV rho point is not well described by the even-only model.

What is new and useful: the use of CT18 PDFs in this framework, the explicit separation into TOTEM and ATLAS ensembles, and the parameter tables. The model itself goes back to earlier work by the group, but the update is clean and the fit quality is acceptable. The authors also state plainly which parameters are fixed (gamma=0.7, mu-_soft=0.5 GeV) and which are fitted, which makes the analysis reproducible in principle.

The soft spot is the inference, not the computation. The paper says 'regardless of which normalization ... is accurate, a satisfactory description of rho necessitates the inclusion of an odd component.' That is not supported by the evidence. The residual at 13 TeV shows only that this particular even-only model with those fixed parameters misses one point. It doesn't rule out freeing gamma and mu-_soft, adjusting pTmin or the PDF set, or adding a simple soft-odderon term, any of which could absorb the same residual. Worth noting: with nu around 160, a single bad rho point contributes little to chi2/nu, so the good global chi2 doesn't strengthen the claim. The paper even ends by deferring the odd-semihard calculation to 'an extension of this study,' which confirms that the headline is a prediction of future work, not a result of this one.

So who is this for? A specialist in high-energy forward scattering might want the fit tables and the ensemble comparison. But anyone citing this for the odd semihard component would be over-reading. The authors are capable and the framework is coherent; they just haven't done the calculation they claim points to necessity.

I would treat this as a solid conference report whose conclusion overstates its evidence. If the venue wants the necessity claim, a serious referee should send it back for either the full implementation or a heavily toned-down conclusion. I wouldn't desk reject, though the paper needs revision to earn the central claim.

Read it as a cautionary example of residual-driven speculation, not as evidence for an odd semihard amplitude.

Referee Report

3 major / 5 minor

Summary. This short proceedings paper presents a QCD-based eikonal minijet model for pp and \bar{p}p forward scattering. The even semihard eikonal is computed with NLO partonic cross sections (Eqs. 2–7), and the soft eikonal is parameterized with even and odd terms (Eqs. 8–9). The model is fitted to two ensembles of high-energy forward data, one including TOTEM and one including ATLAS/ALFA; the fits give \chi^2/\nu = 1.18 and 1.10 (Table I). The authors report that the \rho data at \sqrt{s} = 13 TeV are not well described and use this residual to conclude that an odd semihard component is necessary at high energies, although such a component is not implemented in the fits.

Significance. If the claimed necessity of a high-energy odd semihard amplitude were demonstrated, the result would be noteworthy: it would indicate that the standard even-semihard minijet picture is incomplete and would motivate a new class of models for the forward amplitude. The paper's positive features are the explicit NLO treatment of the jet cross section and the separate fits to the TOTEM and ATLAS/ALFA data, which document the known normalization tension. However, the central claim is not tested: no model containing an odd semihard eikonal is fitted, no alternative explanation (fixed soft parameters, PDF choice, normalization offsets) is quantified, and no statistical significance of the 13 TeV \rho residual is reported. The conclusion therefore outruns the presented analysis.

major comments (3)

[Section III; Table I] The central claim that an odd semihard component is necessary is not supported by any fit containing such a component. The model fitted in Table I uses \chi^-_{SH} = 0 (Section II), so the residual in \rho at \sqrt{s} = 13 TeV can only show that the even-only model fails for that point. The paper does not report \Delta\chi^2, pulls, or an alternative fit with a nonzero odd semihard eikonal; the final paragraph of Section III explicitly defers this calculation to a future study. Without such a comparison, the residual is not evidence that an odd component is required.
[Section III, paragraph 2] The claim that dispersion relations 'necessitate' an odd semihard component is not quantitative. Dispersion relations connect the real and imaginary parts of the amplitude but do not determine the parity decomposition of the semihard eikonal. The authors do not test whether the same \rho residual could be absorbed by freeing \gamma and \mu^-_{soft} (which are fixed to 0.7 and 0.5 GeV), by varying pTmin, by changing the PDF set, or by applying the known TOTEM/ATLAS normalization offsets. Any of these alternatives could absorb the residual within an even-only model.
[Table I; Section III] The reported goodness of fit does not establish the significance of the 13 TeV \rho discrepancy. With \nu = 168 (TOTEM) and 158 (ATLAS), a single deviant point contributes little to \chi^2/\nu = 1.18 or 1.10. The authors should report the per-point \chi^2 of the 13 TeV \rho measurements, the fitted \rho values, and the change in \chi^2 when these points are removed. Without this information, the statement that the data are 'not well-described' cannot be weighed.

minor comments (5)

[Abstract and Section I] There are typographical errors: 'ATLAS/ALF A' should be 'ATLAS/ALFA' in the abstract and in Section I.
[Equation (6)] Equation (6) contains a formatting error in the PDF product: the second factor should read f_{j/B}(x2, |\hat t|), not f_{j/B}(x2, |\hat t)|).
[Section II] The PDF set (CT18) and the value of \alpha_s used are not specified; these details are needed for reproducibility of the NLO jet cross section calculation.
[Section III] The construction of the \chi^2 function is not described. It is unclear whether normalization uncertainties of TOTEM and ATLAS/ALFA were treated as free shifts or as fixed offsets in the fits.
[Figures 1 and 2] The figures show the fitted curves and data, but the text does not discuss the residuals. A plot of the \rho residuals at LHC energies would directly illustrate the claimed problem.

Circularity Check

1 steps flagged · score 4.0 of 10

Central inference rests on the residual of a fit to the same 13 TeV rho data; no odd semihard amplitude is implemented, so the claimed necessity is under-determined rather than derived.

fitted input called prediction [Section III, Results and Conclusions, paragraph beginning 'We achieve a good statistical fit...']
"However, the ρ data at √s = 13 TeV are not well-described, consistent with expectations based on dispersion relations. These relations connect the central value of ρ(s) to the growth behavior of σtot(s). Consequently, regardless of which normalization of the data proposed by TOTEM or ATLAS/ALFA is accurate, a satisfactory description of the ρ parameter necessitates the inclusion of an odd component in the semihard amplitude that persists at high energies."

The 13 TeV ρ points are part of the global fits that determine N, ν_SH, A, B, C, D, and μ+ (Table I, χ2/ν = 1.18/1.10). Their residual is therefore an in-sample property of the fitted model, not an out-of-sample prediction. The proposed odd semihard component is never written down or fitted—the final sentence defers it ('As an extension of this study...')—so 'necessitates' only restates that this particular even-only parameterization leaves a residual at that data point. It does not eliminate alternative explanations, such as freeing the fixed γ = 0.7 and μ−_soft = 0.5 GeV or adjusting TOTEM/ATLAS normalization, and thus the evidence cited is the residual of the fit to the very data used to draw the conclusion.

full rationale

The mathematical core—Eqs. (1)-(12) and the Table I fits—is self-contained in the sense that no equation is defined in terms of its own output and no fitted parameter is renamed as a prediction. The self-citations [3-11] supply the eikonal framework and prior model choices, but they are not invoked as a uniqueness theorem, and the fits use external data and CT18 PDFs. The circularity concern is confined to the interpretive step in Section III: the 13 TeV ρ points that motivate the odd-semihard-component claim are included in the very global fits summarized in Table I, so the 'not well-described' residual is an in-sample fit diagnostic, not a prediction. Moreover, the paper explicitly states the odd semihard component is not implemented ('As an extension of this study, we aim to examine the impact...'), so the claim that this term is necessitated is not tested against alternatives or against an actual implementation. This makes the headline inference under-determined by the calculation, but it does not reduce an equation to its input; hence the moderate score of 4 rather than a higher score. The model's descriptive fits may still be useful, but the central 'necessity' conclusion is not independently established.

Assumptions & free parameters 10 free parameters · 7 assumptions · 1 invented entities

The central claim rests on a model with many adjustable parameters (seven fitted, three fixed by hand) and several phenomenological assumptions about form factors, soft amplitudes, and the K-factor. The proposed odd semihard component is not included in the fits, so the ledger shows that the model's conclusions are not self-contained derivations from QCD.

free parameters (10)

N (semihard normalization) = 1.49 +/- 0.50 (TOTEM), 1.83 +/- 0.46 (ATLAS)
Absorbs the NLO K-factor and the pTmin uncertainty; a free parameter adjusted to the data in the global fits.
nu_SH (semihard form factor scale) = 1.32 +/- 0.12 GeV (TOTEM), 1.42 +/- 0.08 GeV (ATLAS)
Controls the transverse size of the parton overlap in the semihard eikonal; fitted to data.
A (soft eikonal even real constant) = 2.38e3 +/- 0.24e3 GeV^-2 (TOTEM), 2.11e3 +/- 2.00e3 GeV^-2 (ATLAS)
Constant real part of the even soft eikonal; fitted.
B (soft eikonal even imaginary constant) = -79.2 +/- 130.8 GeV^-2 (TOTEM), -76.31 +/- 148.3 GeV^-2 (ATLAS)
Constant imaginary part of the even soft eikonal; fitted.
C (soft eikonal even energy-dependent coefficient) = 33.6e3 +/- 11.2e3 GeV^-2 (TOTEM), 31.2e3 +/- 35.5e3 GeV^-2 (ATLAS)
Coefficient of the (s/s0)^gamma term in the even soft eikonal; fitted.
mu+_soft (soft even form factor scale) = 2.58 +/- 0.05 GeV (TOTEM), 2.55 +/- 0.39 GeV (ATLAS)
Scale in the dipole form factor for the even soft eikonal; fitted.
D (soft odd amplitude coefficient) = 149.7 +/- 11.4 GeV^-2 (TOTEM), 149.5 +/- 11.4 GeV^-2 (ATLAS)
Coefficient of the crossing-odd soft eikonal term; fitted.
gamma (soft even energy exponent) = 0.7 (fixed by hand)
Exponent in the energy-dependent even soft eikonal; assigned, not fitted.
mu-_soft (soft odd form factor scale) = 0.5 GeV (fixed by hand)
Scale in the dipole form factor for the odd soft eikonal; assigned, not fitted.
pTmin (minimum transverse momentum for jets) = 1.1 GeV (fixed)
Kinematic cutoff in the semihard jet cross section; chosen, not fitted. Its uncertainty is partly absorbed into N.

assumptions (7)

domain assumption The forward scattering amplitude is described by an eikonal model, with sigma_tot and rho computed from the eikonal via Eqs. (11)-(12).
This relies on unitarity and analyticity of the scattering amplitude, standard assumptions in high-energy forward scattering.
ad hoc to paper The parton transverse distribution has a dipole form with a single scale nu_SH (Eq. 4).
This specific form is chosen for calculational convenience and is not derived from QCD.
ad hoc to paper The soft eikonal parameterization of Eqs. (8)-(9) with the fixed values gamma=0.7 and mu-_soft=0.5 GeV adequately describes the non-semihard part of the amplitude.
The functional form and the fixed constants are phenomenological inputs, not derived from first principles.
ad hoc to paper The crossing-odd semihard eikonal chi-_SH decreases rapidly with increasing s and can be set to zero (Section II).
This assumption is stated in the model setup and later contradicted by the paper's own conclusion that an odd semihard component is needed at high energies.
ad hoc to paper The NLO QCD correction to the jet cross section can be absorbed into a constant K-factor, combined with the pTmin uncertainty into the single parameter N (Eq. 7).
This treats N as energy and process independent, which is an approximation.
domain assumption CT18 parton distribution functions, evaluated at Q^2 = pT^2, are the correct input for the semihard jet cross section at NLO.
The PDFs come from an external global analysis and are treated as known inputs.
domain assumption Gluon-dominated processes (at least one gluon in the initial state) dominate the semihard cross section at small x.
This motivates the selected partonic subprocesses in the jet cross section calculation.

invented entities (1)

Crossing-odd semihard eikonal component (chi-_SH)
purpose: Proposed to explain the 13 TeV rho discrepancy by adding an odd amplitude that does not vanish at high energies.
The paper does not implement or fit this term; it is announced as future work, so there is no falsifiable prediction attached to it in this preprint.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Semihard interactions at high energies." pith.science (2026). https://pith.science/paper/YV46YNP4

@misc{pith2026250203168,
  author       = {Pith},
  title        = {Pith review of: Semihard interactions at high energies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YV46YNP4}},
  note         = {Machine review of arXiv:2502.03168}
}

abstract

We revisit a minijet model to examine the behavior of the total cross section, $\sigma_{tot}$, and the ratio of the real to imaginary parts of the scattering amplitude, $\rho$, at high energies. In this framework, the growth of $\sigma_{tot}$ in $pp$ and $\bar{p}p$ channels is driven by semihard partonic processes dominated by gluon interactions. The QCD contribution to $\sigma_{tot}$ for the jet production is computed in the next-to-leading order. We analyze data separately from the TOTEM and ATLAS/ALFA Collaborations and find evidence in both cases suggesting the necessity of an odd semihard component that becomes asymptotically significant at high energies.

Figures

Figures reproduced from arXiv: 2502.03168 by the authors.

**Figure 2.** FIG. 2. The energy behaviour of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

Soft and semihard components of multiplicity distributions in the $k_T$ factorization approach
hep-ph 2025-06 conditional novelty 5.0 of 10

Using a transverse momentum cutoff in kT factorization, the authors fix the soft and semihard mean multiplicities in a double negative binomial fit and find that KNO scaling holds only for narrow rapidity windows and ...

Reference graph

Works this paper leans on

22 extracted references · 21 canonical work pages · cited by 1 Pith paper

[1]

L. V. Gribov, E. M. Levin, and M. G. Ryskin, Phys. Rep. 100, 1 (1983)

work page 1983
[2]

E. M. Levin and M. G. Ryskin, Phys. Rep. 189, 267 (1990)

work page 1990
[3]

Durand and H

L. Durand and H. Pi, Phys. Rev. Lett. 58, 303 (1987)

work page 1987
[4]

E. G. S. Luna, A. F. Martini, M. J. Menon, A. Mihara, and A. A. Natale, Phys. Rev. D 72, 034019 (2005)

work page 2005
[5]

E. G. S. Luna, A. A. Natale, Phys. Rev. D 73, 074019 (2006)

work page 2006
[6]

E. G. S. Luna, Phys. Lett. B 641, 171 (2006)

work page 2006
[7]

D. A. Fagundes, E. G. S. Luna, M. J. Menon,and A. A. Natale, Nucl. Phys. A 886, 48 (2012)

work page 2012
[8]

P. C. Beggio and E. G. S. Luna, Nucl. Phys. A 929, 230 (2014)

work page 2014

Show all 22 references

[9]

C. A. S. Bahia, M. Broilo, E. G. S. Luna, Phys. Rev. D 92, 074039 (2015)

2015
[10]

Broilo, D

M. Broilo, D. A. Fagundes, E. G. S. Luna, M. J. Menon, Phys. Lett. B 799, 135047 (2019)

2019
[11]

Broilo, D

M. Broilo, D. A. Fagundes, E. G. S. Luna, M. J. Menon, Eur. Phys. J. C 79, 1033 (2019)

2019
[12]

R. L. Workman et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2022, 083C01 (2022)

2022
[13]

Aad et al., Nucl

ATLAS Collaboration, G. Aad et al., Nucl. Phys. B 889, 486 (2014)

2014
[14]

Aad et al., Eur

ATLAS Collaboration, G. Aad et al., Eur. Phys. J. C 83, 441 (2023)

2023
[15]

Aaboud et al

ATLAS Collaboration, M. Aaboud et al. , Phys. Lett. B 761, 158 (2016)

2016
[16]

Antchev et al

TOTEM Collaboration, G. Antchev et al. , Europhys. Lett. 96, 21002 (2011)

2011
[17]

Antchev et al

TOTEM Collaboration, G. Antchev et al. , Phys. Rev. Lett. 111, 012001 (2013)

2013
[18]

Antchev et al

TOTEM Collaboration, G. Antchev et al. , Europhys. Lett. 101, 21002 (2013)

2013
[19]

Antchev et al

TOTEM Collaboration, G. Antchev et al. , Europhys. Lett. 101, 21004 (2013)

2013
[20]

Antchev et al., Eur

TOTEM Collaboration, G. Antchev et al., Eur. Phys. J. C 76, 661 (2016)

2016
[21]

Antchev et al., Eur

TOTEM Collaboration, G. Antchev et al., Eur. Phys. J. C 79, 785 (2019)

2019
[22]

Tie-Jiun Hou et al. , Phys. Rev. D 103, 014013 (2021). 4 FIG. 1. The energy behaviour of σtot (left) and ρ (right) from Ensemble A. FIG. 2. The energy behaviour of σtot (left) and ρ (right) from Ensemble T. TABLE I. Values of the parameters obtained in the global fits to the E...

2021

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [1]

L. V. Gribov, E. M. Levin, and M. G. Ryskin, Phys. Rep. 100, 1 (1983)

work page 1983

[2] [2]

E. M. Levin and M. G. Ryskin, Phys. Rep. 189, 267 (1990)

work page 1990

[3] [3]

Durand and H

L. Durand and H. Pi, Phys. Rev. Lett. 58, 303 (1987)

work page 1987

[4] [4]

E. G. S. Luna, A. F. Martini, M. J. Menon, A. Mihara, and A. A. Natale, Phys. Rev. D 72, 034019 (2005)

work page 2005

[5] [5]

E. G. S. Luna, A. A. Natale, Phys. Rev. D 73, 074019 (2006)

work page 2006

[6] [6]

E. G. S. Luna, Phys. Lett. B 641, 171 (2006)

work page 2006

[7] [7]

D. A. Fagundes, E. G. S. Luna, M. J. Menon,and A. A. Natale, Nucl. Phys. A 886, 48 (2012)

work page 2012

[8] [8]

P. C. Beggio and E. G. S. Luna, Nucl. Phys. A 929, 230 (2014)

work page 2014