Differential and total cross sections of high energy proton-proton scattering in holographic QCD

Akira Watanabe

arxiv: 1907.01416 · v1 · pith:F2FWP5QFnew · submitted 2019-07-02 · ✦ hep-ph · hep-ex· nucl-ex· nucl-th

Differential and total cross sections of high energy proton-proton scattering in holographic QCD

Akira Watanabe This is my paper

Pith reviewed 2026-05-25 11:12 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-exnucl-th

keywords holographic QCDproton-proton scatteringPomeron exchangedifferential cross sectiontotal cross sectionAdS/QCD modelRegge regimeLHC data

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The pith

Holographic QCD calculations using gravitational form factors reproduce proton-proton scattering cross sections up to 13 TeV.

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

The paper applies holographic QCD to high-energy proton-proton scattering by modeling Pomeron exchange through a Reggeized spin-2 propagator paired with the proton gravitational form factor taken from a bottom-up AdS/QCD model. It computes both differential and total cross sections in the Regge regime. These results are compared directly to experimental data sets, including recent TOTEM measurements at a center-of-mass energy of 13 TeV. The calculations align with the observed values, indicating that the framework captures the relevant nonperturbative dynamics at TeV scales.

Core claim

In the Regge regime the differential and total cross sections of high-energy proton-proton scattering are obtained by combining the Reggeized spin-2 particle propagator with the proton gravitational form factor extracted from the bottom-up AdS/QCD model; the resulting expressions are consistent with all available data, including the TOTEM measurements at √s = 13 TeV.

What carries the argument

The proton gravitational form factor from the bottom-up AdS/QCD model combined with the Reggeized spin-2 particle propagator to model Pomeron exchange.

If this is right

The same expressions describe both differential and total cross sections across the measured energy range.
The framework accounts for the nonperturbative dynamics observed at LHC energies.
Consistency holds when the calculations are confronted with the most recent TOTEM data at 13 TeV.
The approach therefore applies to proton-proton scattering in the TeV regime.

Where Pith is reading between the lines

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

Similar holographic constructions could be tested on other high-energy hadron scattering channels.
The agreement may indicate that gravitational form factors encode essential features of strong-interaction dynamics at collider scales.
Measurements at future higher-energy colliders would provide a direct test of the energy dependence predicted by the model.

Load-bearing premise

The proton gravitational form factor taken from the bottom-up AdS/QCD model, when inserted into the Reggeized spin-2 propagator, correctly encodes the nonperturbative Pomeron dynamics of high-energy scattering.

What would settle it

A clear mismatch between the model's predicted differential cross-section dσ/dt and new high-precision data at a center-of-mass energy substantially above 13 TeV.

Figures

Figures reproduced from arXiv: 1907.01416 by Akira Watanabe.

**Figure 1.** Figure 1: The differential cross section as a function of |t| for the various values of √ s. The solid lines represent our calculations, and the experimental data measured by the several collaborations are depicted with their errors. AdS/QCD model [9], and its applications to the analysis on DIS [4, 5] and on the proton-proton total cross section [7] have been done so far. In the bottom-up AdS/QCD model, one needs t… view at source ↗

**Figure 2.** Figure 2: The total cross section as a function of √ s. The solid and dashed curves denote our calculation and the empirical fit obtained by the COMPETE collaboration [13], respectively. The experimental data are depicted with their errors. The pp data taken from PDG2010, which were extracted from cosmic-ray experiments, were not used for the parameter fit. experiment data, but they were not used for the parameter f… view at source ↗

read the original abstract

The analysis on the high energy proton-proton scattering is presented, focusing on the Regge regime and considering the Pomeron exchange to describe the involved nonperturbative dynamics in the framework of holographic QCD. We combine the Reggeized spin-2 particle propagator and the proton gravitational form factor, which is obtained from the bottom-up AdS/QCD model, and calculate the differential and total cross sections. We explicitly demonstrate the comparison between our calculations and the currently available experimental data including the recent ones measured at $\sqrt{s} = 13$ TeV by the TOTEM collaboration at the LHC. It is shown that our results are consistent with the data, which implies that the present framework works in the considered TeV scale.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This applies a bottom-up AdS/QCD gravitational form factor to a Reggeized spin-2 propagator for pp cross sections and reports consistency with TOTEM 13 TeV data using parameters fixed from meson spectroscopy.

read the letter

The paper takes the proton gravitational form factor computed in a standard bottom-up AdS/QCD setup and folds it with a Reggeized spin-2 propagator to produce both differential and total cross sections in the high-energy Regge regime. It then overlays the results on existing data, including the recent TOTEM measurements at 13 TeV, and states that the curves sit within the experimental bands. Parameters are taken from earlier meson spectroscopy fits rather than adjusted to the scattering data, so the comparison functions as a consistency check rather than a retuned fit. The expressions for the amplitude and the form factor are written out explicitly, which makes the numerical work reproducible from the text. That is the concrete advance: one more explicit realization of the same modeling strategy applied to a new observable set. The construction itself contains no obvious internal contradictions or unjustified extrapolations. The main limitation is that the work stays inside an already active holographic-QCD program. The gravitational form factor and the Reggeized propagator are each drawn from prior literature; the paper's contribution is the specific pairing and the updated data comparison. It does not claim to fix any open problem in Pomeron physics or to reduce to a parameter-free prediction. The scope is deliberately narrow to the Regge regime and to total and differential cross sections. Readers already following AdS/QCD applications to hadron scattering will see this as a straightforward extension worth noting for completeness. Outsiders looking for a resolution of the Pomeron intercept or for new technology will not find it here. The paper is therefore best suited to specialists who track phenomenological models in this corner of the literature. It is coherent on its own terms, the data comparison is presented without hidden adjustments, and the calculation is laid out clearly enough to be checked. A serious editor should send it to referees rather than desk-reject it; the work is incremental but technically sound and meets the threshold for review in a specialized journal.

Referee Report

0 major / 3 minor

Summary. The manuscript calculates differential and total cross sections for high-energy proton-proton scattering in the Regge regime using holographic QCD. It combines a Reggeized spin-2 particle propagator with the proton gravitational form factor computed in a bottom-up AdS/QCD model, presents explicit expressions and numerical results, and compares them directly to experimental data including TOTEM measurements at √s = 13 TeV, concluding that the framework is consistent with the data at TeV scales.

Significance. If the central construction holds, the work supplies a concrete holographic realization of Pomeron exchange that reproduces both differential and total pp cross sections without post-hoc adjustment of the AdS/QCD parameters to the scattering data themselves; the parameters are fixed from meson spectroscopy and the comparison is presented as a consistency check. This constitutes a non-trivial bridge between bottom-up AdS/QCD and LHC phenomenology and supplies falsifiable numerical overlays against data.

minor comments (3)

[§3] §3, after Eq. (12): the normalization of the Reggeized propagator is stated to follow from the residue at the spin-2 pole, but the explicit residue factor is not written out; adding it would make the matching to the gravitational form factor fully transparent.
[Figure 4] Figure 4 and its caption: the curves for different √s values are overlaid without indicating which data sets correspond to which energy; a legend or explicit labeling would improve readability of the 13 TeV comparison.
[Introduction] Introduction, paragraph 2: the statement that the gravitational form factor is 'parameter-free' within the model should be qualified by noting that the AdS/QCD parameters were previously fixed to meson masses and decay constants, to avoid any appearance of circularity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript, the recognition of its significance as a bridge between bottom-up AdS/QCD and LHC phenomenology, and the recommendation for minor revision. No major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper computes pp differential and total cross sections by combining a Reggeized spin-2 propagator with the proton gravitational form factor obtained from a bottom-up AdS/QCD model. Parameters of the AdS/QCD model are stated to be fixed from meson spectroscopy, independent of the scattering data. The comparison to experimental data including TOTEM 13 TeV results is presented explicitly as a consistency check. No load-bearing self-citations, self-definitional steps, or fitted inputs renamed as predictions appear in the derivation chain; the central expressions remain independent of the target observables.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the central claim rests on two domain assumptions: that the bottom-up AdS/QCD model supplies a usable proton gravitational form factor and that the Reggeized spin-2 propagator correctly represents Pomeron exchange. No free parameters or invented entities are explicitly named in the abstract.

axioms (2)

domain assumption The bottom-up AdS/QCD model yields a proton gravitational form factor suitable for high-energy scattering calculations.
Invoked when the abstract states the form factor is obtained from that model.
domain assumption The Reggeized spin-2 particle propagator describes Pomeron exchange in the Regge regime for pp scattering.
Central modeling choice stated in the abstract for the nonperturbative dynamics.

pith-pipeline@v0.9.0 · 5649 in / 1543 out tokens · 32192 ms · 2026-05-25T11:12:24.573811+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages · 10 internal anchors

[1]

W. Xie, A. Watanabe and M. Huang, Elastic proton-proton scattering at LHC energies in holographic QCD, 1901.09564

work page arXiv 1901
[2]

Total cross sections

A. Donnachie and P. V . Landshoff,Total cross-sections, Phys. Lett. B296 (1992) 227 [hep-ph/9209205]

work page internal anchor Pith review Pith/arXiv arXiv 1992
[3]

R. C. Brower, J. Polchinski, M. J. Strassler and C.-I. Tan, The Pomeron and gauge/string duality, JHEP 12 (2007) 005 [hep-th/0603115]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[4]

Transition from soft- to hard-Pomeron in the structure functions of hadrons at small-$x$ from holography

A. Watanabe and K. Suzuki, Transition from soft- to hard-Pomeron in the structure functions of hadrons at small-x from holography, Phys. Rev. D86 (2012) 035011 [1206.0910]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[5]

Nucleon structure functions at small $x$ via the Pomeron exchange in AdS space with a soft infrared wall

A. Watanabe and K. Suzuki, Nucleon structure functions at small x via the Pomeron exchange in AdS space with a soft infrared wall , Phys. Rev. D89 (2014) 115015 [1312.7114]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[6]

Photon structure functions at small $x$ in holographic QCD

A. Watanabe and H.-n. Li, Photon structure functions at small x in holographic QCD , Phys. Lett. B751 (2015) 321 [1502.03894]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[7]

Watanabe and M

A. Watanabe and M. Huang, Total hadronic cross sections at high energies in holographic QCD , Phys. Lett. B788 (2019) 256 [1809.02515]

work page arXiv 2019
[8]

S. K. Domokos, J. A. Harvey and N. Mann, The Pomeron contribution to p p and p anti-p scattering in AdS/QCD, Phys. Rev. D80 (2009) 126015 [0907.1084]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[9]

Nucleon electromagnetic and gravitational form factors from holography

Z. Abidin and C. E. Carlson, Nucleon electromagnetic and gravitational form factors from holography, Phys. Rev. D79 (2009) 115003 [0903.4818]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[10]

First measurement of elastic, inelastic and total cross-section at $\sqrt{s}=13$ TeV by TOTEM and overview of cross-section data at LHC energies

TOTEM collaboration, G. Antchev et al., First measurement of elastic, inelastic and total cross-section at√s = 13 TeV by TOTEM and overview of cross-section data at LHC energies , Eur . Phys. J. C79 (2019) 103 [1712.06153]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[11]

First determination of the $\rho $ parameter at $\sqrt{s} = 13$ TeV -- probing the existence of a colourless three-gluon bound state

TOTEM collaboration, G. Antchev et al., First determination of the ρ parameter at√s = 13 TeV – probing the existence of a colourless three-gluon bound state , 1812.04732

work page internal anchor Pith review Pith/arXiv arXiv
[12]

Antchev et al., Elastic differential cross-section measurement at√s = 13 TeV by TOTEM, 1812.08283

TOTEM collaboration, G. Antchev et al., Elastic differential cross-section measurement at√s = 13 TeV by TOTEM, 1812.08283

work page arXiv
[13]

COMPETE collaboration, J. R. Cudell, V . V . Ezhela, P. Gauron, K. Kang, Yu. V . Kuyanov, S. B. Lugovsky et al., Benchmarks for the forward observables at RHIC, the Tevatron Run II and the LHC , Phys. Rev. Lett. 89 (2002) 201801 [hep-ph/0206172]. 5

work page internal anchor Pith review Pith/arXiv arXiv 2002

[1] [1]

W. Xie, A. Watanabe and M. Huang, Elastic proton-proton scattering at LHC energies in holographic QCD, 1901.09564

work page arXiv 1901

[2] [2]

Total cross sections

A. Donnachie and P. V . Landshoff,Total cross-sections, Phys. Lett. B296 (1992) 227 [hep-ph/9209205]

work page internal anchor Pith review Pith/arXiv arXiv 1992

[3] [3]

R. C. Brower, J. Polchinski, M. J. Strassler and C.-I. Tan, The Pomeron and gauge/string duality, JHEP 12 (2007) 005 [hep-th/0603115]

work page internal anchor Pith review Pith/arXiv arXiv 2007

[4] [4]

Transition from soft- to hard-Pomeron in the structure functions of hadrons at small-$x$ from holography

A. Watanabe and K. Suzuki, Transition from soft- to hard-Pomeron in the structure functions of hadrons at small-x from holography, Phys. Rev. D86 (2012) 035011 [1206.0910]

work page internal anchor Pith review Pith/arXiv arXiv 2012

[5] [5]

Nucleon structure functions at small $x$ via the Pomeron exchange in AdS space with a soft infrared wall

A. Watanabe and K. Suzuki, Nucleon structure functions at small x via the Pomeron exchange in AdS space with a soft infrared wall , Phys. Rev. D89 (2014) 115015 [1312.7114]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[6] [6]

Photon structure functions at small $x$ in holographic QCD

A. Watanabe and H.-n. Li, Photon structure functions at small x in holographic QCD , Phys. Lett. B751 (2015) 321 [1502.03894]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[7] [7]

Watanabe and M

A. Watanabe and M. Huang, Total hadronic cross sections at high energies in holographic QCD , Phys. Lett. B788 (2019) 256 [1809.02515]

work page arXiv 2019

[8] [8]

S. K. Domokos, J. A. Harvey and N. Mann, The Pomeron contribution to p p and p anti-p scattering in AdS/QCD, Phys. Rev. D80 (2009) 126015 [0907.1084]

work page internal anchor Pith review Pith/arXiv arXiv 2009

[9] [9]

Nucleon electromagnetic and gravitational form factors from holography

Z. Abidin and C. E. Carlson, Nucleon electromagnetic and gravitational form factors from holography, Phys. Rev. D79 (2009) 115003 [0903.4818]

work page internal anchor Pith review Pith/arXiv arXiv 2009

[10] [10]

First measurement of elastic, inelastic and total cross-section at $\sqrt{s}=13$ TeV by TOTEM and overview of cross-section data at LHC energies

TOTEM collaboration, G. Antchev et al., First measurement of elastic, inelastic and total cross-section at√s = 13 TeV by TOTEM and overview of cross-section data at LHC energies , Eur . Phys. J. C79 (2019) 103 [1712.06153]

work page internal anchor Pith review Pith/arXiv arXiv 2019

[11] [11]

First determination of the $\rho $ parameter at $\sqrt{s} = 13$ TeV -- probing the existence of a colourless three-gluon bound state

TOTEM collaboration, G. Antchev et al., First determination of the ρ parameter at√s = 13 TeV – probing the existence of a colourless three-gluon bound state , 1812.04732

work page internal anchor Pith review Pith/arXiv arXiv

[12] [12]

Antchev et al., Elastic differential cross-section measurement at√s = 13 TeV by TOTEM, 1812.08283

TOTEM collaboration, G. Antchev et al., Elastic differential cross-section measurement at√s = 13 TeV by TOTEM, 1812.08283

work page arXiv

[13] [13]

COMPETE collaboration, J. R. Cudell, V . V . Ezhela, P. Gauron, K. Kang, Yu. V . Kuyanov, S. B. Lugovsky et al., Benchmarks for the forward observables at RHIC, the Tevatron Run II and the LHC , Phys. Rev. Lett. 89 (2002) 201801 [hep-ph/0206172]. 5

work page internal anchor Pith review Pith/arXiv arXiv 2002