Simulation of single diffraction dissociation in resonance region at LHC energies

D. M. Riabov; D. V. Zhuravel; N. O. Chudak; O. S. Potiienko

REVIEW 4 major objections 6 minor 29 references

Simulation of single diffraction dissociation in resonance region at LHC energies

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper claims that low-mass single diffraction dissociation at LHC energies is described by a single-pomeron dual-Regge model whose nonlinear baryon trajectory generates the resonance peaks, with parameters refined against recent…

desk verdict A routine refit of a published dual-Regge model, with a clear and unaddressed factor-10 inconsistency between the differential and total cross-section fits that currently invalidates the event generator. read the letter →

arxiv 2411.16827 v1 pith:SB45YPJB submitted 2024-11-25 hep-ph

O. S. Potiienko , D. V. Zhuravel , D. M. Riabov , N. O. Chudak This is my paper · ORCID

classification hep-ph

keywords singlediffractiondissociationReggetrajectorynonlinearbaryonpomeronexchangenucleonresonancesdual-Reggemodellowmissingmasseventgeneration

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 tries to establish that the resonance region of single diffraction dissociation in proton-proton collisions at LHC energies is fully described by a single-pomeron dual-Regge model: a model whose amplitude is a sum over Regge trajectories, linking the pomeron exchange in the $t$-channel to the baryon resonances in the $M_X^2$-channel. The load-bearing object is a nonlinear, complex baryonic Regge trajectory whose poles are the known nucleon resonances, so the peaks in the missing-mass spectrum are not added by hand but come from the trajectory itself. Fitting the two free parameters to the measured differential cross-section converges with $\chi^2/d.o.f.\approx 1.07$, giving $A_0=35.58$ mb/GeV$^2$, $t_0=1.486$ GeV$^2$, and a constant background $b_0=8.2$ mb/GeV$^2$. If correct, the same expression provides an event generator for $2 \le M_X^2 \le 8$ GeV$^2$ at $\sqrt{s}=7$--8 TeV, and it predicts a non-monotonic rapidity-gap distribution that differs sharply from an existing simulation.

What carries the argument

The key object is the nonlinear complex baryonic Regge trajectory $\alpha(s)$, defined by dispersion relations that express its imaginary part as a sum of threshold terms and its real part as the corresponding dispersion integral. It is fitted to the masses and widths of N(939), N(1680), N(2220), and N(2700). Its real part gives the resonance angular momenta and masses; its imaginary part gives the Breit-Wigner widths. Both enter the imaginary part of the dual-Regge amplitude, which is converted into the proton structure function $W_2$ through the analogy between the Pomeron-proton vertex and deeply virtual Compton scattering with $Q^2=-t$. This chain reduces the full model to the compact differential cross-section (10), which depends on only two fitted parameters, $A_0$ and $t_0$, plus a background.

What would settle it

Measure the double differential cross-section in $2 \le M_X^2 \le 8$ GeV$^2$ at $\sqrt{s}=8$ TeV with enough statistics to resolve individual resonances: the model predicts peaks at the positions and widths inherited from N(1680), N(2220), and N(2700), so a flat spectrum or peaks shifted by more than the fitted widths would falsify it. A faster check is to refit after removing the lowest-$|t|$ points, where the $Q^2=-t$ analogy is least credible; the claimed $\chi^2/d.o.f.\approx 1.07$ should degrade markedly if the mapping is wrong.

Watch

Extended reading notes

Core claim

The central claim is that Eq. (10), obtained by inserting the dual-Regge amplitude with the nonlinear baryon trajectory into the Pomeron-proton structure function, reproduces the measured double and single differential cross-sections of single diffraction dissociation in the resonance region $2 \le M_X^2 \le 8$ GeV$^2$. The nucleon resonances N(1680), N(2220), and N(2700) appear as poles of the trajectory: the real part of the trajectory fixes their masses through the angular-momentum relation and the imaginary part fixes their widths through the Breit-Wigner formula, so the resonance bumps in the cross-section are inherited from the trajectory rather than parametrized independently. The parameters $A_0$ and $t_0$, together with a flat background, are obtained by fitting the integrated cross-section to the LHC data; the total single-diffraction cross-section over a wide energy range is then reproduced with the same $t_0$ and a separately fitted constant background.

Load-bearing premise

The load-bearing premise is that the strongly-interacting Pomeron-proton transition can be represented by the electromagnetic vertex of deeply virtual Compton scattering with $Q^2=-t$, so that the measured electromagnetic structure function $F_2$ fixes the strong-interaction structure function $W_2$.

Editorial extensions

If this is right

The fitted cross-section with $A_0=35.58$ mb/GeV$^2$, $t_0=1.486$ GeV$^2$, and $b_0=8.2$ mb/GeV$^2$ describes the measured $d\sigma/dt$ in the resonance region at $\sqrt{s}=8$ TeV with $\chi^2/d.o.f.\approx 1.07$.
The same model, with a separately fitted constant background, reproduces the total single-diffraction cross-section over a wide energy range from fixed-target to LHC energies.
Normalizing the double differential cross-section produces a joint probability density for $(M_X^2,t)$, so the model can generate low-mass diffractive events with resonance structure preserved.
In the rapidity-gap variable $\eta=-\log(M_X^2/s)$, the model predicts multiple peaks in the interval $\eta\sim 15.6$--$17$ at $\sqrt{s}=7$ TeV, where an existing simulation gives a nearly flat distribution.

Reading between the lines

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

Editorial inference: because the same trajectory controls both the resonance positions and the cross-section normalization, extending the fitted trajectory to additional $N^*$ states would produce a concrete prediction for the missing-mass spectrum above $M_X^2=8$ GeV$^2$, a region the authors leave to other Regge mechanisms.
Editorial inference: the constant background is fitted independently in the differential and total cross-section fits, so a physical model of the elastic tail could shift the reported $A_0$ and $t_0$; testing this by replacing the constant with a modelled elastic contribution would quantify the sensitivity.
Editorial inference: the analogy to deeply virtual Compton scattering suggests that the fitted proton trajectory could be reinterpreted through low-$x$ parton distributions, connecting the resonance-region vertex to collinear QCD and giving an independent cross-check of the parameter set.

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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

Short version: this is an incremental application of Jenkovszky's dual-Regge diffraction model to the 2020 ATLAS single-diffraction data, with new fitted values of A0, t0, b0 and a comparison with Pythia MBR. The trajectory machinery is taken from Fiore et al. and Jenkovszky et al.; the genuinely new piece is the refit and the event-generation recipe. That part is worth a look.

What it does well: the differential dσ/dt fit to ATLAS is clean (χ²/dof ≈ 1.07), the paper is transparent about both fits, and the trajectory construction is a faithful reproduction of [21] with the resonances listed. If you work on low-mass diffraction in generators, having a resonance-region alternative to MBR is useful in principle.

The soft spot is not small. A0 is defined as a single energy-independent normalization in Eq. (10), but the differential fit needs A0 = 35.58 mb/GeV² while the total cross-section fit needs A0 = 565 or 378 mb/GeV², a factor 10–16 larger. The two fits are not independent calibrations; Eq. (12) is just the integral of Eq. (11), so the same A0 should enter both. As it stands, the event generator in Sec. 5 samples from a density whose numerator uses one normalization and whose denominator σSDD uses another, unless the authors silently switch. That is a load-bearing inconsistency, not a cosmetic one.

Second issue: the resonance peaks in M_X are built in, not predicted, because the nonlinear trajectory was fitted to the masses and widths in Table 1. That said, the trajectory parameters come from the earlier [21] fit, so the circularity is inherited rather than new. The photon–Pomeron analogy behind W2 is also untested and adopted from [11]; I would not hang the paper's validity on it, since the internal normalization problem is already decisive.

Verdict: conditional, and the condition is a refit with a common A0 plus a physically motivated background. The paper is honest enough to show its own bad numbers, and the flaw is repairable. I would send it to a referee — it is the kind of paper a specialist needs to see — but the letter should demand the common-normalization fit before the generator can be used.

Who is this for: people building low-mass diffraction into Monte Carlo generators, and diffraction phenomenologists. Not for a general audience.

Referee Report

4 major / 6 minor

Summary. The manuscript presents a dual-Regge model with a nonlinear baryon trajectory for single diffraction dissociation in the resonance region 2 ≤ M_X^2 ≤ 8 GeV^2 at LHC energies. The model cross-section, Eq. (10), is fitted to ATLAS dσ/dt data and to total single-diffraction cross-section data. The authors report a good differential fit with A0 = 35.58 mb/GeV^2, t0 = 1.486 GeV^2, and b0 = 8.2 mb/GeV^2 (χ^2/d.o.f. ≈ 1.07), and a poor total fit with A0 = 565 mb/GeV^2 (χ^2/d.o.f. = 14.03) or A0 = 378.43 mb/GeV^2 with a background b = 1.85 mb (χ^2/d.o.f. = 10.72). They then use these cross-sections to construct an event generator and compare its rapidity-gap distribution with the MBR simulation.

Significance. If the model were internally consistent, it would provide a useful analytic tool for low-mass single-diffraction event generation at the LHC, with a concrete prediction for resonance structure in dσ/dη that differs from MBR. The paper's strengths are its explicit analytic expression, the detailed reporting of parameter values and goodness-of-fit metrics from ROOT/Minuit fits, and a reasonable differential-shape fit to ATLAS data. However, the central claim is weakened by the order-of-magnitude inconsistency in the normalization A0 between the differential and total fits, and by the fact that the resonance peaks are inserted by construction through the trajectory fitted to the known resonance masses and widths. As it stands, the event generator of Sec. 5 is not self-consistent.

major comments (4)

[Sec. 4, Eqs. (10)-(12)] The global normalization A0 is a single constant multiplying d^2σ/dtdM_X^2 in Eq. (10). The differential fit gives A0 = 35.58 mb/GeV^2, while the total cross-section fit requires A0 = 565 ± 3.11 mb/GeV^2 without background, or A0 = 378.43 ± 16.68 mb/GeV^2 with b = 1.85 mb. Because both fits use the same double-differential cross-section, these values are mutually incompatible: the two fits differ by a factor of 10-16. This is not a harmless redefinition, because the event generator of Sec. 5, Eq. (13), uses σSDD from Eq. (12) as a normalization while the numerator uses Eq. (10) with the differential-fit parameters. A joint fit with a single consistent normalization is required before the model can be used as an event generator.
[Sec. 5 and Sec. 3, Fig. 10] The paper claims that the model 'predicts highly non-monotonical dependency with multiple peaks corresponding to the resonances.' However, the peak positions and widths are determined by the nonlinear trajectory α(M_X^2) fitted to the N(1680), N(2220), and N(2700) masses and widths in Table 1 and Eqs. (7)-(8). The appearance of these peaks in the predicted cross-section is therefore guaranteed by construction; the comparison with MBR is a difference between models, not a successful prediction. This should be presented as a consistency check rather than as a prediction.
[Sec. 2, Eqs. (2)-(3)] The central formula Eq. (10) inherits the identification ν W_2(M_X^2,t) = F_2(x,t) with Q^2 = -t, which maps the strongly interacting Pomeron-proton vertex to the electromagnetic γ* p vertex. This assumption is adopted from Ref. [11] without independent derivation or validation. Because all subsequent fits and the event generator depend on it, the authors should either defend this mapping for the t range used or provide a sensitivity study; at minimum, this is a model assumption that limits the physical interpretation of the fitted parameters.
[Sec. 4, background terms b0 and b] The two background constants b0 and b are fitted independently and no connection is imposed, even though both are introduced as constant backgrounds to the same underlying resonance cross-section. With b0 = 8.2 mb/GeV^2, integration over the nominal t range [0, 0.5] GeV^2 would contribute about 4.1 mb to σSDD, whereas the total fit uses b = 1.85 mb. The paper acknowledges the lack of a background model, but the ad hoc treatment of two unrelated constants should be addressed, for example by fitting b0 and b jointly or by removing the total cross-section data from the fit until a background model is available.

minor comments (6)

[Abstract and Sec. 1] There are typos in the abstract and introduction: 'investiaged' should be 'investigated', 'disssociation' should be 'dissociation', and 'Mandelstam analiticity' should be 'Mandelstam analyticity'.
[Eq. (12)] The integration limits in Eq. (12) are unclear: the text says to integrate over t ∈ [0, 0.5], but the displayed equation appears to integrate from -s to 0, which is not the intended domain for s = (7 TeV)^2. Please correct the notation.
[Fig. 6 and Fig. 7 captions] The captions of Figs. 6 and 7 appear to be duplicated or mislabeled; each caption repeats the 'left' and 'right' panel descriptions. Please revise for clarity.
[Sec. 3 and Sec. 5] Section 3 states that there is 'The single peak in M_X^2 dimension' in the resonance region, while Section 5 refers to 'multiple peaks corresponding to the resonances'. The model's peak structure should be described consistently.
[Sec. 3, parameter values] In Section 3, the values A0 = 103 mb/GeV^2 and t0 = 0.71 GeV^2 are described as 'unfitted', but this is easy to confuse with the fitted values of Section 4. Please state explicitly that these are preliminary values used only for illustration.
[Ref. [10]] Reference [10] should be attributed to the ATLAS Collaboration rather than to 'G Aad and The ATLAS collaboration'.

Circularity Check

1 steps flagged · score 2.0 of 10

No load-bearing circularity; one resonance-peak 'prediction' is a built-in consequence of the previously fitted baryon trajectory.

fitted input called prediction [Sec. 6, Fig. 10 discussion]
"The MBR simulation demonstrates the close to constant behavior of the cross-section in the region of low missing masses. Whereas our model predicts highly non-monotonical dependency with multiple peaks corresponding to the resonances."

The peaks are a direct consequence of the Breit-Wigner denominators in Eq. (10): d2σ/dtdMX2 contains Im α(MX2)/([2n+0.5-Re α(MX2)]2+[Im α]2). The trajectory α(MX2) was fitted in [21] (Eqs. (6)-(8), Tables 1-2) to the very same N(1680), N(2220), N(2700) masses and widths, with Re α(sn)=2n+0.5. Thus the non-monotonic peaks are guaranteed by construction, so calling them a prediction restates the input rather than deriving a new result. This is a presentational overstatement, not the main claim: the ATLAS dσ/dt fit integrates over MX2 and does not test the resonance positions.

full rationale

The paper's numerical results are fits to external data, not derivations from the target quantities. The cross-section formula Eq. (10) is imported from [11] (DAMA dual amplitude and DVCS analogy) and the trajectory parameters from [21]; neither is a self-citation, and the A0/t0/b0/b parameters are fitted to ATLAS [10] and total-cross-section data [5-9,22-28] with quoted χ2. The one circular flavor is the 'prediction' of resonance peaks in Sec. 6, which is pre-determined by the trajectory fitted to the same resonances; I flag it as a minor overstatement. The well-known internal inconsistency between A0 values from the differential fit (35.58 mb/GeV2) and total fits (565 or 378.43 mb/GeV2) is a correctness/consistency problem, not a circularity, and does not by itself raise the circularity score. Since the central model is benchmarked against external data and no load-bearing step reduces to its own input, the circularity score is low.

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

The central calculation rests on an imported model: the DAMA amplitude and structure-function analogy come from Ref. [11]; the proton trajectory parameters were fitted to resonance data in Ref. [21]; the pomeron trajectory and dipole form factor are standard inputs. On top of these, the paper fits A0, t0, b0, b to the ATLAS and older total cross-section data. The integration windows (M_X^2 in [2,8] GeV^2, |t| in [0,0.5] GeV^2) and the two independent constant backgrounds are ad hoc choices that the paper itself flags as unmodeled.

free parameters (7)

A0 (overall normalization) = 35.58 mb/GeV2 from dsigma/dt fit; 565 +/- 3.11 and 378.43 +/- 16.68 mb/GeV2 from total cross-section fits
Combines the factors a and beta from Eqs. (1) and (5). Fitted separately to two datasets, producing inconsistent values.
t0 (Pp->Pp form-factor parameter) = 1.486 GeV2; 0.71 GeV2 in exploratory plots
Controls f(t) = (1 - t/t0)^-2 in the transition amplitude (4). Fitted to ATLAS dsigma/dt.
b0 (background in dsigma/dt) = 8.2 mb/GeV2
Constant background added in Eq. (11). Fitted to ATLAS data.
b (background in total cross-section) = 1.85 +/- 0.16 mb/GeV2
Separate constant background in Eq. (12), deliberately decoupled from b0.
Proton trajectory parameters alpha(0), delta, c1, s1, c2, s2, cx, sx = alpha(0)=-0.41, delta=-0.46, c1=0.51, s1=1.16 GeV2, c2=4.0, s2=2.44 GeV2, cx=4.6e3, sx=11.7 GeV2
Fitted to N-resonance masses and widths in Ref. [21]. Inherited as fixed inputs, so their uncertainties are not propagated.
Pomeron trajectory parameters = alpha_P(t) = 1.08 + 0.25 t
Standard simple-pole pomeron parameters taken from [11, 18]. Not fitted here.
Proton elastic form-factor dipole parameter = 0.71 GeV2
F_p(t) = (1 - t/0.71)^-2. Standard input from prior electron-scattering fits.

assumptions (7)

domain assumption The dual-Regge amplitude with Mandelstam analyticity (DAMA) can be written as a sum of Regge poles, Eq. (4).
Adopted from [11]; the resonance decomposition is the basis for W2.
domain assumption The Pomeron-proton inelastic vertex equals the virtual-photon proton structure function with Q^2 = -t, Eqs. (2)-(3).
This mapping is the key step connecting the diffractive vertex to F2; no independent justification is given in this paper.
domain assumption Single pomeron exchange with a simple pole trajectory alpha_P(t) = 1.08 + 0.25 t is sufficient for this process.
Other exchanges, such as odderon or dipole pomeron, are mentioned but not included.
domain assumption The proton trajectory parameters in Eqs. (7)-(9) and Table 2 from [21] are correct and can be used as fixed inputs.
The fits for alpha(0), delta, cn, sn come from matching resonance masses and widths; their uncertainties are not propagated.
ad hoc to paper The resonance region is 2 <= M_X^2 <= 8 GeV^2, with elastic contributions negligible above 2 GeV^2 and other Regge mechanisms negligible above 8 GeV^2.
These cuts are stated after Fig. 4 but are not derived.
ad hoc to paper Background contributions can be represented by two independent constants b0 and b in Eqs. (11) and (12).
The paper explicitly says there is no reliable background model and fits b0 and b separately.
standard math Dispersion relations leading to Eqs. (7)-(9) are applicable to the baryonic trajectory.
Unproved but standard analyticity input inherited from [21].

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Cite this review

Pith. "Pith review of Simulation of single diffraction dissociation in resonance region at LHC energies." pith.science (2026). https://pith.science/paper/SB45YPJB

@misc{pith2026241116827,
  author       = {Pith},
  title        = {Pith review of: Simulation of single diffraction dissociation in resonance region at LHC energies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SB45YPJB}},
  note         = {Machine review of arXiv:2411.16827}
}

abstract

A comprehensive review of the single diffraction dissociation duality-based model at low missing masses have been presented. The distinguishing feature of the model is the nonlinear Regge proton trajectory used to account for the resonances contributions to the cross-sections. It helps classify and understand the spectrum of excited states of proton and their decays, providing insights into the internal structure and dynamics of particles. The behavior of the differential cross-section in the resonance region at small missing masses $M_x$ is investiaged. The model parameters are refined in the light of new experimental data.

Figures

Figures reproduced from arXiv: 2411.16827 by the authors.

**Figure 2.** Deeply virtual Compton scattering process [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** The fit [21] of the proton trajectory to N-resonances data. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: The differential cross-section d 2σ/dtdM2 X (10) in t, M2 X plane. There are two missing mass MX regions: elastic peak region (M2 X < 2 GeV2 ), and the resonance region (2 GeV2M2 X ⩽ 8 GeV2 ). distinct model. Thus we focus on the contributions from the resonance region…

**Figure 5.** Figure 5: The differential cross-section d 2σ/dtdM2 X (10) in the t, M2 X plane (a), and its logarithm (b), plotted in the resonance region for 0 ⩽ −t ⩽ 0.5 GeV2 . 6 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: The differential cross-section d 2σ/dtdM2 X (10) in the t, M2 X plane in the resonance region for 0 ⩽ −t ⩽ 0.5 GeV2 (left), and multiple regular plots in M2 X at fixed values of t (right). 0.0 0.1 0.2 0.3 0.4 0.5 |t|, [GeV 2 ] 0 50 100 150 200 d 2 /dtd M2 X , [m b/G e …

**Figure 7.** Figure 7: The differential cross-section d 2σ/dtdM2 X (10) in the t, M2 X plane in the resonance region for 0 ⩽ −t ⩽ 0.5 GeV2 (left), and multiple regular plots in t at fixed values of M2 X (right). 4 Cross-sections In this section we calculate total and differential cross-secti…

**Figure 8.** Figure 8: The next step, is to integrate 11 over t ∈ [0, 0.5] to calculate the total cross-section 7 [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

**Figure 8.** Figure 8: The differential cross-section dσ/dt of single diffraction dissociation as a function of |t|. The dashed line is the exponential fit to the experimental data [10]. The solid line is the model fit with the constant background contribution b0. 100 101 102 10−2 10−1 100 1…

**Figure 9.** Figure 9: The total single diffraction dissociation cross-section as a function of [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

**Figure 10.** Figure 10: The comparison of the our model agains the MBR simulation in Pythia 8 at [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]

Discussion (0). Continue with ORCID to comment.

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