[Paper Review] Leading Pomeron Contributions and the TOTEM Data at 13 TeV

M. Broilo, E. G. S. Luna+1 more|arXiv (Cornell University)|Mar 17, 2018

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper investigates leading Pomeron contributions to proton-proton and antiproton-proton scattering using a general analytic model with poles in the complex angular-momentum plane, fitting total cross sections and $ρ$-parameters from 5 GeV to 13 TeV. Despite fitting the TOTEM data at 13 TeV, the model fails to simultaneously describe both $σ_{\text{tot}}$ and $\rho$ within uncertainties, suggesting Pomeron dominance is insufficient compared to Odderon-based models, as previously found by Martynov and Nicolescu.

ABSTRACT

The recent data by the TOTEM Collaboration on $σ_{tot}$ and $ρ$ at 13 TeV, have shown agreement with a leading Odderon contribution at the highest energies, as demonstrated in the very recent analysis by Martynov and Nicolescu (MN). In order to investigate the same dataset by means of Pomeron dominance, we introduce a general class of forward scattering amplitude, with leading contributions even under crossing, associated with simple, double and triple poles in the complex angular momentum plane. For the lower energy region, we consider the usual non-degenerated Regge trajectories, with even and odd symmetry. The analytic connection between $σ_{tot}$ and $ρ$ is obtained by means of dispersion relations and we carry out fits to $pp$ and $\bar{p}p$ data in the interval $\sqrt{s}=5$ GeV - 13 TeV; following MN we consider only the TOTEM data at the LHC energy region. From the fits, we conclude that the general analytic model, as well as some particular cases representing standard parameterizations, are not able to describe satisfactorily the $σ_{tot}$ and $ρ$ data at 13 TeV. Further analyses in course and some perspectives are outlined.

Motivation & Objective

• To test whether a general analytic Pomeron model with leading Regge pole contributions can describe the TOTEM data on $\sigma_{\text{tot}}$ and $\rho$ at 13 TeV.
• To examine the compatibility of Pomeron dominance with the latest LHC data, particularly in light of recent Odderon-based analyses.
• To assess the limitations of standard Regge pole models in fitting the combined $\sigma_{\text{tot}}$ and $\rho$ data at high energies.
• To explore whether the inclusion of higher-order logarithmic terms (log, log²) improves the fit quality compared to standard parameterizations.

Proposed method

• A general forward scattering amplitude is constructed with simple, double, and triple poles in the complex angular-momentum plane, corresponding to power-law, logarithmic, and logarithmic-squared energy dependencies.
• The model includes both even- and odd-under-crossing Reggeons and four even-Pomeron contributions (power, log, log², and constant terms).
• Analytic expressions for $\rho(s)$ are derived using singly subtracted derivative dispersion relations with an effective subtraction constant $K$.
• Fits are performed using the TMinuit package on $pp$ and $\bar{p}p$ data from 5 GeV to 13 TeV, with only TOTEM data at 13 TeV used at LHC energies.
• Two specific models are tested: Model I (no log or log² terms) and Model II (no constant or log terms), with $K$ either free or fixed to zero.
• Goodness-of-fit is evaluated via $\chi^2/\nu$ and integrated probability $P(\chi^2)$, with convergence requiring positive-definite covariance matrices.

Experimental results

Research questions

• RQ1 Can a general analytic Pomeron model with leading Regge pole contributions simultaneously describe $\sigma_{\text{tot}}$ and $\rho$ at 13 TeV?
• RQ2 Does the inclusion of logarithmic and logarithmic-squared terms improve the fit quality compared to standard parameterizations?
• RQ3 Is Pomeron dominance compatible with the TOTEM data at 13 TeV, given that Odderon dominance fits the same data well in prior work?
• RQ4 Are the fit results sensitive to the choice of the subtraction constant $K$ in the dispersion relations?
• RQ5 Can the model achieve acceptable fit quality when the number of free parameters is reduced to standard cases?

Key findings

• The general model with 10 free parameters failed to converge to a solution with a positive-definite covariance matrix, indicating overfitting or instability.
• Model I (with $A=C=D=0$) yielded $\chi^2/\nu = 1.273$ and $P(\chi^2) = 2.3 \times 10^{-3}$, indicating poor fit quality.
• Model II (with $B=C=0$, $\epsilon=0$) gave $\chi^2/\nu = 1.192$ and $P(\chi^2) = 2.0 \times 10^{-2}$, still indicating inadequate agreement with data.
• At 13 TeV, the best-fit curves for both models lie above the upper error bar of the $\rho$ measurement and below the lower error bar of $\sigma_{\text{tot}}$, showing a clear tension.
• The results are robust across variants: the fit quality does not improve when $K$ is fixed to zero.
• The authors conclude that Pomeron dominance, even in its most general analytic form, cannot satisfactorily describe the TOTEM data at 13 TeV, in contrast to Odderon-based models.