[Paper Review] On the $ ρ$ and $ σ_{tot} $ measurement by the TOTEM Collaboration: in the wake of recent discoveries

В. В. Ежела, В. А. Петров+1 more|arXiv (Cornell University)|Mar 8, 2020

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper reanalyzes TOTEM Collaboration data from 13 TeV proton-proton scattering using a modified Coulomb-nuclear interference (CNI) formula, challenging the original claim of a very low ρ parameter (ρ ≈ 0.1). The reanalysis yields ρ = 0.123 ± 0.010 and σ_tot = 111.4 ± 1.8 mb, indicating no sign of slowing total cross-section growth, and contradicts the assertion that COMPETE models are excluded by the data.

ABSTRACT

We show that extraction of the quantities} $ρ(s)=\mbox{Re}[T_{N}(s,0)]/\mbox{Im}[T_{N}(s,0)]$ {\it and} $σ_{\mbox{tot}}(s)$ {\it from the data on the $pp$ differential cross-section at $\sqrt{s} = 13$} TeV {\it obtained by the} TOTEM {\it Collaboration gives results essentially different from those presented in publication} \cite{Ant} {\it if to use a modified formula for Coulomb-nuclear interference. The physical interpretation of these data changes accordingly.

Motivation & Objective

• To re-express the extraction of ρ and σ_tot from TOTEM's 13 TeV differential cross-section data using a revised Coulomb-nuclear interference (CNI) formula.
• To challenge the original TOTEM interpretation of ρ ≈ 0.1 as evidence for the maximal Odderon or suppressed total cross-section growth.
• To test the robustness of the TOTEM claim that COMPETE models are excluded by the data, particularly at high energies.
• To assess whether the product ρ·σ_tot reaches a maximum near 7 TeV, implying deceleration of σ_tot growth, as suggested in the original analysis.

Proposed method

• Replaces the standard CNI formula used in TOTEM [1] with a modified version based on the Bethe parametrization, incorporating the logarithmic phase function φ(t) = ln(0.08/|t|) − 0.5772.
• Applies the modified CNI formula to TOTEM's 13 TeV data (|t| ≤ t₀), fitting for σ_tot, ρ, and b (slope parameter) using a three-parameter model.
• Performs systematic fitting with varying t₀ cutoffs (from 0.000879 to 0.012 GeV²) to assess stability and sensitivity of ρ and σ_tot to low-t data selection.
• Uses the TOTEM model's σ_tot(s) parametrization (Eq. 3) as input for the fitting procedure to maintain consistency with the original analysis framework.
• Compares results from the modified CNI model with the original TOTEM values and with the COMPETE parametrization to evaluate model compatibility.
• Analyzes the χ²/ndf behavior as a function of t₀ to validate the fitting stability and determine the optimal data truncation point (t₀ ≈ 0.012 GeV²).

Experimental results

Research questions

• RQ1 How does the choice of Coulomb-nuclear interference (CNI) formula affect the extracted values of ρ and σ_tot from TOTEM 13 TeV data?
• RQ2 Does the observed low ρ ≈ 0.1 in TOTEM [1] genuinely indicate a slowing of total cross-section growth or a model-dependent artifact?
• RQ3 Is the claim that COMPETE models are excluded by the TOTEM data at 13 TeV valid, given the sensitivity of ρ to CNI treatment?
• RQ4 Does the product ρ·σ_tot reach a maximum near 7 TeV, as implied by the original TOTEM analysis, suggesting deceleration of σ_tot?
• RQ5 What is the stability of ρ and σ_tot extraction when systematically varying the low-t data cutoff (t₀) in the fitting procedure?

Key findings

• Using the modified Bethe-formula CNI treatment, the reanalysis yields ρ = 0.123 ± 0.010 and σ_tot = 111.4 ± 1.8 mb, significantly higher than the original TOTEM value of ρ = 0.09 ± 0.01.
• The χ²/ndf remains stable and near unity for t₀ ≤ 0.012 GeV², indicating reliable and consistent fitting results across the tested range.
• The product ρ·σ_tot does not show signs of saturation or maximum near 7 TeV, contradicting the original claim of decelerating total cross-section growth.
• The results from the modified CNI model are consistent with the COMPETE parametrization, which predicts ρ ≈ 0.1 only at √s ≈ 10⁶ TeV, thus invalidating the claim that COMPETE models are excluded.
• The original TOTEM conclusion of a maximal Odderon or suppressed σ_tot growth is shown to be highly sensitive to the CNI model choice, not a robust feature of the data.
• The analysis confirms that ρ extraction is model-dependent, and the use of different CNI formulas leads to significantly different physical interpretations of the same data.