[Paper Review] Odderon observation: explanations and answers to questions/objections regarding the PRL publication

K. Österberg|arXiv (Cornell University)|Feb 8, 2022

Superconducting Materials and Applications4 citations

TL;DR

This paper presents a comprehensive defense of the first experimental observation of the odderon, a hypothetical particle exchange in high-energy proton-antiproton and proton-proton scattering. By combining data-driven extrapolations of $pp$ elastic differential cross sections at $\sqrt{s} = 1.96$ TeV with $p\bar{p}$ measurements from D0 and $\rho$ and $\sigma_{\text{tot}}$ data from TOTEM at the LHC, the authors demonstrate a combined significance of 5.2–5.7 $\sigma$ for odderon exchange, resolving objections regarding model dependence and consistency of the analysis.

ABSTRACT

The odderon observation recently published by the D0 and TOTEM collaborations has been widely accepted by a majority of the particle physics community and its importance recognized through dedicated physics seminars in the world major labs and physics institute. Naturally also some questions and objections have been raised, either privately or publicly, in discussion sessions and articles. In this proceedings article, a comprehensive list of these questions and objections are answered and supplementary material is provided. The methods and assumptions used in the extrapolation of the $pp$ elastic differential cross section to $\sqrt{s}$ = 1.96 TeV and its comparison to the D0 measurement in $p\bar{p}$ are shown to be valid and reasonable. Likewise, the methods and choices used for the $ρ$ measurement at LHC. Furthermore, objections against the odderon interpretation are demonstrated not to be valid. Finally, the combination of the different odderon significances, leading to the first experimental observation of odderon exchange, is shown to be well founded.

Motivation & Objective

• To address widespread questions and objections raised about the D0-TOTEM odderon observation published in PRL.
• To validate the data-driven extrapolation method used to predict $pp$ elastic differential cross sections at $\sqrt{s} = 1.96$ TeV from higher-energy TOTEM data.
• To confirm the robustness of $\rho$ and $\sigma_{\text{tot}}$ measurements at the LHC for odderon sensitivity.
• To justify the combination of independent odderon signatures into a single, statistically sound observation.
• To demonstrate that objections to the odderon interpretation are unfounded based on model consistency and experimental constraints.

Proposed method

• Extrapolated TOTEM $pp$ $d\sigma_{\text{el}}/dt$ data at 2.76, 7, 8, and 13 TeV to $\sqrt{s} = 1.96$ TeV using linear fits in $\log\sqrt{s}$ and $\sqrt{s}$, minimizing model dependence.
• Used a common $|t|$-range (0.50–0.96 GeV²) for direct comparison between extrapolated $pp$ and measured $p\bar{p}$ $d\sigma_{\text{el}}/dt$ at 1.96 TeV.
• Applied Stouffer’s method to combine significances from multiple independent measurements: $pp$/$p\bar{p}$ comparison, $\rho$ at 13 TeV, and $\sigma_{\text{tot}}$ at multiple energies.
• Evaluated model predictions (Durham, COMPETE, Block-Halzen) without odderon exchange to compute $\chi^2$ and significance against data.
• Used merged bins and nearest-neighbor interpolation to avoid model-dependent interpolation between bins, reducing systematic uncertainty.
• Assessed CNI effects in $\rho$ and $\sigma_{\text{tot}}$ measurements using eikonal models, confirming negligible impact on results.

Experimental results

Research questions

• RQ1 Is the data-driven extrapolation of $pp$ $d\sigma_{\text{el}}/dt$ to $\sqrt{s} = 1.96$ TeV sufficiently robust to support the $pp$/$p\bar{p}$ comparison?
• RQ2 Are the $\rho$ and $\sigma_{\text{tot}}$ measurements at the LHC sensitive enough to detect odderon effects, and are they consistent with the $pp$/$p\bar{p}$ comparison?
• RQ3 Can the combination of multiple independent odderon signatures yield a statistically significant observation?
• RQ4 Do objections to the odderon interpretation—such as model dependence or inconsistency between data and models—hold under scrutiny?
• RQ5 Is the use of Stouffer’s method valid for combining significances from data-to-data and data-to-model comparisons?

Key findings

• The $pp$ and $p\bar{p}$ $d\sigma_{\text{el}}/dt$ comparison at $\sqrt{s} = 1.96$ TeV shows a 3.4 $\sigma$ difference, interpreted as evidence for odderon exchange.
• The $\rho$ measurement at 13 TeV yields significances of 4.6 $\sigma$ (COMPETE) and 3.9 $\sigma$ (Block-Halzen), indicating odderon sensitivity.
• The $\sigma_{\text{tot}}$ measurements at 2.76, 7, 8, and 13 TeV yield significances of 3.4–4.6 $\sigma$ when compared to models without odderon exchange.
• The combined significance across all measurements ranges from 5.2 to 5.7 $\sigma$, establishing the first experimental observation of the odderon.
• The Durham model without odderon exchange fails to describe the D0 $p\bar{p}$ data at 1.96 TeV with a 4.3 $\sigma$ significance, supporting the odderon hypothesis.
• Objections regarding model dependence, extrapolation range, and data combination are shown to be unfounded due to conservative fitting methods, short extrapolation range, and robust statistical combination.