Odderon

In particle physics, the odderon corresponds to an elusive family of odd-gluon states, dominated by a three-gluon state. When protons collide elastically with other protons or with anti-protons at high energies, gluons are exchanged. Exchanging an even number of gluons is a crossing-even part of elastic proton–proton and proton–antiproton scattering, while odderon exchange (i.e. exchange of odd number of gluons) corresponds to a crossing-odd term in the elastic scattering amplitude. In turn, the odderon's crossing-odd counterpart is the pomeron.

It took about 48 years to find a definite signal of odderon exchange.²

In elastic collisions, the total kinetic energy of the system is conserved. Thus the identity of the scattered particles is not modified, no excited states and/or new particles are produced. The kinematics of these collisions is governed by the conservation of both energy and momentum.

Data on high-energy elastic proton–proton collisions provided by the TOTEM Collaboration in a teraelectronvolt energy range, together with data from the DØ experiment on elastic proton–antiproton collisions at the Tevatron collider were key ingredients in the discovery of the odderon-exchange. The observed characteristics of the proton–proton collisions did not match the characteristics of the proton–antiproton collisions. As a result, there is an interaction-mediating family of particles (Regge trajectory) that can result in such a deviation in the range of strong interactions.

The first paper on the theoretical prediction of possible odderon exchange was published in 1973 by Basarab Nicolescu and Leszek Łukaszuk.¹ The odderon name was coined in 1975 in a paper from the same group (Joynson, D.; Leader, E.; Nicolescu, B. and Lopez, C.)³

In December 2020, the DØ and TOTEM Collaborations made public their CERN and Fermilab approved preprint² later published in Physical Review Letters in August 2021.² The DØ and TOTEM extrapolated TOTEM proton–proton data in the region of the diffractive minimum and maximum from 13, 8, 7 and 2.76 TeV to 1.96 TeV and compared this to DØ proton–antiproton measurement at 1.96 TeV in the same t-range finding an odderon significance of 3.4 σ. TOTEM observed an independent odderon signal at low four-momentum transfers at 13 TeV. When a partial combination of the TOTEM ρ and total cross section measurements is done at 13 TeV, the combined significance ranges between 3.4 and 4.6 σ for the different models. Combining this with the 3.4 σ effect on the extrapolated proton–proton differential cross-sections resulted in an at least 5.2 σ statistical significance. This is the first statistically significant observation of odderon exchange effects by experimental collaborations.²

A Hungarian-Swedish scaling analysis introduced a new scaling function and observed, model dependently, that in a limited energy range, that includes the DØ energy of 1.96 TeV and the TOTEM energies of 2.76 and 7 TeV, the elastic proton–proton collisions are within the experimental uncertainties independent of the energy of the collision.⁴

In this model dependently determined domain of validity, the Hungarian-Swedish team utilized a direct data-to-data comparison and showed that energy independent scaling function of elastic proton–proton collisions is significantly different from the scaling function of elastic proton–antiproton collisions, hence providing a statistically significant signal for the exchange of the elusive odderon. The preprint of this analysis was made public in December 2019 and its final form it was published in February 2021.⁴

This paper has been seconded in July 2021 by a theoretical paper of Tamás Csörgő, and István Szanyi, increasing the statistical significance of odderon observation to at least 7.08 σ signal.⁵ This paper utilized a previously published theoretical model, the so-called real-extended Bialas-Bzdak model, to extrapolate not only the elastic proton–proton scattering data from the LHC energies to the DØ energy of 1.96 TeV but also to extrapolate the elastic proton–antiproton scattering data from 0.546 and 1.96 TeV to the LHC energies of 2.76 TeV and 7 TeV. Evaluating the proton–proton data with a model increased the uncertainty and decreased the odderon signal from proton–proton scattering data alone, but this decrease was well over-compensated with the ability of the model to evaluate theoretically the proton–antiproton scattering at the LHC energies, leading to an overall increase of the statistical significance from 6.26 to 7.08 σ signal.⁵