And to complement the title: "...and what the heck is that, anyway?" 

I know the feeling. In a sense, I share it with all bystanders, although I belong to the world of "experts". The feeling is a mixture of annoyance and curiosity. Why, did you particle physicists not discover all the fundamental particles of Nature, and with the much heralded 2012 discovery of the Higgs boson as "the missing piece", settled the matter for good? Is it not the Standard Model an as-of-yet-unbroken, although ok, we know it, incomplete, theory of fundamental interactions? And why should we be looking into this new claim of another elementary particle, rather than focus on more interesting science coming from, e.g., exoplanetology, or crispr techniques? 

Well, indeed. Why should you. So let me give you a reason, and nudge you a bit, inviting you on a trip to the mysteries of quantum chromodynamics in non-perturbative regimes. The reason is in the interesting gestation that this result had. The story shares some flavour with the old CDF sagas I described in all the gory detail in my 2016 book "Anomaly! Collider Physics and the Quest for New Phenomena at Fermilab" (see below for a link and an offer of free PDF of that text). 

Note, there is no controversy on the true nature of the discovery, which, as you will soon find out, is genuine, and worth your attention anyway. There is, however, some due care in the collaborations reporting the result, as individuals outside of their circle have been questioning the patronimity of the discovery. Hence it is good if we clarify how the discovery really came about here. You know, physicists are quite serious with their discovery claims - they even invented a prescription for allowing themselves to go public with a claim, the "five-sigma criterion". But I do not wish to divagate... (don't get me started with the topic of sigma counting, or we'll still be here tomorrow morning).

The abstract

In a joint pre-print, approved and published simultaneously by CERN and Fermilab in December, the TOTEM and D0 experiments have shown the first experimental observation of a particle, a 3-gluons compound named Odderon in pre-QCD physics. The result has been presented with a first discovery talk at the LHC Forward Physics Workshop at CERN and is going to be made public in the physics community with an invited talk at the Moriond Conference in a few days.


Whoa, already there is so much to explain in the above sentence. So, TOTEM is an experiment looking in the forward and backward direction around the CMS collision point of the Large Hadron Collider at CERN. While the giant CMS detector carefully watches collisions of very high energy, which throw debris in all directions around its center, TOTEM does the opposite: it looks where CMS cannot, i.e. in the very forward region where particle exit CMS from the same holes that allow the beams of protons to enter it. It is composed of spectrometers placed up- and downstream of CMS; if you're a clockwise-running proton you'll know what I mean, otherwise please look at the diagram below.

(Above, the TOTEM spectrometers lay on both sides of CMS, along the LHC tunnel).

BY studying those particles, that are produced when two protons softly bounce off one another and continue their trip almost unscattered, TOTEM collects information on the strong interaction in a regime that is very, very complicated to even formulate in a theory, leave alone make calculations with. This is called "diffractive physics", and it counts many passionate addicts in what is a niche research area, but an important one, of collider physics.

And what is D0? D0 is the now dismantled companion of CDF. D0 is the name of one of the collision points of the Fermilab Tevatron collider, called A0, B0, C0, D0, E0, F0. B0 was the site of CDF, and A0, C0, E0 and F0 were not used for relevant physics. In the years of the CDF-D0 competition, around and following the joint discovery of the top quark in 1995, I used to joke that also D0 was "essentially uninstrumented, for all practical purposes", to try and infuriate my colleagues with less sense of humour. In truth, D0 was a worthy detector, and it could do diffractive physics better than CDF because it had paid more attention to instrumenting both the forward (in the proton direction) and backward (in the direction of antiprotons, the other projectiles circulating in the Tevatron ring) direction.

(Above, a view of the central piece of the D0 detector at Fermilab. The spectrometers used for the measurement discussed in this article are not visible, as like in TOTEM they were placed along the beam on the sides of the detector. For some strange reason these people do not wear masks, hmm.)

Gluons and the Odderon

As for gluons, they are the carriers of the strong "QCD" force, and work to some extent in analogy with the photon, which transmits the electromagnetic "QED" force. The analogy in truth stops very quickly, as gluons are themselves a bit odd: they carry the charge of the field they themselves mediate, and in so doing open the door to a wealth of crazy phenomena. We are still only scratching  the surface of the mess of complicated "exotic" hadrons today, in fact. But that's another story. Three gluons can anyway bind in a colourless state, i.e. one that has total zero colour charge, and hence be given a name of their own, Odderon.

The 3-gluons compound is exchanged in the t-channel of proton-proton and proton-antiproton nuclear elastic scattering and is responsible for the difference observed in the multi-TeV energy range between the proton-proton and proton-antiproton differential cross-section as a function of the four-momentum transfer "t". 

When I say "t-channel", what I mean is that a proton arrives from one direction, another proton comes in from the opposite one, and they pass close to one another, exchanging momentum via the three-gluon state. We can see this happening by looking at the rate of these events as a function of the momentum that the odderon has transferred from one proton to the other, if we count protons emitted in the forward and backward direction. This is what making a "differential cross section" means. But only showing differences between the proton-proton cross section and the proton-antiproton cross section can we prove that an Odderon is responsible. Which is what has been now done.

A bit of history

The Odderon was predicted in 1973 by some Nicolescu and Lukaszuk in the framework of an extended Regge theory as a mathematical object with C-odd properties, i.e. able to potentially explain differences in the strong interaction at any energy between proton-proton and proton-antiproton, e.g. ones beyond the energy range investigated by the ISR and the SpS accelerators, where differences can be due to virtual mesons exchange. C-odd here means "odd under the charge conjugation transformation", in the sense that if we take a system and exchange all particles with their antiparticle counterparts, some systems exhibit a complete invariance (they are C-even), and others change sign in a multiplicative "quantum number" that determines some of the observable properties of the reactions.

In the following decades the Odderon has been represented in non-perturbative Quantum Chromodynamics as a compound of 3 or odd number of gluons, thus a color-neutral "closed" object for which the self-interaction of the gluons dominates over their interaction with the protons they are coupling to. The Odderon thus became an intrinsic QCD prediction with notable implications at the theoretical level.

At the multi-TeV energy scale the proton-proton and proton-antiproton elastic hadronic interaction is purely mediated by gluons exchange. The elastic scattering requires the protons or antiprotons to change direction maintaining their integrity, i.e. without fragmenting, and therefore the gluons exchange has to be colorless.

Getting a bit technical - I hope you will forgive me -, the colorless requirement implies combinations of specific numbers of gluons being exchanged (e.g. 2 or 3, while 1 is forbidden). If there is evidence of difference between proton-proton and proton-antiproton differential cross-section, then there has to be a C-Odd amplitude contributing to the scattering (because even numbers of gluons give identical contributions to proton-proton and proton-antiprotons amplitudes).

If such difference manifests in the low-t (Optical Point and diffractive cone) or medium-t range (diffractive dip and second maximum), then the gluons are exchanged as a whole (not resolved individually), i.e. an aggregate or compound with its own properties. This is the magic of the whole thing: it is a particle, not a random effect due to multiple gluons flying around.

In addition, this is what makes the elastic cross-section so large (~25% of the total hadronic cross-section) because the color-neutral requirement is fulfilled "by construction" rather than combinatorially as in a multiple exchange of individual/independent gluons.

And now the claim

In a joint-analysis combining LHC and Tevatron data, the TOTEM collaboration and the D0 collaboration have searched for differences in the elastic differential cross-section of proton-proton vs proton-antiproton at sqrt(s) collision energy of 1.96 TeV in the medium t-range, in a region that aficionados have dubbed "diffractive dip and second maximum".

LHC proton-proton data analysed and published by TOTEM at 13 TeV, 8 TeV, 7 TeV , 2.76 TeV have been extrapolated to 1.96 TeV with a model-independent method, being then compared to the proton-antiproton data formerly acquired and published by D0 at 1.96 TeV. Because, you know, D0 is now dismantled - it did not take more data after 2012, and even the original collaboration is pretty much dispersed in other experiments, where they spend the largest fraction of their time. But some analyses, like this one, still is worth their time, apparently!

The analysis has been performed with different test statistics, to compare in a sound way the proton-proton and proton-antiproton cross-sections at the same energy, and accounting for correlations and constraints. The results  show an incompatibility of the proton-proton vs proton-antiproton elastic differential cross-section at the level of 3.4 sigmas, thus showing evidence for the Odderon in themselves. In truth, one could question whether one really needs an Odderon to make a difference in those measured differential rates, but okay, the Odderon is the natural explanation.

But as we say, we require five sigma to claim a discovery. So more evidence is needed. And this comes from previous data. TOTEM had already obtained evidence for the Odderon in the low-t range at sqrt(s) 13 TeV in 2018 [TOTEM rho paper 13 TeV], by analysing the real to imaginary ratio of the nuclear scattering amplitude at t~0. Such extremely high precision measurement was also characterized by calculating relative differences wrt measurements at former lower energies accelerators (e.g. ISR , SPS), thus factorizing out the main sources of systematic uncertainties.

Given the complete independence of the data used in the TOTEM low-t analysis at 13 TeV and the joint D0-TOTEM analysis at 1.96 TeV, the results have been combined, producing an overall significance larger than 5 sigmas, therefore they constitute the first experimental observation of the Odderon.

In summary, the discovery of the Odderon probes the deepest features of Quantum Chromodynamics, notably the self-interaction of the gluons and the fact that an odd number of gluons may be colorless, hence shielding the strong interaction.

After two years of analysis by TOTEM and D0, as well as over 6 months of internal reviews, the refereed and approved CERN preprint and Fermilab preprint in December have been the de-facto publication of the Odderon observation in the HEP community, while waiting for the publication also in whatever chosen physics journal. 

In the meantime, the Odderon discovery has already been published also on the CERN Courier and on the Symmetry Fermilab/SLAC magazine in the US. And now here. At this point, I wonder whether a refereed publication is really needed before the TOTEM and ex-D0 collaborator uncork a good bottle... So, my due congratulations to all my colleagues involved in this!


Tommaso Dorigo (see his personal web page here) is an experimental particle physicist who works for the INFN and the University of Padova, and collaborates with the CMS experiment at the CERN LHC. He coordinates the MODE Collaboration, a group of physicists and computer scientists from eight institutions in Europe and the US who aim to enable end-to-end optimization of detector design with differentiable programming. Dorigo is an editor of the journals Reviews in Physics and Physics Open. In 2016 Dorigo published the book "Anomaly! Collider Physics and the Quest for New Phenomena at Fermilab", an insider view of the sociology of big particle physics experiments. You can get a copy of the book on Amazon, or contact him to get a free pdf copy if you have limited financial means.