At 10:00 AM this morning, my smartphone alerted me that in two months I will have to deliver a thorough review on the physics of boson pairs - a 50 page thing which does not yet even exist in the world of ideas. So I have better start planning carefully my time in the next 60 days, to find at least two clean weeks where I may cram in the required concentration. That will be the hard part!

Because of that, rather than an article about things that I know about boson pairs, this is a post about things I do not know well enough now, but on which my knowledge will see a rapid expansion in the near future. Don't get me wrong: I know the matter, from the history of research in this interesting sub-field of Standard Model and beyond-the-Standard-Model physics, to the most interesting recent results. But there's a big difference between knowing the boundaries and getting all the details sorted out in my mind, so that a clear picture can be drawn for a general reader.
So, here's what you might be interested to know, too, about why the topic is exciting. First of all, let's dispel a misunderstanding: we are talking about pairs of elementary particles here, produced in particle collisions at accelerators. If you say "boson pairs" to a condensed matter physicist, e.g., you make him happy, as he will say he is the true expert on that field: why, he studies them day in and day out!

In fact, bosons have the general property that they like to condense into a quantum state where every one of them has the identical same quantum numbers. So you can get helium-4 atoms to create a superconducting fluid, for instance, by exploiting that property if you cool the substance enough. Here, though, the bosons we study are elementary, and we only consider what happens when we produce them in energetic particle collisions. Or so I understood from the stipulation of the contract I signed for the review article I am going to write.

The play

So let me start from the beginning. The actors are the W boson and the Z boson - two particles discovered in 1983 by the UA1 experiment at CERN, which are indeed elementary and possess a spin equal to 1. That property makes them regular "vector bosons" (they are vectors because their spin possesses a direction in space, although the matter would be a bit more complex if we had to deepen it more). 

But wait. Two more particles belong to the cast. One is the photon - the quantum of electromagnetic radiation. Massless and with spin 1 as well, the  photon exhibits similar physics to W and Z bosons when studied as an elementary particle at colliders. And the other is the Higgs boson, the particle discovered in 2012 at the Large Hadron Collider (LHC), the 27 km synchrotron colliding protons at CERN. The Higgs boson here is the oddball: its spin is zero, so it is a scalar boson. The Higgs is the only elementary scalar particle we know, which makes it doubly interesting to study nowadays.

We have four actors, and the main stage is the center of the ATLAS and CMS detectors at the LHC; other experiments have the right to claim they studied boson pairs, too, but they are only going to be minor players here. The simplified plot is the following: protons come in from two opposite directions at relativistic speeds, a pair of their constituents (quarks or gluons) interact, and two bosons come out with large energy, along with a lot of uninteresting debris. The two bosons then decay into stable particles (except if they are photons, as the photon is stable, thank God), and the detectors measure the energy and direction of the decay products. From that information, physicists can infer the production mechanism that took place in the proton-proton collision, and compare it to models. 

Self interaction

There is in principle nothing very special about the above process - many other reactions are similarly studied by the ATLAS and CMS collaborations that way. But boson pairs have something interesting to tell us, in several ways. First of all, they can tell us how bosons self-interact. In other words, if you see a W and a Z boson emerge from a collision, you may be tempted to ask yourself whether what brought them to you was a collision that first created a single W boson with excess energy, and then that "off-shell" W boson (one with rest energy far exceeding its nominal mass) shrugged off the extra energy in the form of a Z boson. 

Taken as a single particle species, the "weak boson" category to which both W and Z belong, this radiation process is a  true self-interaction. By studying how often the process takes place we infer how strong that self-interaction is, and learn interesting bits of information about the inner workings of the Standard Model. Or, if we find that the rate of the process is abnormally high, we start to entertain thoughts that there is a new force at work, or that the model needs to be enlarged or modified by other new physics mechanisms. That is very interesting to us!

So, we study boson pairs to picture the "three-boson vertex": a boson comes in, two come out. There is a whole literature about "anomalous gauge boson couplings" that indeed deals with measurements of this self-interaction in all the possible declinations we are allowed to probe. So far, no anomaly has been detected, but we continue to look.

Probing WW scattering to check whether it behaves

With boson pairs there is a whole lot of other things you can do. A cool one is to study their scattering at high energy. Take two protons again, and imagine that they interact in a rare but possible way: rather than getting two of their constituents directly hit one another, each proton emits a W boson just before getting in touch with its counterpart. It may then be the two emitted W bosons that interact, creating what is called "vector boson scattering". Now, again we are in the realm of the self-interaction of vector bosons, but here we are not interested directly in the "three boson vertex" as above. We allow ourselves to consider all possible ways by means of which two W boson can scatter off one another. They may indeed fuse into a Z boson, and there you have a three-boson vertex and the consequent studies of self-interactions; but they may also interact by exchanging a photon, or a Higgs boson. Whatever they do, if they emerge at the end and get detected, we have access to a measurement of the reaction rate. It is now that things get interesting. Let me explain why.

The Higgs boson was introduced in the early sixties by a bunch of visionary theorists who were dealing with several shortcomings of the theory setup then available. The Higgs field was the solution of the riddle of unifying the highly asymmetric situation of electromagnetic and weak interactions, when the weak W boson was thought to possess a very large mass while the photon (the quantum of the electromagnetic field) was hugely different, being exactly massless. By making the W a triplet of fields (W+, W-, and a new massive neutral boson, the Z) and by introducing the Higgs field with a funny "mexican hat" potential which has a circle of minima for non-zero values of the field, one allowed for the symmetry of weak and electromagnetic forces to be hidden from our view. 

That was by itself a miracle. But the introduction of the Higgs boson did more than that: it also allowed the restoring of a thing called "unitarity" of weak interactions at high energy. Without the Higgs boson, the scattering of two W bosons above a certain (large) energy would exceed some theoretical bound, making the whole theory look a bit dumb. The topic is rather advanced so I will not delve in it here; suffices to say that the Higgs boson is a true panacea for electroweak interactions, as it fixes many things in one shot!

Now, with the LHC we are in the position of being able to actually verify whether the WW scattering does behave the way we expect, i.e. if the Higgs boson exchange keeps the reaction rate from diverging at high energy. This is something we have been recently able to start testing, and it is a very exciting new development of particle physics in the recent years.

New particles

But boson pairs yield much more than what I have been able to discuss above. In fact, they can be sensitive probes of new physics. For imagine there exists a massive new particle out there, which we have not yet been able to discover. It would be very hard to imagine that such a particle did not have any involvement with the weak interactions. So if it does, it can "couple" to W and Z bosons. And in that case, it must decay, with some unknown but non-zero probability, into pairs of those particles. 

Now, here's another reason why collecting all the WW, WZ, and ZZ pairs we can (as well as pairs including the photon and the Higgs boson) is a fruitful occupation: by computing the invariant mass of those particles we have direct access to the measurement of the mass of the new particle. And since vector boson pairs are not very frequently produced in proton-proton collisions, they offer a not-so-background-ridden signature! That is why the searches for new resonances decaying into boson pairs is a hot topic nowadays at the LHC: dozens of scientific articles are produced yearly discussing the null results - which push the mass scale of new physics further and further. 

There are heaps of other very interesting things we can do with boson pairs... I realize I have not even scratched the surface yet. For instance I could talk of photon pairs, or Higgs boson pairs (the latter is the topic of the research I have been doing with the CMS experiment in the recent past). Or I could discuss how we have come to manage to reconstruct very high-energy boson pairs within a single observed jet of hadrons - a very recent and shocking realization, which has entirely revolutionized the field. Unfortunately, this article has become already a bit longer than I wanted it to be. So the four remaining readers who got to this line must excuse me if I leave those topics to another post. For me, writing this was a bit cathartic, as I wrote it in just 30 minutes without ever reading back what I had written. It tells me it will not be too hard to fill up 50 pages of text with just a bit more detail and rigor, and a few fancy pictures cut and paste from recent ATLAS or CMS publications!


Tommaso Dorigo is an experimental particle physicist, who works for the INFN at the University of Padova, and collaborates with the CMS experiment at the CERN LHC. He coordinates the European network AMVA4NewPhysics as well as research in accelerator-based physics for INFN-Padova, and is an editor of the journal Reviews in Physics. In 2016 Dorigo published the book “Anomaly! Collider physics and the quest for new phenomena at Fermilab”. You can purchase a copy of the book by clicking on the book cover below.