I began writing this somewhere between Ho Chi Minh City and Singapore, on the way home after week lecturing at the 22nd Vietnam School of Physics. The school was in the seaside town of Quy Nohn, and attracts students not just from Vietnam but from India, Thailand, Malaysia and more. Sample questions over dinner: Where are the best places to study particle physics? Have you met Stephen Hawking? Why did Britain vote to leave the EU? Do you support Manchester City or United?*
Talking to new audiences, I find that I see things partly through their eyes, and the new perspective nearly always throws up delights which had become blunted by familiarity. Watching a favourite film with family or friends who are seeing it for the first time has a similar effect. As long I avoid spoilers. (Mum, why did dad go weird when Leia kissed Luke like that? Hush, kids, he’s just weird. Watch the wookie.)
One of the delights this time was the plot below, the wonders of which I am now going to try to share with you, too, if you have the inclination.
This jumble of data points is telling us a lot about the basic constituents of the universe. It is made from recordings of proton-proton collisions at the Large Hadron Collider. Each collision entering the plot contained four leptons – electrons, or their heavier cousins muons, or the corresponding antiparticles.
First the axes.
The horizontal axis is the ‘mass’ of the four leptons. This doesn’t mean just adding up their masses, it means calculating the mass of the total four-lepton system. That is the same as hypothesising that they were all produced from the decay of a single particle, and working out what its mass must have been. The unit is GeV – “Giga electronVolt” – which is actually a unit of energy. Since energy is proportional to mass (E = mc2) this is ok. One GeV is a bit more than one proton mass.
The vertical axis indicates how many events were seen. The units are femtobarns, which isn’t really important, but if you want to know what they mean try here.
Now the data, and what that means.
There are several different ways of producing four leptons at the LHC. We calculate the probabilities using the Standard Model of particle physics, and in particular the diagrams invented by the great 20th Century physicist Richard Feynman. All the relevant diagrams have to be included or you don’t get the correct answer. Here is one of them (A).
In this diagram, a quark and an anti-quark come in from the left side of the diagram (one from each proton). They scatter and produce two Z bosons. The Z is the carrier of the weak force and has a mass of about 91 GeV. Both Zs decay rapidly to two leptons each, giving us the four leptons required. How does this diagram affect the plot?
Because each Z has a mass of 91 GeV, you might expect this diagram to show up in the plot only when the four-lepton mass is twice this or more – that is 182 GeV and above. And indeed there is a big rise between the fifth and sixth data points from the left, at about 182 GeV. But because quantum mechanics is slippery, the Z bosons don’t have to have exactly 91 GeV of mass. That’s why they have little asterisks on them in the diagram, they are what we call virtual particles. There are contributions all across the plot from this diagram. But there is a big enhancement when the Zs can have the right mass, and that’s the rise at 182 GeV.
There are other features and other diagrams though. Next look at the leftmost bin of the plot, which is pretty high too. This is about 91 GeV, which correctly suggests that the Z might be involved again. The relevant diagram is (B).
In this diagram, there is a big enhancement in the number of events when the first Z from in the diagram has the ‘correct’ mass of 91 GeV. In that case, the second Z (further to the right) has a much lower mass. In fact that “Z” could quite often be a virtual photon instead of a Z. Effectively all four leptons come from the first Z, and their combined mass will be 91 GeV, reflecting that. If we had the mass plot for events containing only two leptons, there would be a huge peak at 91 GeV. The extra Z we have here is an unlikely ‘higher order correction’ to that process, but because we demanded four leptons, we see it.
The final feature of the plot is probably the most interesting. The third bin from the left is also very high compared to its neighbours. It is at a mass of about 125 GeV, and it comes from digrams like this (C).
Here, two gluons (the carriers of the strong force) come in, one from each proton. There is a triangular loop, which would mainly have a top quark going around it (not labelled), which produces a Higgs boson. The Higgs then decays to two Zs (at least one of which much have the ‘wrong’ mass, i.e. below 91 GeV). Once more, the Zs decay to two leptons each. There is a peak when the Higgs boson has its correct mass of 125 GeV.
The red lines, with the shaded bands around them, show the theoretical calculation, which is scattered around the measurement a bit but basically tracks the features of the data very nicely once all the right diagrams are included. Leaving any of these contributions out would give the wrong answer.
So in the one plot you have virtual and real particles, the carriers of the weak and electromagnetic forces, higher-order radiative corrections, and the particle (or field) responsible for giving all the other fundamental particles mass. Quite a rich seam of physics. I especially like that fact the measurement is rather simple and assumes nothing about the theory - it just counts events with four leptons and plots their mass – yet leads to a richly-featured distribution which is understood using such a wide range of aspects of the theory.
The full publication is here.
Finally, Quy Nhon is lovely, Le Duc Ninh was a fantastic host, the students and fellow lecturers were great and I hope to get the chance to visit Vietnam again another day and see more of it. Here’s the view from the ICISE:
And following the trend of twitter being the first draft of newspapers which are the first draft of history, below are some others I tweeted while there in case you’re interested. I began missing it already in the taxi to the airport.
Breakfast on the shore of the South China Sea. Partial to the Cha Bong in foreground, sort of pig-flavour candyfloss pic.twitter.com/vIc0NdPzkB
— Jon Butterworth (@jonmbutterworth) September 3, 2016
I like a bar that is confident enough to put "Established 2014" on its cushions. pic.twitter.com/n6jTmqiD1l
— Jon Butterworth (@jonmbutterworth) September 3, 2016
The best way to spell beer/bier/birra etc? pic.twitter.com/YiihYBE0f1
— Jon Butterworth (@jonmbutterworth) September 4, 2016
Some of the great students at the 22nd Vietnam School of Physics. And me. And palm trees. pic.twitter.com/FFBiHU74pl
— Jon Butterworth (@jonmbutterworth) September 4, 2016
Taxi to UIG racing the train through an ideal gas of mopeds. pic.twitter.com/CT1UhgHtSi
— Jon Butterworth (@jonmbutterworth) September 6, 2016
Back from Vietnam with souvenirs, all ready to blend into N London politics. pic.twitter.com/luWrF3Zrrs
— Jon Butterworth (@jonmbutterworth) September 7, 2016
* Answers: a long list including UCL and some places nearer to Vietnam; yes, briefly and I once borrowed his office; argh argh argh; City, hooray!
Jon Butterworth’s book Smashing Physics is available as “Most Wanted Particle” in Canada & the US.
