Higgsteria - How to interpret the mass spectrum graph

The seminar on the 4th of July held at CERN in Geneva - despite the use of Comic Sans font - gave very interesting news to the Physics community.

ATLAS and CMS, two experiments from LHC, both discovered a new particle (5-sigma level is a requirement for a discovery) at 126 GeV in the mass spectrum.

Jargon apart, if you are not a physicist, you can read info about the Higgs boson (such as what is the Higgs, what is a boson, how does it give mass to other particles...) pretty much everywhere nowadays.

What many people may wonder is: what is this 5σ? And what about this 95% confidence level (CL)? But, most importantly, what is 126 GeV?
In this post I will give you an idea, with simple language, about these concepts and you will be finally able to understand this (not-so) mysterious graph.

 

The basics

The LHC is a particle accelerator. The scope of this machine is to literally accelerate particles (protons in this case) to very high speeds and smash them together front-to-front to see what happens.
In the case of protons, we know they have a substructure (3 quarks) and very exotic things happen when they are involved in the frontal particle accident.

In order to make these 3 quarks inside the proton interact in the collision, we need highly energetic protons. That is why this experiment is new. We needed a bigger ring (the LHC) to accelerate the protons to higher energies, high enough to allow the possibility to produce new - previously unknown - particles.

But why do we need a higher energy to produce new particles?
This is because of the sacred principle of Energy Conservation, which (to Niels Bohr's disappointment) has never been violated and most probably it will never be. Particles have mass (which is ultimately the reason for our mass) and Einstein said, through the famous relation E=mc^2, that mass is energy. When we smash the particles in the collider, the more energy we give to the particles, the more mass we can get out of the colliding particles after they recombine their internal structure.
If a particle is quite naturally heavy and the previous detector did not have enough energetic collisions to produce it, it will never be discovered!

Mass spectrum

Knowing how to produce new particles, how do you detect it and identify it? The common way is to look for particle properties and try to pinpoint it thanks to the existing model.
For example, we know that electrons have electric charge. Then, if you detect your particle and see that it has charge, you can correctly guess that it can be an electron, or any other particle having charge.

The properties we look for, to identify a particle, are mainly: charge, mass, spin. As the Higgs boson has no charge in the theoretical models, and the spin must be unitary (in order to be a boson), the best discriminator to see if the experimentally detected Higgs agrees with the theoretical models is to measure its mass.

The x-axis, Mass (GeV)

For the reasons explained above, people at CERN have been looking for a big span of collisions giving particles with different masses, in the hope to find the Higgs.

This is what you find on the x-axis of the common graph. It is the mass of the particle produced for a single collisional event.

What are the units of this mass? We are used to kilograms, what is GeV?
Einstein is again playing a role here. As mass is energy, scientists at CERN are measuring the mass of the particles in units of energy! GeV stands for giga-electronvolts, which is a billion electronvolts. An electron volt is a unit of energy (much like Joules, or Ergs, or even Calories!) which is very convenient to measure particle energy, and then also mass.

The strategy is to measure the mass of every single particle produced from the collision. As we know most of the particles in the selected mass range, we have an expectation for what the line will look like (that is the dashed line in the graph). This brings me into the next topic.

The y-axis, Number of Events

The quantity on the y-axis is the number of events observed for that specific mass. As we have an expectation for how many particles will be produced for a specific mass, if there is a new particle which has been produced, it will result in an excess of production.

The excess, of course, will be reported around the mass region for the mass of the new, unknown, particle.

This is why we measure number of events on the y-axis. Because we would expect an anomaly, a bigger number of particles produced when the energy (mass) is close to the one of the new particle, as this "new" particle was not considered in the model.

Now you can truly understand the graph. The peak around 126 GeV is the excess given by the production of this new particle, weighting around 126 GeV, which was not expected before.

But, what if it is just a mistake? It could be that the detector is not working properly or that there are so few events that there is not enough statistic and the peak is just a fluctuation around the model. This is why you need statistical evidence: the sigma.

5-sigma = discovery

As your result in the graph could be biased by low statistics or just be a work of chance, in order to shout for discovery, particle physicists usually need a 5-sigma certainty of the result. What does it mean?

Sigma is the Greek letter for standard deviation in statistics. Standard deviation is a measure of how far away is a measurement from its expectation. A result 5 sigmas away, means that it is five times the standard deviation off the expectation. And this means that, in order to be a statistical fluctuation, a measurement 5 sigmas away has a chance of one in three millions to be a random fluctuation.

This is a pretty safe assumption to make sure that the measurement is (relatively) certain!

 95% CL Limit on μ

This sentence, which lies on the y-axis of the graph is not referring to the actual value on the y-axis, but it is a statement. It could be read like:

"95% Confidence Level Limit on the mean"

It means that there is a probability of 95% that the value of the measurement ( 126 GeV ) covers the true value of the parameter.
The true value is the value which we are trying to measure (the one set by God, one would say) and this is just a limit we are setting to express how much confident we are on the measurement we are taking.

What about the other weird symbols

In the graph there are two lines expressing two different set-up parameters.
I will only explain one, as the other is essentially the same.

$ \sqrt{s}=7 TeV $

is the indication of the centre of mass energy used to collide the particle. It is essentially the energy available to produce new particle after the collision. You can see that it is measured in tera-electronvolts, which is even higher than the previous scales used (giga-electronvolts), as one TeV is 1000 GeV.

$  \int Ldt=4.6-4.8Fb^{-1} $

is the integrated luminosity collected for the specified centre of mass energy. It is essentially a measure of how many collisions happened in total for the data shown in the graph.

Conclusions

What is the conclusion you can draw from the graph? Many newspaper and media were shouting for "Higgs discovered" already. Any good scientist would not.

The only certainty that the graph is showing is that a new boson has been observed at a mass of 126 GeV. Nobody is telling that it is the Higgs, even if there are strong hints towards it.

That is because the Higgs mechanism is the only good model around that could explain an excess of mass at 125 GeV. This would be a big coincidence, but there are still many particles that could be discovered and assuming the particle IS the Higgs, would actually be the most un-scientific thought anyone can have about it.

The particle could very well be something more exotic (to be read: more exotic to us!) which we could not yet explain, and actually, it is much more probable that it is.
The Higgs mechanism was built with the only purpose to explain the unexpected mass of the weak-force carriers: W and Z bosons (all force carriers should be massless in the Standard Model).
It was essentially like a back-up plan to save the most accepted model in particle physics. It was a Plan B. I would find it very improbable if it was true, a big shot of luck and intuition from Peter Higgs, even if still fascinating.

Finding a new particle's mass and saying that it is the particle you built your model for, is like finding a new skull which weights halfway between a chimpanzee's and a human's skull and pretending to have found the missing link between humans and monkeys.
There are other factors which need to be checked, so stay tuned folks and do not rush into hasty conclusions. This is an exciting time for Physics and we will have an answer soon, a definitive one.