When a new particle physics discovery is made, you may have heard the term “sigma” being used. What does this mean? Why is it so important to talk about sigma when making a claim for a new particle discovery? And why is five sigma in particular so important?

Why does particle physics rely on statistics?

Particles produced in collisions in the Large Hadron Collider (LHC) are tiny and extremely short-lived. Because they almost immediately decay into further particles, it is impossible for physicists to directly “see” them. Instead, they look at the properties of the final particles, such as their charge, mass, spin and velocity. They work like detectives: the end products provide clues to the possible transformations that the particles underwent as they decayed. The probabilities of these so-called “decay channels” are predicted by theory.

In the LHC, millions of particle collisions per second are tracked by the detectors and filtered through trigger systems to identify decays of rare particles. Scientists then analyse the filtered data to look for anomalies, which can indicate new physics.

As with any experiment, there is always a chance of error. Background noise can cause natural fluctuations in the data resulting in statistical error. There is also potential for error if there isn’t enough data, or systematic error caused by faulty equipment or small mistakes in calculations. Scientists look for ways to reduce the impact of these errors to ensure that the claims they make are as accurate as possible.

What is statistical significance?

Imagine rolling a standard die. There is a one in six probability of getting one number. Now imagine rolling two dice – the probability of getting a certain total number varies – there is only one way to roll a two, and six different ways to roll a seven. If you were to roll two dice many, many times and record your results, the shape of the graph would follow a bell-curve known as a normal distribution.

The normal distribution has some interesting properties. It is symmetrical, its peak is called the mean and the data spread is measured using standard deviation. For data that follows a normal distribution, the probability of a data point being within one standard deviation of the mean value is 68%, within two is 95%, within three is even higher.

Standard deviation is represented by the Greek letter σ, or sigma. Measured by numbers of standard deviations from the mean, statistical significance is how far away a certain data point lies from its expected value.

What has this got to do with physics?

When scientists record data from the LHC, it is natural that there are small bumps and statistical fluctuations, but these are generally close to the expected value. There is an indication of a new result when there is a larger anomaly. At which point can this anomaly be classified as a new phenomenon?  Scientists use statistics to find this out.

Imagine the dice metaphor again. Except this time, you are rolling one die, but you do not know if it is weighted. You roll it once and get a three. There is nothing particularly significant about this – there was a one in six chance of your result – you need more data to determine if it is weighted. You roll it twice, three times, or even more, and every time it lands on a three. At what point can you confirm it is weighted?

There isn’t a particular rule for this, but after around eight times of getting the same number, you’d be pretty certain that it was. The chance of this happening as a fluke is only (1/6)⁸ = 0.00006%.

In the same way, this is how physicists determine if an anomaly is indeed a result. With more and more data, the likelihood of a statistical fluctuation at a specific point gets smaller and smaller. In the case of the Higgs boson, physicists needed enough data for the statistical significance to pass the threshold of five sigma. Only then could they announce the discovery of “a Higgs-like particle.”

What does it mean when physicists say data has a statistical significance of five sigma?

A result that has a statistical significance of five sigma means the almost certain likelihood that a bump in the data is caused by a new phenomenon, rather than a statistical fluctuation. Scientists calculate this by measuring the signal against the expected fluctuations in the background noise across the whole range. For some results, whose anomalies could lie in either direction above or below the expected value, a significance of five sigma is the 0.00006% chance the data is fluctuation. For other results, like the Higgs boson discovery, a five-sigma significance is the 0.00003% likelihood of a statistical fluctuation, as scientists look for data that exceeds the five-sigma value on one half of the normal distribution graph.

Why is five sigma specifically important for particle physics?

In most areas of science that use statistical analysis, the five-sigma threshold seems overkill. In a population study, such as polls for how people will vote, usually a result with three sigma statistical significance would suffice. However, when discussing the very fabric of the Universe, scientists aim to be as precise as possible. The results of the fundamental nature of matter are high impact and have significant repercussions if they are wrong.

In the past, physicists have noticed results that could indicate new discoveries, with the data having only three to four sigma statistical significance. These have often been disproven as more data is collected.

If there is a systematic error, such as a miscalculation, the high initial significance of five sigma may mean that the results are not completely void. However, this means that the result is not definite and cannot be used to make a claim for a new discovery.

Five sigma is considered the “gold standard” in particle physics because it guarantees an extremely low likelihood of a claim being false.

But not all five sigmas are equal…

Five sigma is generally the accepted value for statistical significance for finding new particles within the Standard Model – those particles that are predicted by theory and lie within our current understanding of nature. Five sigma significance is also accepted when searching for specific properties of particle behaviour, as there is less chance of finding fluctuations elsewhere in the range.

Whether five sigma is enough statistical significance can be determined by comparing the probability of the new hypothesis with the chance it is a statistical fluctuation, taking the theory into account.

For physics beyond the Standard Model, or data that contradicts generally accepted physics, a much higher value of statistical significance is required – effectively enough to “disprove” the previous physics. In his paper “The significance of five sigma,” physicist Louis Lyons suggests that results for more unlikely phenomena should have a higher statistical significance, such as seven sigma for the detection of gravitational waves or the discovery of pentaquarks.

In this paper, Lyons also deems five sigma statistical significance to be enough for the Higgs boson discovery. This is because the theory for the Higgs boson had been predicted, mathematically tested, and generally accepted by the particle physics community well-before the LHC could generate conditions to be able to observe it. But once this was achieved, it still required a high statistical significance to determine if the signal detected was indeed a discovery.

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A statistical significance of five sigma is rigorous, but it is really a minimum. A higher value for statistical significance cements data as being more reliable. However, achieving results with statistical significance of six, seven, or even eight sigma requires a lot more data, a lot more time, and a lot more energy. In other words, a probability of at most 0.00006% that a new phenomenon is not a statistical fluke is good enough.

Find out more:

• Paper: The significance of five sigma
• Video: The Higgs boson discovery, explained
• Online article: One and two sided probability 

The LHC will not generate black holes in the cosmological sense. However, some theories suggest that the formation of tiny 'quantum' black holes may be possible. The observation of such an event would be thrilling in terms of our understanding of the Universe; and would be perfectly safe. More information is available here.

Is the Large Hadron Collider dangerous?

No. Although powerful for an accelerator, the energy reached in the Large Hadron Collider (LHC) is modest by nature’s standards.  Cosmic rays – particles produced by events in outer space – collide with particles in the Earth’s atmosphere at much greater energies than those of the LHC. These cosmic rays have been bombarding the Earth’s atmosphere as well as other astronomical bodies since these bodies were formed, with no harmful consequences. These planets and stars have stayed intact despite these higher energy collisions over billions of years.

Read more about the safety of the LHC here

What happened with the LHC in 2015 and what does CERN plan to do in the future?

The Large Hadron Collider (LHC) restarted at a collision energy of 13 teraelectronvolts (TeV) in June 2015. Throughout September and October 2015, CERN gradually increased the number of collisions, while remaining at the same energy. In November, as with previous LHC runs, the machine run with lead ions instead of protons until mid-December when it had its winter technical stop.

After a successful run in 2016, the most powerful collider in the world was switched back on in spring 2017, followed by a period of tests. After a period of commissioning, the LHC experiments began taking physics data for 2017. Over the coming years, the LHC operators plan to increase the intensity of the beams so that the machine produces a larger number of collisions. This will enable physicists to have a better understanding of fundamental physics.

Why is the Higgs boson referred to as the God particle?

The Higgs boson is the linchpin of the Standard Model of particle physics but experimental physicists weren’t able to observe it until the arrival of the LHC, nearly 50 years after the particle was first postulated. Leon Lederman coined the term ‘the God particle’ in his popular 1993 book ‘The God Particle: If the Universe Is the Answer, What is the Question?’ written with Dick Teresi. In their book, Lederman and Teresi claim the nickname originated because the publisher wouldn’t allow them to call it ‘the Goddamn Particle’ – a name that reflected the difficulty in observing the elusive boson. The name caught on through the media attention it attracted but is disliked by both clerics and scientists.

Is CERN's aim to prove that God does not exist?

No. People from all over the world work together harmoniously at CERN, representing all regions, religions and cultures. CERN exists to understand the mystery of nature for the benefit of humankind. Scientists at CERN use the world’s largest and most complex scientific instruments to study the basic constituents of matter – the fundamental particles. Particles are made to collide together at close to the speed of light. This process gives the physicists clues about how the particles interact, and provides insights into the fundamental laws of nature.

Why does CERN have a statue of Shiva?

The Shiva statue was a gift from India to celebrate its association with CERN, which started in the 1960’s and remains strong today. In the Hindu religion, Lord Shiva practiced Nataraj dance which symbolises Shakti, or life force. This deity was chosen by the Indian government because of a metaphor that was drawn between the cosmic dance of the Nataraj and the modern study of the ‘cosmic dance’ of subatomic particles. India is one of CERN’s associate member states. CERN is a multicultural organisation that welcomes scientists from more than 100 countries and 680 institutions. The Shiva statue is only one of the many statues and art pieces at CERN.

What are the shapes in the CERN logo?

The shapes in CERN’s current logo represent particle accelerators. The logo in this form dates back to 1968, when a decision was made to change the CERN logo from the original one, seen here. Some 114 new designs were proposed, many of which used CERN’s experiments as inspiration. The final design used the original lettering, surrounded by a schematic of a synchrotron, beam lines and particle tracks. Today’s logo is a simplified version of this.

Will CERN open a door to another dimension?

CERN will not open a door to another dimension. If the experiments conducted at the LHC demonstrate the existence of certain particles it could help physicists to test various theories about nature and our Universe, such as the presence of extra dimensions. There is more information here.

What did Stephen Hawking say about Higgs potential destroying the Universe?

Hawking was not discussing the work being done at the LHC.

The LHC observes nature at a fundamental level but does not influence it. Measurements of the Higgs bosonhave allowed us to learn more about the intrinsic nature of the Universe, and it is this that Hawking was discussing. The measured properties of the boson suggest that the Universe is in a quasi-stable equilibrium, though with a lifetime far exceeding anything we can imagine (10¹⁰⁰ years). This is explained further in the TEDxCERN talk below:

http://tedxcern.web.cern.ch/video/2013/what-higgs-might-mean-fate-universe

Why does CERN appear in Google Maps when I type certain keywords?

Many of these associations have no grounding in fact, and are a possible result of several users renaming locations on their own maps, keyword searches, or from lots of users creating custom maps, which utilise those search terms.

Can the LHC have an influence on weather patterns and natural phenomena?

No. The magnets at CERN have an electromagnetic field, which is contained with the magnets themselves and therefore cannot influence the Earth’s magnetic field, nor the weather. The strength of the LHC magnets (8.36 teslas) is comparable to the magnetic field found in PET-MRI scanners (up to 9.4 tesla), which are regularly used for brain scans.

Will CERN generate a black hole?

The LHC will not generate black holes in the cosmological sense. However, some theories suggest that the formation of tiny 'quantum' black holes may be possible. The observation of such an event would be thrilling in terms of our understanding of the Universe; and would be perfectly safe. More information is available here.

I saw a video of a strange ritual at CERN, is it real?

No, this video from summer 2016 was a work of fiction showing a contrived scene. CERN does not condone this kind of action, which breaches CERN’s professional guidelines. Those involved were identified and apropriate measures taken.

Does the LHC trigger earthquakes?

The LHC does not trigger earthquakes. Earthquakes are a natural hazard caused by the movement of tectonic plates. As these rigid plates move towards, apart or past each other they can lock up and build up huge stresses at their boundaries, such as the middle of the Atlantic Ocean, or along the Pacific rim. When the plates suddenly slip apart, this stress is relieved, releasing huge amounts of energy and causing an earthquake.

Several million earthquakes occur across the Earth each year but most are too small to be detected without monitoring equipment. There is no means by which the LHC could trigger earthquakes, and no correlation between LHC operation and the occurrence of earthquakes.

Anecdote: Some high precision instruments at CERN are able to detect earthquakes due to their sensitivity to tiny movements. In the LHC, there are more than 100 Hydrostatic Levelling Sensors that monitor the relative displacements of the magnets that steer beams of particles around the LHC’s 27 km ring. These sensors can detect the waves emitted by earthquakes occurring even very far away after their journey through the Earth. Another tool, the Precision Laser Inclinometer, is used to measure the movements of underground structures that can affect the precise positioning of the LHC’s particle detectors. These are also sensitive enough to detect earthquakes.