4 July 2012: People had been waiting in CERN’s large auditorium since the evening before. There was tension in the air. Finally, two spokespersons for the collaborations ATLAS and CMS entered. There were whispers and smiles in the audience as they started showing curves indicating a small peak in a critical area. After the presentation, the director general stood up and said, victoriously, ‘I think we’ve got it!’
The BEH Mechanism, the Higgs Particle and How Particles Get Mass
The curves had shown traces of the long-searched-for Higgs particle, or the Higgs boson. Two collaborations each involving 3,000 researchers of whom 1,000 were doctoral students from over 100 countries had worked for 20 years to get to this point. They had built the world’s largest accelerator, the Large Hadron Collider (LHC), and the most complex computer system ever constructed, the World Wide Grid. It took 30 years of planning. They had studied billions of proton-proton collisions and found indications of the presence of a Higgs particle in a few dozen of them. The scientists use the 27 km long and ring-shaped LHC to collide protons travelling almost at the speed of light. When in use, the tunnel contains as much energy as a high-velocity train travelling at full speed. When the accelerator was closed down last spring for a two-year inspection, the scientists had produced maybe a million Higgs particles, of which they had been able to identify a few hundred. So, what’s the point of this gigantic project? The answer is that the Higgs particle was the last and very crucial piece of the puzzle that scientists refer to as the Standard Model of particle physics.
The Four Fundamental Forces of Nature
We have long been familiar with two of the four fundamental forces of nature – the gravitational force and the electromagnetic force. When observing them at particle level, we find that the electromagnetic force is much stronger than the gravitational force – in fact about 1040 times stronger. As a result, the gravitational force has been ignored in studies of elementary particles. Then there are two more fundamental forces of nature, which only occur in microcosmos: the strong force, which holds the nuclei of atoms together, and the weak force, which is responsible for radioactive decay.
During the latter part of the 1940s, Sin-Itiro Tomonaga, Richard Feynman and Julian Schwinger (Nobel Prize 1965) managed to formulate a seemingly problem-free quantum theory of electromagnetism, Quantum ElectroDynamics (QED). Could similar quantum theories be found for the strong and weak forces? An obvious problem was that the force-mediating particle in QED, the photon, is massless, meaning it travels at the speed of light and yields a force with long range. For a short range to be possible, as for the weak and strong forces, the force-mediating particles have to be massive. If the scientists tried to give the photon mass, all the good characteristics disappeared. It seemed like the theory used for electromagnetism didn’t apply for the other forces.
In the late 1950s, scientists started realising that protons and neutrons are not fundamental particles. They found many new strongly interacting particles that could be arranged in new inner symmetries, and Murray Gell-Mann could finally propose that these particles were actually bound states of more fundamental particles, called quarks (Nobel Prize 1969).
The WEAK interaction received attention after it was discovered that it violates the so-called parity law, or left-right symmetry (Nobel Prize to Chen-Ning Yang and Tsung-Dao Lee in 1957). A theory that was consistent with the experiments yet incomplete was quickly formulated. Could it help the development of a more fundamental theory?
Spontaneous symmetry breaking and the BEH mechanism
During his attempt to understand the mechanism behind superconductivity, which is the phenomenon of certain metals losing their resistance to the flow of electricity when cooled down below a critical temperature, Yoichiro Nambu 1960 formulated the theory of spontaneous symmetry breaking in 1960 (Nobel Prize 2008). He suggested the feasibility of theories where the normal state is not symmetrical while the underlying equations remain symmetrical. This offered a way to have the cake and eat it too.
Imagine a small ball placed on top of a sombrero. This situation is completely symmetric. If we let go of the ball, it will roll down and end up somewhere in the brim. If we think of the brim as a circular valley, the ball can obviously roll freely around the brim. If we use a potential like the sombrero in a field theory, it corresponds to a massless particle. In the perpendicular direction, a force is required for the ball to roll up the brim. This corresponds to a massive particle.
The solution to how it is possible to have a theory with short range but still have all the good characteristics as in electrodynamics was presented in a few short papers in 1964. In the first, Robert Brout and François Englert combined electromagnetism with two scalar fields boasting the potential described above. They found that the massless scalar particle merges with the massless photon, which carries the electromagnetic force, and as a result a massive particle is formed. The interaction then became short range!
A few months later, Peter Higgs studied the same theory as Brout and Englert and found the same results. He also showed more explicitly than Brout and Englert that the massive scalar particle remains, and he calculated its mass. This field came to be known as the Higgs field and its particle as the Higgs particle, or Higgs boson. The mechanism of having a so-called gauge theory with short range came to be called the BEH mechanism
A third independent study was conducted around the same time in the Soviet Union by two 19-year-old students, Alexander Migdal and Alexander Polyakov. Their more complete quantum mechanical calculations yielded the same results as those presented previously. However, their work met significant resistance in their home country, and initially they were not even allowed to submit their article to a journal. This delayed the publication of their results by one year.
The Standard model of particle physics
So how did the scientific community react to the solution of the problem? Well, the scientific community generally ignored it, assuming it would not stand the test of time. It took a full seven years before a young Dutch student, Gerhard ’t Hooft, showed that the theories indeed held water. This led to a revolution in the field of particle physics. Scientists realised that Brout’s, Englert’s and Higgs’ ideas could be used to formulate a theory for all the three interactions – the standard model for particle physics – and they realised that all particles with mass obtain this property in their interaction with the Higgs field. All particles in the model were quickly identified, with one exception – the Higgs particle. This would be the last piece of the puzzle. The link between the Higgs field and the massive particles is proportional to their mass.
This means that it is only in the link to the very heavy particles that we can expect to create Higgs particles to any significant extent. Thus, identification of a Higgs particle is not possible without the creation of high-energy particle beams. This conclusion was reached already in the late 1970s, and preparations for the construction a very large accelerator soon started both at CERN in Geneva and in USA. The U.S. project was cancelled in the 1990s, while the formal decision to build the Large Hadron Collider in Geneva was made in 1993. The plan was to establish two experimental collaborations, ATLAS and CMS, each of which was to build a detector. The accelerator ring was built and the huge computer system World Wide Grid was established to handle the enormous amounts of data involved in the experiments. On 30 March 2010, the scientists witnessed the first collision between two protons, and on 4 July 2012, the much-wanted results were presented.
Englert and Higgs could finally get their Nobel Prize. Unfortunately, Brout passed away a few years ago.
Beyond the Standard model
The spectacular transition from all the unanswered questions we were facing when I started my doctoral studies in the late 1960s to having a theory that can explain practically everything that happens in the smallest possible context has been fantastic. Today we understand three of the fundamental forces, but what about the gravitational force? The classical theory, Einstein’s general relativity theory, may be the most beautiful theory the world has ever seen. However, it can’t be transferred to the quantum world. A group of colleagues and I have been working on this issue since the 1970s, and in the 1980s we suggested another starting point for the development of a quantum gravity theory.
Whereas the standard model is based on the notion that the fundamental particles are point-like, we assumed that they are one-dimensional, like strings. This led to the superstring theory, which is a quantum gravity theory encompassing the standard model of particle physics. It has been the most popular model in basic physics ever since. However, the superstring theory has turned out to be deeper and more complicated than we could ever imagine. We are only starting to understand it but believe that it can be the theory that brings all four fundamental forces together.
This has been and still is the guiding idea for our research team, and this journey has been fantastic as well. It’s our hope to within reasonable time find the underlying theory of all fundamental interaction.