What is this mysterious particle that the mainstream media calls "the God particle" and that governments spend billions trying to find?

Scientists working in particle physics were under real pressure to deliver something new, when the Large Hadron Collider at CERN near Geneva started measuring its first low energy collisions in March 2010. They were particularly eager to find the last particle predicted by the Standard Model which so far had escaped detection: The Higgs boson. First proposed in 1964 by Englert, Brout, Higgs, Guralnik, Hagen and Kibble, about three years later Salam and Weinberg incorporated the new particle into a theory, which came to make up the electroweak part of the Standard Model. A work for which they were awarded the 1979 nobel price in physics. Still, even though the theory had been established since the mid-late 60's, the Higgs particle evaded detection. Every experiment conducted in search of it, had come up empty-handed. That was until the 4th of July of this year when scientists at CERN were finally able to announce that their experiments had observed a "particle consistent with [the] long-sought Higgs boson." In spite of the fact that some of the data collected is still under analysis, the CERN Research Director Sergio Bertolucci was right in saying that “It’s hard not to get excited by these results.” But what is all the fuss about? 

What is the “God particle”?

The Higgs particle serves a very special role in physics, different to any other particle. In order to understand the Higgs, one has to know that symmetries are of central importance in particle theories. A symmetry is the invariance of the equations of a theory under a certain set of transformations. For example it should not matter if one performs an experiment in Berlin or New York, the outcome should be the same. That is natural laws should be invariant under translations and rotations. A very powerful theorem in theoretical physics (the so called Noether's theorem) states that any such symmetry gives rise to a conserved quantity. For example invariance under temporal translations (doing an experiment tomorrow rather then today) gives energy conservation. This correspondence of symmetries and conservation laws is heavily used in particle physics and, among other things, gives the conservation of the electric current.

All the processes and physical effects that we observe in our universe can be traced back to the workings of one or several of four elementary forces. The Standard Model of particle physics captures three of these four, only leaving out gravity. The forces that it does describe are electromagnetism and the so called strong- and weak force. The strong force, among other things, being responsible for the holding together of the atomic nucleus, the weak for some forms of radioactivity. In the Standard Model all forces are mediated by force carrying particles called bosons. The bosons of the electromagnetic force are well known to us. They are nothing less than the particles that make up light: photons. It is somewhat tautological to note that they move at the speed of light, however it might not be all too obvious that this is only possible because they have no mass. In contrast, the bosons of the weak interaction (the W and Z particle) are not massless, but actually quite heavy.

Ever since Maxwell, we have known the equations that govern electromagnetism. In fact it were his equations that unified electricity and magnetism and made them appear as different sides of the same coin. Salam and Weinberg added the weak force to this story of unification in providing a theory that incorporated both Maxwell's equations and a description of the weak force. However, Salam and Weinberg had first to overcome some serious obstacles. The new equations, even though they were very similar to Maxwell’s, needed to include mass. Standard mass terms for bosons however are not invariant under the transformations that were a symmetry of the rest of the theory. Thus by including mass terms for bosons there was no way to ensure that the weak charge would be conserved in the new theory. There was, however, another obstruction when dealing with mass in the weak theory. Not only force mediating particles (bosons) caused problems, but also the matter particles (fermions) like electrons or quarks. The naive mass terms for fermions in the electroweak theory simply do not exist.  That is, when you add them to the theory, you find that they just equate to zero. So your fermions are left as before: massless. Physicists seemed to be in need of something more elaborate. There appeared to be something at work behind the masses not just of the massive W and Z bosons, but of mass in general. A possible theoretical answer to the problem was found by the 1964 papers. Mass terms for fermions and bosons were written down as coupling terms between the particle that is supposed to acquire mass, and a new field later to be called the Higgs. These terms preserved the weak symmetry and thus the weak current. It was this particle that made Salam and Weinberg's unification possible. As a result mass was no longer understood as a mere feature of a particle, but as the result of an interaction with a new field. It is in this sense, that the Higgs is truly unique.                                                                                                                                                       

How does the Higgs work? How does it give mass to particles?

Drawing the comparison between the invariance of a theory under translations and the invariance that give the conservation of the weak current, was not entirely accurate. Physicists actually distinguish between inner (or gauge) and outer symmetries. Translations belong to the later kind. In a translation the whole experimental setup is shifted from A to B, we do not just change some of the substances or particles we have set up to react, but shift the whole experiment, from the outside if you want. In contrast, inner symmetries are transformations where the experimental steup itself is changed. That is, e.g. we do not study photons reacting with some other particle type, but instead we exchange the photons by a particular combination of W and Z particles. So we change the inner setup of the experiment rather than displacing the whole laboratory. If the outcome of the experiment (or any experiment) cannot tell the difference between whether we have replaced the photons or not, this replacement must count a symmetry of nature.The qualitative difference between these two families of symmetries is reflected in the kind of conserved quantities they give rise to. Via Noether's theorem the outer symmetries result in the conservation of energy and momentum, whereas inner symmetries give rise to the conservation of a specific current or charge, be it electric, weak or strong.

However beautiful this connection might be, the full electroweak symmetry is not what we see in nature! The W and Z bosons are distinct from photons. For one, any combination of the W and the Z would have mass and the photon does not. So what happened? Physicists went through all this trouble to save a symmetry in their theories that does not exist? The key to answering this question is the distinction between symmetries of the equations that make up a theory and symmetries of a particular solution of those equations. To give an example: Picture a perfectly symmetric stick standing up vertically. When we apply an increasing force to its top side, at some critical value the stick will break in a specific direction. Although the initial situation was completely symmetric, the outcome or solution distinguishes a particular direction and has thus lost the initial symmetry. Physicists say that the symmetry of the theory is spontaneously broken. The vacuum solution of the Higgs field, so the state the Higgs field is in without the presence of any other particles or energy, breaks the inner symmetry of the electroweak theory. That is, it distinguishes between the weak bosons and the photon. The word "broken" might seem a misnomer, as the theory is still invariant under the same transformations. Only the solution that our universe chose to settle in after the big bang hides part of these invariances.

Higgs – The end of the hunt?

A theoretical consequence of spontaneous symmetry breaking in particle physics is the appearance of new, so called Goldstone particles. This first presented a problem, as no such particles had been observed. However, in their 1964 papers, the above authors found a way to get rid of these particles which subsequently earned the telling prefix "would-be." In this mechanism, later named after Peter Higgs, the gauge bosons "eat up" the would-be Goldstone particles to acquire their mass. What left the theory with only one additional particle (the Higgs) may sound like a happy end to a theoretician, but had experimentalists baffled for decades. All experiments conducted in the years that followed failed to produce evidence for the existence of the Higgs. Only now, almost 50 years later, luck may have shifted and one of the greatest hunts in the history of science might be coming to an end.