Close, but no cigar

Particle physicists are not easily satisfied. Our guiding text, the Standard Model, is arguably the most successful theory of all time, marrying quantum mechanics with special relativity and detailing the properties and interactions of the most fundamental particles of nature, along with three of the four known forces. It has been built, bit by bit, by tens of thousands of scientists in the last fifty-something years, and is now being tested to its limit at experiment sites around the world. The precision measurements we make at colliders like the Large Hadron Collider at CERN, where protons are smashed together to create sprays of new particles, have all been perfectly and devastatingly in agreement (within uncertainty, of course) with predictions made by the Standard Model (edit: recent results here and here display hints of new physics but should, for now, be treated with caution). We have discovered every particle it demands, the last of which was the Higgs boson in 2012. The most precise measurement of the theory is the electron magnetic moment, which has been recorded with the precision of one part in a billion. So, shall we call it a day then? Not quite. The hunt for physics Beyond the Standard Model is in full swing, with physicists searching to fill the holes that the theory has left.

Higgs hunters guide to the galaxy

The most famous prediction of the Standard Model is the Higgs boson. Foretold in 1964 and discovered in 2012 by the ATLAS and CMS projects at CERN (and announced, inexplicably, in comic sans font), the Higgs was the final particle predicted by the Standard Model to show up, fashionably late and absolutely crucial to the functioning of the theory. To understand why it is needed, let’s run through the structure of the model.

Take, for example, the thing on which you are likely seated, be you perched on a wooden chair or sinking into a soft couch cushion. Whatever it is, it’s made of atoms, each of which is a nucleus of protons and neutrons at its centre with clouds of electrons taking up the rest of the space. Although this is where high school science stops, the protons and neutrons themselves possess a substructure; quarks and gluons. To be exact(ish), a proton is composed of two up quarks and a down quark, and they are glued together by the very aptly named gluons, which carry the strong force, one of the three forces encoded in the Standard Model (gravity, the fourth force, is left out). It turns out that there are four additional quarks, and two additional leptons (the family to which the electron belongs), each with their own neutrino. Also included in the theory are anti-particles for each. To complete the zoo, we need to mention the remaining four force carriers (the two W bosons, the Z boson, and the photon). The photon carries the electromagnetic force and the W and Z bosons the weak force. And last but not least, the Higgs.

The Standard Model ecosystem is controlled by its Lagrangian, an equation which encodes all the information in the theory. It contains kinetic terms, mass terms, a potential term (for the Higgs) and interaction terms. As an example, consider three particles φ, ψ and χ. If you see a term φχψ in your Lagrangian, that means that those three particles can interact with each other in one go. The full expanded form of the Lagrangian looks like this,

but we can also write it in a compact form as shown on the mug below that every particle physicist, including the one writing this article, owns.

Symmetries make the world go round

The rules underpinning the Standard Model are based on symmetries. Consider a perfect unmarked sphere. It has rotational symmetry - that means that if I act on it with some rotation in space, it will not look any different to you. It turns out that rotations in three dimensional space form a group which we call SO(3). If I mark the sphere by drawing on it with a permanent marker, it will no longer have the symmetry. If I rotate it, you will know; the symmetry will have been broken. Now, the guiding principle of the Standard Model is that the Lagrangian is invariant under SU(3) x SU(2) x U(1). These are three more symmetries (don’t worry too much about the form of them) to which every term in the Lagrangian must conform. It turns out that a term giving the W and Z bosons mass would be forbidden under the required symmetries, which is a problem because we know that these particles are, in fact, massive (we have measured this). The beautiful thing about the Higgs field is that it spontaneously breaks the symmetry protecting those terms, and our W and Z bosons can acquire mass. ‘Spontaneous’ breaking means that the symmetry is not broken at the level of the Lagrangian, but rather in the physical state. This is where the famous Mexican Hat potential comes into play; by rolling down the slope to the minimum of the potential, the Higgs breaks the symmetry of the system.

Something’s missing

Unfortunately, the unveiling of the Higgs featuring the world’s most hated font was not the last of its problems. It features in the Standard Model as an elementary particle, like all the others in the zoo. This means that it is only composed of itself, and has no substructure (unlike, for example, a proton). However, this turns out to cause some very real limitations in the theory, summarised in the hierarchy problem. Because the Higgs is the only scalar elementary particle in the theory, it is subject to corrections to its mass which should push it far higher than what we observe. Really, the problem lies with the massive discrepancy between the scale of the weak force and the scale of gravity; the masses of the Z and W bosons are about 10,000,000,000,000,00 smaller than the Planck mass, the mass of the smallest possible black hole. This shows us that we are missing something in our description of the Higgs, and forces many of us to look beyond the Standard Model. In one possible solution, some (myself included) hope to strip the Higgs of its elementary status, revealing it instead as a composite particle. Others still hold a candle for supersymmetry (SUSY). Perhaps the solution to the dark matter question may be revealed here too; both composite Higgs models and SUSY can yield viable candidates.

In all cases, the hope is that new physics lies just around the corner (if the corner is a higher energy scale) and that we might access it at more powerful colliders. At this stage, nothing has been uncovered at the LHC- either the solution is really well hidden, or we don’t understand the questions we are asking. The hope is that the solution to the Higgs question is close - we just have to reach out and grab it.