The Standard Model of particle physics and beyond

I still have no idea about to go about writing science stuff in this blog, who to pitch at, who would actually care to read it, but somehow it feels weird to start talking about things like the LHC, SUSY etc without explaining them. And since when I'm ranting about stuff I am bound to refer to them I'm going to have to go down the pedagogical route initially.

So a little bit about what I do to start off.

Matter and Forces

Roughly speaking particle physics is the study of what the fundamental constituents (i.e. things with no substructure) of matter are and how they interact, i.e what forces govern their dynamics. On the constituent side we currently know that we are made up of molecules, molecules are made up of atoms, atoms are made up of protons, neutrons and electrons and finally the proton and neutron are made of 'up' and 'down' type quarks. In radiation experiments where the electron is emitted (beta radiation) another particle with no electric charge, called the neutrino was discovered, and together electrons and neutrinos are referred to as leptons. So we have quarks and leptons, but for some unknown reason we also have 2 more generations of heavier quarks and leptons, with only the first generation making up ordinary matter. The forces through which they interact are gravity, which is so weak we can't measure it's effect when studying these subatomic particles, electromagnetism, more familiar as electricity and magnetism, the less familiar weak force and finally the strong force which binds quarks into hadrons like the proton and neutron.

We currently have a model which describes all (excluding gravity) of this and it is called the Standard Model of particle physics.

Shown in the figure to the left are all the particles in the Standard Model. As well as the matter particles which can collectively be referred to as fermions, there are also bosons in the Standard Model which 'carry' the forces. Fermions and bosons are separated by an internal quantum number called spin, which is like angular momentum, but is a fundamental property of that particle rather than being generated by dynamics. Fermions have half integer spins, while bosons only possess integer values of spin.

This internal quantum number spin was famously observed in the Stern-Gerlach experiment. The observation that the electron carried half integer spin was crucial to the development of quantum mechanics in using it describe emission spectra (wavelengths of the radiation) from atoms.

Experimentalists and Theorists

In particle physics the workload is somewhat divided between theorists who construct models, test them for internal consistency and perform the complicated calculations needed to make predictions and experimentalists who do the really hard work of designing, building and running machines capable of testing the theories, as well as sifting through the enormous reams of data trying to find the proverbial needle and then finally determine the statistical significance of observation (or non observation as the case may be) of said needle .

I belong to the former category, theorists. We are interested in trying to build models which answer deep, fundamental questions (puzzles) about how the world around us is constructed. It is important that the models we construct satisfy all current data and are internally consistent. In addition we also want to explain the puzzles without actually introducing new ones. One current question we are interested in is how fundamental particles, like the electron and the quarks obtain mass.

The Higgs Mechanism

The observed interaction of these particles are all beautifully predicted by postulating symmetries of nature, called gauge symmetries. While this may sound rather abstract the important point to grasp is the predictive power of symmetries. If you know you are looking into a mirror, you can predict what you will see when you turn around because there is a symmetry between the reflected image and what is actually behind you. Specifically it is a spacial inversion symmetry. The gauge symmetries predict how matter interacts, though the symmetries are more complicated than the mirror symmetry and can be best seen using a mathematical description of the physics which I don't present here (so you shouldn't worry about this if you don't know it already).

For electromagnetic and weak interactions we can postulate the electroweak symmetry. Unfortunately the electroweak symmetry forbids the introduction of explicit masses for fundamental particles from the outset, making it is challenging to have a theory which predicts the interactions correctly while allowing fundamental particle masses in accordance with observation. This challenge is solved by the Higgs mechanism, where by electroweak symmetry is broken in the vacuum, generating particle masses but maintaining the elegant (and incredibly well tested) symmetry predictions of the interactions between the fundamental particles.

This is achieved by introducing a Higgs field which can be described by an electroweak symmetric theory. However if the Higgs field has a vacuum expectation value, meaning there is a non-zero probability for the Higgs to exist within the vacuum (so we have a non empty vacuum, which may seem a strange notion) , this breaks the electroweak symmetry. A common analogy used to give people a picture of how this works is to imagine travelling through treacle. As you move through the treacle interacts with you slowing your progress. In a similar sense we postulate that the vacuum is filled with the Higgs which the interacts with any fundamental particle propagating in the vacuum. The Higgs interacts with (sticks to if you like the analogy) different fundamental particles with different strengths, giving them the appearance of different masses.

The Standard Model

Associated with this Higgs field is the Higgs boson. Currently the experimentalists are searching for this particle to see if it exists (it may not, there are alternatives) at the new Large Hadron Collider (LHC) in Geneva. The simplest model with this Higgs mechanism and Higgs boson which can describe all current observations is called the Standard Model (SM) of particle physics. While there may not be a fundamental Higgs boson, the SM certainly provides a very good description of nature at low energies. Through the Higgs mechanism all particles can have mass, while the strong symmetry and the (broken) electroweak symmetry correctly predict all interactions observed.

The SM is an astounding achievement in science. It ties together two of the most remarkable theories, quantum mechanics, the physics of the very small, and Einstein's special relativity, the physics of the very fast, and is founded on very elegant ideas about symmetries. Einstein's special relativity tells us that time is another dimension like the three spatial ones and that instead of just considering the physics to be invariant when we perform a Galilean transformation on the spatial coordinates from one reference frame to another (e.g. from an axis sitting on the earth to an axis sitting on a bus moving at speed v) we should apply the relativistic transformations of the Lorentz symmetry group to the four dimensional space-time. In addition as I have already mentioned all interactions are predicted by introducing the gauge symmetry groups for the strong and electroweak forces. When considering these symmetries we can write everything in terms of classical fields, but then we insist that they appear in small lumps, or quanta, exhibiting their particle nature and consistent with quantum mechanics.

The standard model makes one of the most precisely tested predictions in all of science, that of the anomalous magnetic moment of the electron:

However it not simply a few very precise tests, which verify the SM, it has survived decades of intense testing in particle colliders around the world. The measurements made from these tests are all summarised in the huge review of particle physics by the particle data group.

The Hierarchy Problem

Despite the strong agreement with observation some theorists are not convinced that the SM is a complete theory of nature because we feel it introduces further puzzles which are left unexplained. One of these puzzles is known as the Hierarchy Problem.

The Higgs is unique amongst the fundamental particles of the standard model, not just because it is the only particle yet to be discovered, but also because it transforms trivially under the Lorentz transformations and we say such particles are Lorentz scalars. If you add a scalar to the SM one can perform calculations to show that it’s mass is quadratically sensitive to any new physics from high energies which it couples to. Since we know that at very high energies some new gravitational physics must be introduced, we expect the Higgs mass to receive quadratic contributions from this very high energy scale (called the Planck scale). However the Higgs mass is some 17 orders of magnitude smaller than this energy scale. In order for this to be the case, within the SM we assume that these contributions are canceled by a free parameter in the theory. While this is mathematically consistent, the enormous coincidence seems improbable and that is the hierarchy problem. Theoretical physicists feel that there is no imaginable explanation for this free parameter to cancel so precisely with the high energy scale (called the Planck scale).

In fact we calculate how improbable this cancellation is, with “fine-tuning measures”. If the free parameter is randomly chosen the chance of getting a Higgs boson as light as it needs to be in order for the SM to work would be a 1 in 1000000000000000000000000000000000, which is about as likely as winning the lottery 5 times in a row! Nonetheless it is important to understand what this means. I do not claim there is pure objective scientific evidence ruling the SM out, so this is not the same as stating that the chances of a model reproducing experimental observations are so small, if that were true the model would be falsified. The Standard Model fits observation very well and as such cannot be ruled out as a valid description of nature. There could be some deep fundamental reason which we have not thought of which explains why this parameter is set so close to the the Planck scale, forcing the cancellation to take place. However in our current understanding we cannot imagine how this could be as the Planck scale is totally unrelated to the parameter with which it cancels. Therefore Hierarchy Problem is an unexplained puzzle, namely how can the Higgs particle mass be much lighter than the Planck scale, the answer to which we would like to investigate.

Supersymmetry

Theorists have come up with a number of solutions. One idea I really like is to cancel these large contributions to the Higgs mass from high energies by introducing a new symmetry of nature. This is achieved by extending the space time symmetries of special relativity. It has been proven that there is only one way to extend the space-time symmetries and that is by introducing a supersymmetry which combines Lortentz space-time transformations with transformations over the internal spin quantum number. Supersymmetry (SUSY) is a then is a symmetry between fermions and bosons. Since the SM particle content does not possess this symmetry, SUSY predicts many new particles, which are the supersymmetric partners of the standard model ones. It is precisely the symmetry between the known SM particles and their SUSY counterparts that leads to cancellation of the quadratic dependence on high energy physics in the Higgs mass.













(Figure from: http://www.physics.gla.ac.uk/ppt/susy.htm)


There are many other unanswered puzzles in the SM which motivate new physics, perhaps at some point I will discuss them also but for now I simply want to point out that many of them can also be solved by introducing the new physics at energies being probed by the Large Hadron Collider, used to look for the Higgs and also have a solution in common with the Hierarchy Problem, namely SUSY.

Other ideas include unobserved extra dimensions, which bring the new physics of gravitation down to lower energies as the apparent weakness of gravitation is caused by dilution into these extra dimensions and Technicolor, where the electroweak symmetry is not broken by a fundamental scalar but by a condensate bound by some unknown, very strong force. Each of these ideas would be worthy of a blog entry on it's own (though I don't plan to do this :) ) and might solve several problems but I am showing my prejudices here (and that is sort of the point of this blog) because I find Supersymmetry the most attractive and this is the direction my research has taken.


I hope my lightning tour of the Standard Model to Supersymmetry has not left you feeling entirely like my pseudonym on here, but if it is all new to you and you still find it puzzling that is to be understood. Hopefully though this post will help you understand the references I make in later posts.