The Standard Model: What is it, how does it look, and how does it taste?

Hi All,

Today’s post is an introduction to the Standard Model of Particle Physics. First off, saying “Standard Model of Particle Physics” is long-winded, so it is often shortened to “Standard Model” or abbreviated by “SM”. In short, the SM is presently the best description of how matter behaves, interacts, and works at very small distances and very high energies. High and small, of course, compared to our everyday experiences.

Elementary: In the SM is a collection of particles believed to be the elementary building blocks/constituents of all known matter and energy. By “elementary”, I mean that there are no smaller pieces inside these objects. To put this into perspective, humans (~2 meters) are made of cells (~10 μm); cells are made of molecules (~1 nm), or chains of atoms. Atoms (~100 pm = 1 angstrom) are made of electrons (?) that orbit a central nucleus (1~10 fm). A nucleus is comprised of protons (1 fm) and neutrons (1 fm). Both of these are made of quarks (?) and gluons (?). However, as far as experiments have shown, SM particles are not made of smaller objects. Therefore, we call call them “elementary”, “fundamental”, and “point-like.” If there comes a day where we discover that quarks have sub-structure, then quarks will lose their “elementary” status.

Spin: Elementary particles are separated into three categories: matter, force carriers, and Higgs bosons (or fermions, gauge bosons, and the Higgs bosons). Fermions and gauge bosons have small but nonzero, intrinsic angular momentum, called spin. Angular momentum is a measure of how energetically and how quickly an object is rotating. Think of a bike wheel that never stops spinning and has only two speed: fast and half-fast. A standard unit of angular momentum at small distances is an ћ (pronounced: “h-bar”). This is like a mile or kilometer being a standard unit of distance, or a day being that for time. All gauge bosons carry the same amount of spin, 1ћ; all elementary fermions carry half as much spin, ћ/2. Particles that carry no spin are called scalars. More broadly, a boson is any particle with an integer amount of spin, i.e., 1 ћ, 2 ћ, 3 ћ, …, and a fermion is any particle with half-integer spin, i.e., ћ/2, 3 ћ/2, 5 ћ/2, … Spin is an example of a spacetime quantum number. Even sets of fermions make a composite boson; odd sets of fermions make composite fermions, like the proton.



Charge: There are 12 elementary fermions: the up (u), down (d), charm (c), strange (s), top (t), and bottom (b) quarks; the electron (e), muon (μ), and tau (τ) charged leptons; and the electron-neutrino (νe), muon-neutrino (νμ), and tau-neutrino (ντ) leptons. These labels/names represent another quantum number called flavor. In addition to spin, these particles also carry several different charges that cause them to be repelled or attracted when in proximity to each other, in other words to experience a force. There is the electric (or electromagnetic) charge, weak hyper charge, weak isospin charge, and strong (or color) charge. Quarks carry all charges; charged leptons carry all charges except for color; and neutrinos carry only weak charges. In fact, electric charge is a combination of hyper and isospin charges. Charges are examples of internal quantum numbers. In addition, each particle has a partner particle called an antiparticle. Particles and antiparticles have the same spacetime quantum numbers but opposite internal quantum numbers. For example: an electron is a spin-1/2 fermion with -1 electric charge; a positron (an antielectron) is a spin-1/2 fermion with +1 electric charge.

Forces: Gauge bosons are the mediators of the electromagnetic, weak, and color forces, and each force is associated with a conservation law. Fermions interact, exchange momentum, and scatter off each other by exchanging gauge bosons. For example, an electron and positron can interact by exchanging a photon. Throughout this whole process, the electric charges of the electron and positron were individually conserved.

The photon (γ) is the gauge boson for electromagnetism, and the rules of electromagnetism at small distances and high energies are called quantum electrodynamics, or QED.The gluon (g) is the gauge boson for the strong force, and its rules are called quantum chromodynamics (QCD). The strong force is responsible for holding the proton together: protons and neutrons are made up quarks that are bound together by gluons. Weak forces are responsible for certain types of radioactive decay and flavor-changing interactions. For example: an electron can radiate a W boson and become an electron-neutrino, and a top quark dominantly decays into a bottom quark and a W boson. The gauge bosons of weak isospin are the W1, W2, and W3 bosons; for weak hypercharge, this is the B boson. However, at low energies, weak charges are no longer conserved. What is conserved is the sum of isospin and hypercharge. The Ws, B, and three Higgs bosons (more on this in a bit) then combine, becoming the W+, W-, and Z bosons, collectively call the weak bosons. These are very massive particles, about 80 and 90 times more massive than the proton.

Higgs Bosons: In the SM, there are four Higgs bosons: H (sometimes call the Higgs boson), φ1, φ2, and φ3. All four Higgs are scalars (zero spin) and carry both weak isospin and weak hypercharge; two carry nonzero electric charge. A summary of all particles and how they can interact are described in this image:

Any two particles connected by a line can interact. Some bosons can interact with bosons of their own type.

Mass and Electroweak Symmetry Breaking: In the early universe, all elementary fermions and gauge bosons were massless. At some point, everything underwent a phase transition that broke the hypercharge and isospin conservation laws. During this phase transition, quarks and charged leptons acquired mass. The massless hypercharge and isospin gauge bosons along with φ1, φ2, and φ3 mixed and became the massive W+, W-, and Z bosons. Because of this, the W+, W-, and Z bosons can mediate weak interactions but, under the right conditions, behave like the scalars φ1, φ2, and φ3. This phenomenon is called electroweak symmetry breaking (EWSB). After EWSB, there is one remaining physical Higgs boson, H, which was only just discovered in 2012.

To summarize:

The Standard Model of Particle physics is presently our best description of how matter behaves and interacts at very small distances and very high energies. Elementary particles are not made of any smaller particle and are divided into two categories: fermions (half-integer spin) and bosons (integer spin) Fermions make up matter (like protons and atoms), and come in 12 different varieties, or flavors. Gauge bosons mediate forces: the photon mediates electromagnetism, the gluon mediates the strong force, and the W+, W-, and Z bosons mediate the weak forces. The Higgs bosons are scalars (zero spin) and facilitate electroweak symmetry breaking. After EWSB, only one Higgs boson, H, remains. Only the photon and gluon are massless; everything else has a mass. Not everything in the SM agrees with data, but we have yet to find a better theory.

Happy Colliding

– Richard (@BraveLittleMuon)