Lesson Video: The Higgs Boson Physics

In this video, we will learn the basic properties of the Higgs Boson and what decay modes the Higgs Boson has.

12:35

Video Transcript

In this lesson, we’re going to learn about the Higgs boson, a particle that helps fill in an important part of the standard model of particle physics. Like all particles in the standard model, we represent the Higgs boson with a particular symbol. And the particle itself has a possibly zero relative charge and a possibly zero mass. The symbol for the Higgs boson is a capital letter H with a superscript zero.

The Higgs boson is named after the physicist Peter Higgs. And that’s where the H comes from in the symbol. The superscript zero is used because like the Z weak boson and the photon, the Higgs boson has a zero charge. As for its mass, the Higgs boson is actually the second most massive particle in the standard model. At approximately 125 giga-electron volts per speed of light squared, the only particle heavier than the Higgs boson is the top quark, at about 173 giga-electron volts per speed of light squared.

These units, giga-electron volts per speed of light squared, are typical units used by particle physicists. In metric units, one giga-electron volt per speed of light squared is approximately 1.78 times 10 to the negative 27th kilograms, which is just a little bit heavier than a proton. So one Higgs boson is about as massive as 133 protons or equivalently one cesium atom.

Because as its name suggests the Higgs boson is a boson, there are no conservation rules for this particle like there are for leptons and baryons, where we have lepton number and baryon number that are conserved in particle interactions. Unlike other bosons, the Higgs is not a force mediator, like the photons are for the electromagnetic interaction or the W and Z are for the weak interaction. Rather, interactions with the Higgs boson and the associated Higgs field give rise to what’s known as the Higgs mechanism, which is thought to give particles their mass. This applies specifically to the fundamental particles of the standard model and not their composite particles, like hadrons.

The stronger a particle’s interaction with the Higgs field, the larger its mass. So quarks, for example, have masses that are orders of magnitude larger than the masses of the neutrinos because their interactions with the Higgs field are orders of magnitude stronger. Massless particles like the photon don’t interact with the Higgs field at all.

It’s worth mentioning that the Higgs mechanism is particularly important for explaining the mass of the W and Z weak bosons. This is because before the Higgs mechanism was included in the standard model, theoretical calculations predicted that the mass of the W and Z bosons would be exactly zero. But experimental results showed that they were definitely not zero. As a particle, the Higgs boson is quite short-lived, with an estimated lifetime of around 10 to the negative 22 seconds. Eventually, a Higgs boson decays, typically into a particle–antiparticle pair, like in the process of pair production.

Here are simplified diagrams of the five most common decays of the Higgs boson. In each case, we’ve cut out any intermediary mechanism to just show the Higgs boson that enters the interaction and the particle pair that leaves the interaction. In the three most common interactions, the products are a particle and its corresponding antiparticle with a charge of equal magnitude but opposite sign. Therefore, the total charge after each interaction is zero. And the Higgs boson is neutral, so the total charge before each interaction is also zero and charge is conserved. For the two less common interactions, the products are a pair of Z bosons and photons, both of which have a charge of zero. So total charge is again conserved.

Note that these are also technically particle–antiparticle pairs because both Z bosons and photons are their own antiparticles. When the products are a bottom quark and a bottom antiquark, we have to think about baryon number conservation. But since one is a quark and one is an antiquark, the total baryon number after the interaction is just zero, which matches the baryon number of the Higgs boson before the interaction.

When the products are a 𝜏 and anti-𝜏 lepton, we have to think about lepton number conservation. But here we have a lepton and an antilepton. So the total lepton number after the interaction is zero. And the lepton number of the Higgs boson is also zero.

Finally, when the products are a W plus and a W minus boson or a pair of Z bosons or a pair of photons, we don’t need to worry about any additional conservation because the number and type of bosons are not necessarily conserved in an interaction. There is one conservation rule that generally needs to be followed, which is that the relativistic mass and energy of the products must be equal to the relativistic mass and energy of the decaying Higgs boson.

Alright, let’s use some of what we’ve learned to answer some questions about the Higgs boson.

Order the following particles according to their mass from least to greatest: up quark, charm quark, top quark, Higgs boson, electron.

On this list of particles, we have three quarks, one boson, and one lepton. So let’s start by comparing similar particles, that is, quarks to quarks, and then figure out where the Higgs boson and electron fit in. Recall that in the standard model quarks come in three pairs, often called generations. The up and down quark are the first generation. The charm and strange quark are the second generation. And the top and bottom quark are the third generation.

Ordered this way, each of the quarks in a particular generation have greater mass than the quarks in the preceding generations. So the charm and strange quarks of the second generation each have a greater mass than either the up or the down quark of the first generation. And the top and bottom quarks of the third generation each have a greater mass than the charm and strange quarks of the second generation and, in turn, also a greater mass than the up and down quarks of the first generation. So of up, charm, and top, we can clearly see that top has a greater mass than charm, which has a greater mass than up.

Now we just need to figure out where the Higgs boson and the electron fall on this list. Recall that the Higgs boson is actually the second most massive particle in the standard model, second only to the top quark. So on our list, the Higgs boson should go between the charm and the top quark. As for the electron, recall that the electron has about one two thousandths of the mass of a proton, which is a hadron, a composite particle made up of up and down quarks.

Even though only about one percent of the mass of the proton is due to the mass of its constituent quarks, the proton is so much more massive than the electron that it is still clear that the electron is lighter than any of the quarks that make up the proton. Since the proton is made up of quarks from the least massive generation, it’s clear then that the electron is less massive than all of the quarks and actually belongs at the beginning of our list. So our final list is electron with the least mass, then up quark, charm quark, Higgs boson, and finally top quark with the greatest mass.

Great, let’s work through another question.

Each of the following Feynman diagrams shows how the Higgs boson can decay, apart from one. Which diagram shows a decay of the Higgs boson that is not possible?

The Higgs boson can decay in a number of different ways. So to identify the decay that is not possible, we’ll need to identify which decay violates some rule of physics. All of the possible decays of the Higgs boson follow the conservation rules. So let’s find the diagram where the products don’t follow conservation rules like charge, lepton number, and baryon number. Since each of these interactions starts with a single Higgs boson, the overall charge, lepton number, and baryon number of the products will need to be the same as the charge, lepton number, and baryon number of the Higgs boson.

Recall that we write the symbol for the Higgs boson with a superscript zero because the charge is zero. Furthermore, since the Higgs boson is a boson, not a lepton or a quark, its lepton number and baryon number are both zero. Let’s now go diagram by diagram and check that the total charge, lepton number, and baryon number of the proposed products are all zero.

In this first diagram, the proposed products are a pair of neutral Z bosons. Since these are neutral particles, their total charge is zero. And since they are bosons, their lepton number and baryon number are also zero. So a pair of Z bosons has a total charge of zero, a total lepton number of zero, and a total baryon number of zero. So in this interaction, all three quantities are conserved. Therefore, at least according to these three measures, this diagram does show a possible decay of the Higgs boson.

We have another diagram where the decay products are a pair of bosons. In this case, it’s a W plus boson with a relative charge of positive one and a W minus boson with a relative charge of negative one, where the sign of the boson corresponds to the sign of the charge. Here again, since we’re dealing with bosons, total lepton and total baryon number are zero. To find the total charge, we add the positive one charge from the W plus boson and the negative one charge from the W minus boson to get one minus one equals zero. So this diagram also shows a decay that conserves their three quantities.

Moving on to the decay into a 𝜏 and an anti-𝜏 lepton, the relative charge of the 𝜏 is negative one and the relative charge of the anti-𝜏 is positive one. So just like the W plus and W minus bosons, the total charge is zero and is conserved. The 𝜏 and anti-𝜏 are also both leptons, not baryons. So the total baryon number is simply zero. Finally, the 𝜏 contributes a lepton number of one. The anti-𝜏 contributes a lepton number of negative one. And one minus one is zero. So lepton number is still conserved. That is, 𝜏–anti-𝜏 pair has a total charge, lepton number, and baryon number of zero is not surprising. The 𝜏 and anti-𝜏 are antiparticles of each other. And for any pair of antiparticles, even if those particles are themselves composite, the charge, lepton number, and baryon number of one particle will be exactly canceled by the presence of its antiparticle.

With this in mind, we can also see without calculation that the bottom quark–antiquark pair is a possible decay of the Higgs boson, since again we have a particle and its antiparticle. So the charge, lepton number, and baryon number for the pair will be zero. If we were to do the calculation, we’d find that the negative one-third relative charge of the bottom quark is exactly canceled by the positive one-third relative charge of the bottom antiquark. Furthermore, neither of these are leptons, so the total lepton number is still zero.

Finally, the baryon number is a function of the difference between the number of quarks and the number of antiquarks. Since there’s exactly one quark and one antiquark, this difference is zero and the baryon number is zero. Thus, by calculation, we verified what we already knew from the fact that the bottom quark and the bottom antiquark are antiparticles of each other.

At this point, the only diagram left that we haven’t verified conserves charge, lepton number, and baryon number is this one. Let’s make sure that this diagram actually does violate one of these three conservation rules, since there are technically other rules we haven’t considered, like energy and momentum, that we simply don’t have enough information to apply in this question.

In this diagram, the two proposed products are a bottom quark and a charm antiquark. Neither of these is a lepton, so lepton number is conserved. And just like for the bottom quark–antiquark pair, one of these is a quark and one is an antiquark. So the baryon number is also conserved. As for relative charge, recall that the bottom quark has a relative charge of negative one-third. The charm quark has a relative charge of positive two-thirds. Since the charm antiquark is the antiparticle of the charm quark, it has a charge of negative two-thirds. However, when we add up this total charge, negative one-third plus negative two-thirds is negative one. Negative one is not zero. So this interaction doesn’t conserve total charge.

Since every possible decay of the Higgs boson must follow conservation rules, including charge, this must not be a possible decay of the Higgs boson. So the Higgs boson cannot decay into a single bottom quark and a single charm antiquark.

Finally, it’s worth noting that the Z boson is its own antiparticle and the W plus boson is the antiparticle of the W minus boson. So the qualitative argument that we developed for the 𝜏–anti-𝜏 pair that we then applied to the bottom quark–antiquark pair could’ve also been applied to these two diagrams as well.

Alright, now that we’ve seen some examples, let’s review the key points that we’ve learned in this lesson. In this lesson, we learned about one of the particles in the standard model of particle physics called the Higgs boson given the symbol capital H with a superscript zero. The Higgs boson is uncharged and has a mass comparable to that of a cesium atom, making it the second most massive particle in the standard model.

Furthermore, since this particle is indeed a boson, the number of Higgs bosons in a particular particle interaction is not a conserved quantity. Furthermore, the Higgs mechanism, which is a consequence of the existence of the Higgs boson and its associated field, is responsible for the mass of all of the fundamental particles in the standard model.

Finally, we saw that the Higgs boson being an unstable particle can decay in a number of different ways. The five most common decays produce a particle–antiparticle pair. Of these, by far the most common is a bottom quark–antiquark pair and the least common is a pair of photons which are their own antiparticles.

Finally, it’s worth mentioning that the Higgs mechanism filled a very large gap in particle physics by explaining how the W and Z bosons of the weak force can have mass, even though the photon, the boson of the electromagnetic force, is massless.

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