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.
