At a conference like LHCP12, covering all of Large Hadron Collider [LHC] physics and beyond, there’s far too much to summarize: hundreds of talks, with thousands of incremental experimental results and theoretical insights. So instead, today I’ll draw attention to one of the longest-running puzzles of the LHC era, and to a significant step that’s been made toward resolving it. The puzzle in question involves a rare decay of bottom quarks.
[All figures in this post are taken from LHCP12 talks by Zhangqier Wang and Eluned Smith.]
The 12th Large Hadron Collider Physics conference is taking place this week in Boston, and for the first time in a several years, I’ll be able to attend in person. I’ll post about it all week.
As part of the conference activities, I will be participating in a public event Thursday night at the Boston Public Library, a panel discussion entitled “Where the Universe and Humanity Collide.” The other panelists are Yale Professor Sarah Demers, a member of the ATLAS experiment at the Large Hadron Collider, and Dr. Katrina Miller, a particle physicis and a writer and essayist for the New York Times and other publications. We’ll be discussing the future of particle physics, talking about how we got into the field, and answering whatever questions the audience might have for us. If you’re in Boston, please consider attending!
At the core of every atom lies its nucleus, where protons and neutrons are found. As their names suggest, these two subatomic particles are profoundly different.
Protons carry positive electric charge, and can attract negatively-charged electrons, making atoms possible.
Neutrons have no electric charge and are thus electrically neutral, hence their name; they have no impact on the electrons in atoms.
The distinctions extend to their magnetic effects. Both protons and neutrons have a “magnetic moment,” meaning that in a magnetic field, they will point like compasses. But neutrons point in the opposite direction from protons, and less agressively.
Nevertheless, the proton and neutron have almost identical masses, differing by less than two tenths of a percent! If we ignored their electric and magnetic effects, they’d almost be twins. Why are they so different in some ways and so similar in others? What does it reflect about nature?
One thing I emphasized is that while photons [“particles” of light] moving across empty space are always traveling waves moving at the speed of light c, electrons are different. When in motion they too are traveling waves, but unlike photons, they can slow down, and even be stationary. When stationary, they are standing waves, of a somewhat unfamiliar sort (as described here and here). All of this is discussed in detail in the book’s chapters 16 and 17.
Whiteson has sent me a couple of questions that listeners raised with him, and since I imagine some of you might have similar questions, I decided to answer them publicly here.
For forty years, the Canadian Broadcast Company (CBC) has had a famous science radio show called “Quirks and Quarks“; it is currently hosted by science journalist Bob McDonald. I’m pleased to tell you that I was invited onto that show this past week. In my conversation with McDonald, I explained how the Higgs field actually works, avoiding the “molasses”/”snow”/”crowd” analogies that don’t stand up to scrutiny.
(This all happened while I was spending a few days in Ontario. I was meeting all sorts of wonderful people at the Perimeter Institute’s 2024 science communicators conference SciComm Collider 2, organized by Katie Mack. More on that at a later time.)
If you’d like to hear the Quirks and Quarks conversation, or one of the other detailed podcast conversations I’ve had about my book, you can find them here:
From the structure of the Standard Model of particle physics, one might wonder if the electron, muon and tau, so similar except for their masses, might really be the same object seen in three different guises. Last week, starting with a post for general readers, and then looking at the situation in more detail (Part 1 of this two-part series), I showed one way in which this idea fails to agree with experiment. Today I’ll give you another point of failure, focused on a property of particles known as “spin”.
Spin: The Idea In Brief
What is “spin” in physics? It’s related to the word “spin” in English, but with some adjustment. I’ll write a longer article about spin elsewhere, but here’s a brief introduction.
The Earth “spins”, both in the English sense and in the physics sense: it rotates. The same is true of a tennis ball. The rotation can be changed when the ball interacts with a tennis racket or with the ground. It can also be changed when it interacts with another tennis ball. In fact, if two balls strike each other, some of the spin of one ball can be transferred to the other, as in Fig. 1.
Figure 1: (Left) Two balls, the upper one spinning, approach and collide; (Right) The balls recoil from the collision, with some of the spin of the upper ball now transferred to the lower ball.
Elementary “particles” can have spin too, which can be (in part) changed by or transferred to other objects that they interact with. But this type of spin is somewhat different from ordinary rotation.
For example, an electron “spins”. Always. An interaction can change the direction of an electron’s spin, but it cannot change its overall amount. I’ll tell you what I mean by “amount” in a moment, but the quantity of the amount is a famous number:
h / 4π = ℏ / 2
where h, Planck’s constant, shows up whenever quantum physics matters. This amount of spin is tiny; if a tennis ball had this amount of spin, it wouldn’t have even rotated once since the universe was born. But for an electron, it’s quite a lot.
Usually, as shorthand, one takes the ℏ to be implicit, and just says that “the electron has spin 1/2”. I’ll do that in what follows.
How can we visualize this spinning? It’s not easy. It’s best not to visualize an electron as a small rotating ball; it’s the wrong picture. Quantum field theory, the modern theory of “particles”, gives a different picture. Just as we should think of light as a wave made of wave-like photons, we should think of the electron as a wave — specifically, a wave in the electron field. [This wave is not to be confused with a wave function, which is something else]. A wave in the electron field can rotate in ways that a little ball cannot. This, however, is hard to draw, and in any case is a story for another day.
The important point is that the spin of an elementary “particle” is not like the simple rotational spinning of a tennis ball, even though it is in the same category. An electron has spin intrinsically, by its very nature; there is no electron without its spin, just as there is no electron without its internal energy and rest mass (as emphasized in my recent book, Chapter 17). That’s certainly not true for a tennis ball, which can have any spin, including none.
These details won’t matter much in what follows, though, so let’s step away from these subtleties and move on.
Ways to Spin
So far, I’ve suggested two types of spinning:
the intrinsic spinning (or “intrinsic angular momentum”) of elementary particles
the ordinary spinning (or “ordinary angular momentum”) of objects that are rotating, or are in orbit around other objects.
Both contribute to the surprising way that physicists use the word “spin”.
Suppose we have an object that is made of multiple elementary particles. Its total angular momentum involves combining the intrinsic angular momentum of its elementary particles with the ordinary angular momentum that the particles may have as they move around each other. Physicists now do something unexpected: they refer to the object’s total angular momentum as its spin. They do this even though the object is not elementary, meaning that its spin may potentially combine both intrinsic spinning and ordinary spinning of the objects inside it.
So the real meaning of spin, as particle physicists use the term, is this: it is the total angular momentum of an isolated object — an object that may be elementary, or that may itself be formed from multiple elementary objects. That means that the spin of an object like an atom, made of electrons, protons and neutrons, or of a proton, made of quarks, antiquarks and gluons, may potentially arise from multiple sources.
Atoms, Protons and Strings
For example, let’s take a hydrogen atom, made from an electron and a proton. (For starters we’ll treat both of these subatomic particles as though they were elementary. We’ll return to their possible internal structure later.)
I’ll refer in the following to four atomic states, illustrated below in Fig. 2.
The ground state of a hydrogen atom (known as the “1s state”) has spin 0. Nevertheless, it is made of an electron with spin 1/2 surrounding a proton of spin 1/2. The two spin in opposite directions so that their angular momentum cancels.
There is a very slightly excited state, often neglected in first-year physics courses or in quick summaries of atomic physics, where the electron and proton spin in the same direction, and their spins add instead of cancelling. This state of the atom has spin 1; I’ll call it the “spin-flipped 1s state”. (The transition from this excited state to the ground state involves the emission of a radio wave photon with a wavelength of 21 cm, leading to the so-called “21 cm line” widely observed in astronomy. )
There are more dramatically excited states known as the “2s and 2p states”. The 2s state has spin 0, while the 2p state has spin 1. But even though the 2p state and the spin-flipped state both have spin 1, their spins have different origins. The total angular momentum of the 2p state does not come from the intrinsic angular momenta of the electron and proton; those cancel out, just as they do in the 1s and 2s states. Instead, the spin of the 2p state comes from a sort of rotational motion of the electron around the proton.
These four states are sketched in Figure 2. (Spin-flipped versions of the 2s and 2p states exist but are not shown.)
Figure 2: (Bottom left) In the ground state of hydrogen, the spin of the proton (central red dot) is opposite to that of the electron (surrounding blue cloud), so that the atom has spin 0. (Bottom right) If the electron spin is flipped, both the proton and electron spin in the same sense, giving the atom spin 1. (Top) While the 2s state is similar to the 1s state, the 2p state has the electron and proton spinning in opposite directions but has the electron moving around the proton (dashed black line), giving the atom spin 1.
The fact that the ground state has spin 0, and yet the 2p state has larger spin specifically due to the electron’s motion around the proton, illustrates the main point of this post. If an object is made from multiple constituent objects, nothing can prevent those constituents from moving around one another. That means they can have ordinary (or “orbital”) angular momentum, which then contributes, along with the constituents’ spin, to the combined object’s spin — i.e., to its total angular momentum.
Therefore, an object that is not elementary, and so contains multiple objects inside it, will inevitably have excited states with different amounts of spin. Indeed, the hydrogen atom has excited states of total angular momentum 0, 1, 2, 3, and so on. All atoms exhibit similar behavior.
The same applies for protons, which aren’t elementary either. The proton has spin 1/2, but its excited states have spin 1/2, 3/2, 5/2, 7/2, and so on. The first excited state of the proton, the Delta, has spin 3/2. This is most easily understood as a rearrangement of the spins of the quarks, gluons and anti-quarks that it contains (though the exact rearrangement is not obvious, due to the complexity of a proton; see also chapter 6 of the book.) The next excited state, the p(1440), has spin 1/2 like the proton. But many other excited states have been observed, with spin 3/2, 5/2, 7/2, 9/2, and perhaps even 11/2.
A string, such as one finds in string theory, is another object with internal constituents, which one might call bits-of-string. A string can always be spun faster. That’s why, in the superstring theory that is sometimes touted as a potential “theory-of-everything” (or in less grandiose language, a complete theory of space, fields and particles), there are states of all possible spin — any integer times 1/2. Unfortunately, were this really the theory of our universe, the higher-spin states of the string would probably have far too much mass for us to make them in near-term experiments, putting this prediction of the theory out of reach for now.
But string theory isn’t just useful in this rarified context. It can also be used to describe the physics of “hadrons” — objects made from quarks and gluons, including protons. All indications from experiments and numerical calculations do indeed suggest that hadrons come in all possible spins; this includes the excited states of the proton already mentioned above. (That said, the higher the spin, the harder it is to make the states, making it more and more challenging to observe them.)
Spin and the Electron, Muon and Tau
None of this is true for electrons, muons or taus, all of which have spin 1/2. No electron-like particle with spin 3/2 has ever been observed.
This argues strongly against the electron, muon and tau all being made from the same object. Atoms, protons and strings all have excited states with the same spin as the ground state, but at roughly the same mass, they also have excited states with more spin. If the muon were an excited state of the electron, we would expect to see an object with spin 3/2 that has a mass comparable to the muon, and certainly below the mass of the tau. Such a state would easily have been observed decades ago, so it doesn’t exist.
Are there loopholes to this logic? Yes. It is possible, in special circumstances, for the excited states with higher spin to have much larger masses than the excited states which share the same spin as the ground state. This is a long story which I won’t try to tell here, but examples arises in the context of extra dimensions, and others in the related context of exotic theories of quark-like and gluon-like objects (with buzzwords such as “AdS/CFT” or “gauge/string duality”).
However, it’s hard to apply the loophole to the muon and tau. In such a scenario, the electron should have many more cousins than just two, and some of the others should have observed by now.
Furthermore, data now confirms that both the tau and muon get their rest mass from the Higgs field; see Fig. 3. For such particles, the loopholes I just mentioned don’t apply.
Figure 3: The interaction strengths of various types of elementary particles with the Higgs field, plotted versus those particles’ rest masses. Any particle whose rest mass comes entirely or largely from the Higgs field should lie on or near the dashed line. The data shows this is true of both the tau τ and the muon μ, as well as of the bottom and top quarks b, t, and of the W and Z bosons.
We must also recall the arguments given in the first part of this series. If muons and taus are excited states of electrons, it should be possible for any sufficiently energetic collision to turn an electron into a muon or tau, and for decays via photons to do the reverse. But these processes are not observed.
In short, the properties of the electron, muon and tau disfavor the idea that they are somehow secretly the same object in three different quantum states. The explanation of their similarities must lie elsewhere.
