- Quote: The Higgs field gives quarks and anti-quarks their rest masses, but it doesn’t provide us with much of our own. Any ordinary object obtains the majority of its rest mass through the efforts of the strong nuclear force.
- Endnote: The Higgs field’s role in a proton’s rest mass, and thus in yours, depends on which question you ask. The standard way to interpret the question, which I’ve used here, assumes that we leave the strong nuclear force’s strength the same while we switch off the Higgs field; then the Higgs field contributes a small fraction of a proton’s mass. But in a more subtle interpretation, the Higgs field’s role can be substantially larger.
As I mentioned in the endnote, the standard way of asking about the Higgs field’s role in the masses of protons and neutrons is to imagine shutting off the Higgs field’s value, or removing it from the universe altogether, while keeping the strength of the strong nuclear force unchanged. In this case, the proton’s mass changes very little, and thus, the rest masses of atoms and of everything made from atoms remain almost as before.
However, there’s more to this story. It’s subtle, though, and to understand this subtle point is easiest if you’ve read the book to the end.
Quark Rest Masses and the Behavior of the Strong Nuclear Force
As emphasized in chapter 24.1, the size and rest mass of the proton and neutron are tied up with the way in which the strong nuclear force ceases to decrease with distance. Unlike familiar forces such as gravity and electromagnetism which die off rapidly with distance, the strong nuclear force dies off more slowly, and eventually becomes a constant. This feature of the strong nuclear force, which is what produces the trapping effect that creates protons and neutrons, arises from a feedback mechanism involving the gluon field’s interaction with itself.
But (as I omitted from the text, to avoid unnecessary clutter), there’s also an lesser impact on the feedback mechanism coming from the gluon field’s interaction with the quark fields. It’s a relatively small impact, but in the present context, it matters.
If you were to lower a quark field’s stiffness (and thus reduce the corresponding quark’s rest mass), the effect would be to slightly slow down the feedback mechanism on the strong nuclear force. The impact is that the force is slower to become constant with distance, with the result that protons and neutrons become somewhat larger, and have somewhat lower rest masses.
How the Higgs Field Affects the Strong Nuclear Force
Removing the Higgs field from the universe would reduce all six quarks’ rest masses to zero, thereby reducing the strength of the strong nuclear force slightly. The result — if we didn’t change anything else about gravity and about the Standard Model of particle physics, including the details of the strong nuclear force — would be that the distance at which the strong nuclear force becomes constant would roughly double. Correspondingly, this would reduce the rest masses of protons and neutrons by roughly half — a bit more than that, in fact.
Thus, from this perspective, if we hold everything else fixed, the Higgs field is responsible for somewhat more than half of the rest mass of a proton and neutron, and thus for more than half the rest mass of ordinary objects. It’s a rather surprising accident of nature that it is neither responsible for a tiny amount or almost all.
A Minus Sign Among Friends
I had a very amusing conversation about this — at least, it was amusing to me. Back several years ago, (perhaps 2018?), I was visiting the Kavli Institute for Theoretical Physics [KITP] at the University of California, Santa Barbara. At my lunch table was David Gross (KITP director, and winner of the 2004 Nobel prize for his 1973 work with Frank Wilczek [also awarded to David Politzer for his competing work] in understanding the strong nuclear force. Also at the table was a young Daniel Harlow, now an MIT professor. During our conversation, I took the opportunity to point out what I’ve just described above. It quickly became clear that despite four decades having passed since Gross and his colleagues had first understood the feedback mechanism that creates the proton, he had never noticed that (all other things being equal) that the Higgs field’s absence would substantially decrease the proton’s mass.
This is especially striking because the fact that the proton’s mass would decrease, rather than increase, is due to exactly the same minus sign that Gross, Wilczek and (separately) Politzer identified — the one that allows the strong nuclear force to become constant with distance, creating the proton in the first place!
I was surprised, and had a good chuckle. I certainly never expected to tell David Gross anything about the strong nuclear force that he didn’t already know!
