A post for general readers who’ve heard of quarks; if you haven’t, try reading here:
The universe has six types of quarks, some of which are found in protons and neutrons, and thus throughout all ordinary material. For no good reasons, we call them up, down, strange, charm, bottom and top. Today and tomorrow I want to show you how we know their electric charges, even though we can’t measure them directly. The only math we’ll need is addition, subtraction, and fractions.
This also intersects with my most recent post in this series on the Standard Model, which explained how we know that each type of quark comes in three “colors”, or versions — each one a type of strong nuclear charge akin to electric charge.
Today we’ll review the usual lore that you can find in any book or on any website, but we’ll see that there’s a big loophole in the lore that we need to close. Tomorrow we’ll use a clever method to close that loophole and verify the lore is really true.
The Lore for Protons and Neutrons
Physicists usually define electric charge so that
- the proton has electric charge +1
- the electron has charge -1,
- the neutron has charge 0 (i.e. electrically neutral, hence its name).
[Throughout the remainder of this post, I’ll abbreviate “electric charge” as simply “charge“.]
As for the six types of quarks, the lore is that their charges are [using notation that “Qu” means “electric charge of the u quark“]:
- Up, Charm, Top (u,c,t): Qu = Qc = Qt = 2/3
- Down, Strange, Bottom (d,s,b): Qd = Qs = Qb = -1/3
But how do we know this?
Initial evidence comes from the proton and neutron. The 1960’s view of these particles, which is still often found on websites, is that a proton is made from two up quarks and a down quark (uud) and nothing else, while a neutron is the same as a proton with one up quark replaced with a down quark.
Their charges just come from the charges of the quarks they contain, added together:
- proton (uud): Qu + Qu + Qd = 2 ✕ (2/3) + (-1/3) = 4/3 – 1/3 = 1
- neutron (udd): Qu + Qd + Qd = (2/3) + 2 ✕ (-1/3) = 2/3 – 2/3 = 0
But in the 1970’s, people understood that (as I’ve explained here) really a proton’s made from
- 2 up quarks + 1 down quark + many quark-antiquark pairs + many gluons
where the first three quarks are called the “valence quarks“, and the remaining particles are called the “sea“. The sea, however, carries no charge:
- gluons are neutral, and
- in each quark/anti-quark pair the charges always cancel.
That means the proton’s charge arises just from the charge of its valence quarks, and so the algebra we did a moment ago still gives the right answer for the proton’s charge.
(Despite recent press articles, the proton does not have a charm quark inside it. It very occasionally has virtual charm quark/charm anti-quark pairs, whose net charge is zero, contributing to the sea. These quark/anti-quarks pairs must be virtual since otherwise their total mass would be much larger than the proton’s. This issue is far more subtle than I can cover here, and it’s admittedly quite difficult for science journalists to get it right. I’ll come back to this in a future post.)
The Loophole in the Lore
More generally, a “baryon” is any particle with three valence quarks and a sea of gluons and quark/anti-quark pairs. There are lots of them. For example, the Δ++ (“Delta-plus-plus”) has three valence up quarks (uuu) and so its charge is 3Qu = 2. The Ω– (“Omega-minus”) has three strange quarks (sss) and so its charge is 3Qs = -1. The Λ (“Lambda”), with (uds) valence quarks, has charge Qu + Qd + Qs = 0. And so on.
The baryon charges all work out correctly and agree with experiment — of course. That’s why what I just told you about the quark charges is the usual lore. But the reasoning is circular. We assumed we knew what was in the proton and neutron and other baryons, and checked this was consistent. But what if we were wrong? For instance, what if, in every baryon, there were not only three valence quarks and a sea but also one additional valence particle X, perhaps essential for the baryon to form, with charge QX? Then the proton is not (uud) but (uudX); the neutron is (uddX), the Ω– is (sssX), and so on.
With a little algebra you can check that whatever QX you choose, there is some choice of quark charges that still works. For instance, suppose QX=-1; then if you take Qu = +1 and Qd = Qs = 0, you get
- proton (uudX) : 2Qu + Qd + QX = 2 ✕ 1 + 0 + (-1) = 1
- Ω– (sssX): 3Qs + QX = 3 ✕ 0 + (-1) = -1
which are correct. If instead you take QX = +1, then you need Qu = +1/3 and Qd = Qs = -2/3
- proton (uudX) : 2Qu + Qd + QX= 2 ✕ (1/3) + (-2/3) + 1 = 2/3 – 2/3 + 1 = 1
- Ω– (sssX): 3Qs + QX = 3 ✕ (-2/3) + 1 = -2 + 1 = -1
And so on for all the baryons. It always works as long as you take take Qu = (2+QX)/3 and Qd = Qs = Qu-1.
More generally, you can get all the baryon charges right by taking any Qu you like and demanding
- Up, Charm, Top (u,c,t): Qu = Qc = Qt
- Down, Strange, Bottom (d,s,b): Qd = Qs = Qb = Qu – 1
as long as you allow for the possibility of additional particles like X that are common to all baryons. (It must always be that Qd = Qu-1, because the replacement of one u quark with a d quark turns a proton of charge 1 to a neutron of charge 0. Similarly a neutron (udd) has the same charge as a Lambda (uds), so Qd must equal Qs. The presence of additional particles such as X can’t change these fundamental facts.)
How, then, can we exclude the possibility of additional charged valence particles such as the X? I’ll show you tomorrow how we can measure the quark charges. Along the way we will also double-check that each type of quark comes in three “colors” [i..e. versions of strong nuclear charge.] Stay tuned!