W boson mass too high? Charm quarks in the proton? There’s a (worrisome) link.

Two of the most widely reported stories of the year in particle physics,

both depend crucially on our understanding of the fine details of the proton, as established to high precision by the NNPDF collaboration itself.  This large group of first-rate scientists starts with lots of data, collected over many years and in many experiments, which can give insight into the proton’s contents. Then, with a careful statistical analysis, they try to extract from the data a precision picture of the proton’s internal makeup (encoded in what is known as “Parton Distribution Functions” — that’s the PDF in NNPDF).  

NNPDF are by no means the first group to do this; it’s been a scientific task for decades, and without it, data from proton colliders like the Large Hadron Collider couldn’t be interpreted.   Crucially, the NNPDF group argues they have the best and most modern methods for the job  — NN stands for “neural network”, so it has to be good, right? 😉 — and that they carry it out at higher precision than anyone has ever done  before.

But what if they’re wrong? Or at least, what if the uncertainties on their picture of the proton are larger than they say?  If the uncertainties were double what NNPDF believes they are, then the claim of excess charm quark/anti-quark pairs in the proton — just barely above detection at 3 standard deviations — would be nullified, at least for now.  And even the claim of the W boson mass being different from the theoretical prediction,  which was argued to be a 7 standard deviation detection, far above “discovery” level, is in some question. In that mass measurement, the largest single source of systematic uncertainty is from the parton distribution functions.  A mere doubling of this uncertainty would reduce the discrepancy to 5 standard deviations, still quite large.  But given the thorny difficulty of the W mass measurement, any backing off from the result would certainly make people more nervous about it… and they are already nervous as it stands. (Some related discussion of these worries appeared in print here, with an additional concern here.)

In short, a great deal, both current and future, rides on whether the NNPDF group’s uncertainties are as small as they think they are.  How confident can we be?

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A Week On Topic at Fermilab

The blog’s been quiet recently, thanks to a series of unfortunate events, not the least of which were my first (known) Covid-19 infection and an ongoing struggle with a bureaucracy within the government of Massachusetts. But meanwhile there is some good news: it seems I will someday have a book published. More on that another time.

Meanwhile I have also been doing some science. Recent efforts included presenting at a workshop on the potential capabilities of the Future Circular Collider [FCC], a possible successor to the Large Hadron Collider [LHC]. Honestly, my own feeling is that the FCC is an unfortunate distraction from important LHC activities. For my part I remain focused on the latter, and on trying to remind everyone just how much remains to do with the LHC data sets from previous years.

Visiting the LPC at Fermilab

Toward that end, I’ll be at the Fermilab National Accelerator this week, near Chicago. I’ll be visiting their LHC Physics Center [LPC], which is the major US hub for the CMS experiment at the LHC. (CMS is one of the LHC’s two general purpose experiments, the other being ATLAS; these are the experiments that discovered the Higgs particle.)

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Protons and Charm Quarks: A Lesson From Virtual Particles

There’s been a lot of chatter lately about a claim that charm quarks are found in protons. While the evidence for this claim of “intrinsic charm” (a name that goes back decades) is by no means entirely convincing yet, it might in fact be true… sort of. But the whole idea sounds very confusing. A charm quark has a larger mass than a proton: about 1.2 GeV/c2 vs. 0.938 GeV/c2. On the face of it, suggesting there are charm quarks in protons sounds as crazy as suggesting that a football could have a lead brick inside it without you noticing any difference.

What’s really going on? It’s a long story, and subtle even for experts, so it’s not surprising that most articles about it for lay readers haven’t been entirely clear. At some point I’ll write a comprehensive explanation, but that will require a longer post (or series of posts), and I don’t want to launch into that until my conceptual understanding of important details is complete.

Feynman diagram suggesting a photon is sometimes an electron-positron pair.

But in the meantime, here’s a related question: how can a particle with zero mass (zero rest mass, to be precise) spend part of its time as a combination of objects that have positive mass? For instance, a photon [a particle of light, including both visible and invisible forms of light] has zero rest mass. [Note, however, that it has non-zero gravitational mass]. Meanwhile electrons and positrons [the anti-particles of electrons] both have positive rest mass. So what do people mean when they say “A photon can be an electron-positron pair part of the time”? This statement comes with a fancy “Feynman diagram”, in which the photon is shown as the wavy line, time is running left to right, and the loop represents an electron and a positron created from the photon.

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Relatively Confused: Is It True That Nothing Can Exceed Light Speed?

A post for general readers:

Einstein’s relativity. Everybody’s heard of it, many have read about it, a few have learned some of it.  Journalists love to write about it.  It’s part of our culture; it’s always in the air, and has been for over a century.

Most of what’s in the air, though, is in the form of sound bites, partly true but often misleading.  Since Einstein’s view of relativity (even more than Galileo’s earlier one) is inherently confusing, the sound bites turn a maze into a muddled morass.

For example, take the famous quip: “Nothing can go faster than the speed of light.”  (The speed of light is denoted “c“, and is better described as the “cosmic speed limit”.) This quip is true, and it is false, because the word “nothing” is ambiguous, and so is the phrase “go faster”. 

What essential truth lies behind this sound bite?

Faster Than Light? An Example.

Let’s first see how it can lead us astray.

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The Standard Model More Deeply: Lessons on the Strong Nuclear Force from Quark Electric Charges

For readers who want to go a bit deeper into details (though I suggest you read last week’s posts for general readers first [post 1, post 2]):

Last week, using just addition and subtraction of fractions, we saw that the ratio of production rates

  • R = Rate (e+ e ⟶ quark anti-quark) / Rate (e+ e ⟶ muon anti-muon)

(where e stands for “electron” and e+ for “positron”) can be used to verify the electric charges of the quarks of nature. [In this post I’ll usually drop the word “electric” from “electric charge”.] Specifically, the ratio R, at different energies, is both sensitive to and consistent with the Standard Model of particle physics, not only confirming the quarks’ charges but also the fact that they come in three “colors”. (About colors, you can read recent posts here, here and here.)

To keep the previous posts short, I didn’t give evidence that the data agrees only with the Standard Model; I’ll start today by doing that. But I did point out that the data doesn’t quite match the simple prediction. You can see that in the figure below, repeated from last time; it shows the data (black dots) lies close to the predictions (the solid lines) but generally lies a few percent above them. Why is this? The answer: we neglected a small but noticeable effect from the strong nuclear force. Not only does accounting for this effect fix the problem, it allows us to get a rough measure of the strength of the strong nuclear force. From these considerations we can learn several immensely important facts about nature, as we’ll see today and in the next post.

Figure 1: Data (black dots) showing R as a function of the collision energy 2Ee. Horizontal colored lines show the three predictions for R in the regions where the data is simple and 3, 4 or 5 of the quarks are produced. The minor jumpiness in the data is due to measurement imperfections.

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Celebrating the Standard Model: Checking The Electric Charges of Quarks

A post for general readers who’ve heard of quarks; if you haven’t, you might find this article useful:

Yesterday I showed you that the usual argument that determines the electric charges of the various types of quarks uses circular reasoning and has a big loophole in it. (The up quark, for example, has charge 2/3, but the usual argument would actually allow it to have any charge!) But today I’m going to show you how this loophole can easily be closed — and we’ll need only addition, subtraction and fractions to close it.

Throughout this post I’ll shorten “electric charge” to just “charge”.

A Different Way to Check Quark Charges

Our approach will be to study the process in which an electron and a positron (the electron’s anti-particle) collide, disappear (“annihilate”), and are converted into one or another type of quark and the corresponding anti-quark; see Figure 1. The rate for this process to occur, and the rate of a similar one in which a muon and anti-muon are produced, are all we will need to know.

In an electron-positron collision, many things may happen. Among the possibilities, the electron and positron may be converted into two new particles. The new particles may have much more mass (specifically, rest mass) than the electron and positron do, if the collision is energetic enough. This is why physicists can use collisions of particles with small mass to discover unknown particles with large mass.

Figure 1: (Top) an electron and positron, each carrying energy Ee, collide head-on. (Bottom) from the collision with total energy 2Ee , a quark and anti-quark may emerge, as long as Ee is bigger than the quark’s rest mass M times c2.

In particular, for any quark of mass M, it is possible for an electron-positron collision to produce that quark and a corresponding anti-quark as long as the electron’s energy Ee is greater than the quark’s mass-energy Mc2. As Ee is gradually increased from low values, more and more types of quark/anti-quark pairs can be produced.

This turns out to be a particularly interesting observation in the range where 1 GeV < Ee < 10 GeV, i.e. when the total collision energy (2 Ee) is between 2 and 20 GeV. If Ee is any lower, the effects of the strong nuclear force make the production of quarks extremely complicated (as we’ll see in another post). But when the collision energy is above 2 GeV, things start to settle down, and become both simple and interesting.

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Celebrating the Standard Model: The Electric Charges of Quarks

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?

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The Standard Model More Deeply: Gluons and the Math of Quark “Color”

For readers who want to dig deeper; this is the second post of two, so you should read the previous one if you haven’t already. (Readers who would rather avoid the math may prefer this post.)

In a recent post I described, for the general reader and without using anything more than elementary fractions, how we know that each type of quark comes in three “colors” — a name which refers not to something that you can see by eye, but rather to the three “versions” of strong nuclear charge. In the post previous to today’s, I went into more detail about how the math of “color” works; you’ll need to read that post first, and since I will sometimes refer to its figures, you may want to keep in handy in another tab.

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