Of Particular Significance

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

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 11/04/2022

Two of the most widely reported stories of the year in particle physics, (1) the claim by the CDF experiment that the W boson mass is higher than predicted in the Standard Model, and (2) the claim by a group of theorists known as the "NNPDF collaboration" that there are unexpectedly many charm quark/anti-quark pairs in the proton, both depend crucially on NNPDF's understanding of the fine details of the proton. But what if they're wrong?

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?

The problem is that there are very few people who have the technical expertise to check whether NNPDF’s analysis is correct, and the numbers are shrinking.  NNPDF is a well-funded European group of more than a dozen people.  But in the United States, the efforts to study the proton’s details are poorly funded, and smaller than ever.  I don’t agree with Sabine Hossenfelder’s bludgeoning of high-energy physics, much of which seems to arise from a conflation of real problems with imaginary ones — but she’s not wrong when she argues that basic science is under-funded compared to more fancy-sounding stuff.  After all, the US has spent a billionish dollars helping to build and run a proton collider.  How is it that we can’t spend a couple of million per year to properly support the US-based PDF experts, so that they can help us make full use of this collider’s treasure trove of data? Where are our priorities?

A US-based group which calls itself CTEQ-TEA, which has been around for decades and was long a leader in the field, is disputing NNPDF’s uncertainties, and suggesting they are closer to the uncertainties that CTEQ-TEA itself finds in its own PDFs.  (Essentially, if I understand correctly, they are suggesting that NNPDF’s methods fail to account for all possible functional forms [i.e. shapes] of the parton distribution functions, and that this leads the NNPDF group to conclude they know more than they actually do.)  I’m in no position, currently, to evaluate this claim; it’s statistically subtle.  Nor have I spoken to any NNPDF experts yet to understand their counter-arguments.  And of course the CTEQ-TEA group is inevitably at risk of seeming self-serving, since their PDFs have larger uncertainties than those obtained by NNPDF.  

But frankly, it doesn’t matter what NNPDF says or how good their arguments are.   With such basic questions about nature riding on their uncertainties, we need a second and ideally a third group that has the personnel to carry out a similar analysis, with different assumptions, to see if they all come to the same conclusion.  We cannot abide a situation where we depend on one and only one group of scientists to tell us how the proton works at the most precise level; we cannot simply assume that they did it right, no matter how careful their arguments might seem.  Mistakes at the forefront of science happen all the time; the forefront is a difficult place, which is why we revere those who achieve something there.  We cannot have claims of major discoveries (or lack thereof!) reliant on a single group of people.  And so — we need funding for other groups.  Otherwise it will be a very long time before we know whether or not the W boson’s mass is actually above the Standard Model prediction, or whether there really are charm quark/anti-quark pairs playing a role in the proton… and meanwhile we won’t be able to answer other questions that depend on precision measurements, such as whether the properties of the Higgs boson exactly agree with the Standard Model.

Prizes worth millions of dollars a year, funded by the ultra-wealthy, are given to famous theoretical physicists whose best work is already in the past. At many well-known universities, the string theory and formal quantum field theory efforts are well-funded, thanks in part to gifts from very rich people.  That’s great and all, but progress in science depends not only on the fancy-sounding stuff that makes the headlines, but also on the hard, basic work that makes the headline-generating results possible.  Somebody needs to be funding those foundational efforts, or we’ll end up with huge piles of experimental data that we can’t interpret, and huge piles of theory papers that sound exciting but whose relation to nature can’t be established.

I doubt this message will get through to anyone important who can do something about it — it’s a message I’ve been trying to deliver for over 20 years — but in an ideal world I’d like it to be heard by to two groups of people: (1) the funders of particle physics at the National Science Foundation and the Department of Energy, who ought to fund string theory/supersymmetry a little less and proton fundamentals a little more; and (2) Elon Musk, Mark Zuckerberg, Jeff Bezos, Yuri Milner, and other gazillionaires who could solve this problem with a flick of their fingers. 

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59 Responses

  1. Hello, again, this may sound silly but hey I’m retired.

    Is scattering a function of the index of refraction?

    Is there enough “space” in the atom to exhibit (I don’t know if that’s the right word) refraction and reflection?


    1. Dear Matt. I like this discussion because it will give results. Yes, neutron is not an elementary particle. It is a composition of proton and ekectron that are stable. When placed in nucleous neutron is stable. Insteed of neutron we should tking about proton and electron. This means nucleous is composed our of protons and ekectrons that are stable and so nucleous in generally is stable. Proton is a vortex of superfluid space and has no elements. In CERN photons are smashed abd we have a firework. All this lines does not mean much. The fact is that when proton is smashed it turns immediatelly back into the energy of superfluid space. in CERN they make a big fuss about thease lines claiming that they discover particles that are existing in tge universe on theit own. This is a big missunerstanding.
      Yours amrit

      1. In this bizarre theory (wildly inconsistent with data on electron-deuterium scattering), I have a general question: if the neutron is made of a proton and an electron (both of them fermions), why is it a fermion (in this theory?)

          1. Hah! Thank you for this delightful, charming, and wonderfully entertaining answer. This will be a great source of enlightenment and merriment for a long time to come. I’m sure, now, that your theory is correct, and I will gladly associated your name with it.

                1. Dear Matt, I developed bijective research methodology, where every element in the model must be observed and measured. Without inventions out of the blue. Sure, there is no need I waste your time, and You waste my time. Yours Amrit

  2. Fluctuations do *not* imply observable time-dependence in quantum physics unless you make a measurement (Quantum decoherence?), which by construction leads to time-dependence..

    So we agree, time-dependence (Historicism?) arises whenever a state is considered that is not an energy eigenstate (conservation of energy?). But a neutron is *not* an energy eigenstate (so Protons and neutrons have approximately the same mass) of the full Hamiltonian. An electron, by contrast, is an eigenstate (so The positive charge on a proton is equal in magnitude to the negative charge on an electron?). A proton may or may not be, but it if it isn’t, the time dependence is extremely slow (only represent the #momentum of the mass parameter?), since the proton lives at least 10^{34} years (because the mass parameter is Nonradiative or non-fluctuate?).

    “fluctuations” in a proton”: How de-excitation of the first excited state of hydrogen works when it emits a photon, or about how positronium annihilation works (we live in a Holographic and Thermodynamic Universe, lambda CDM, w = -1[3,4], ‘w’ to vary with time ?).

  3. I have an unrelated and very diffuse thought. In one of the references (“with an additional concern here”) in your
    original post appears the phrase “data-driven techniques”. These involve heavy quarks. The same techniques involving heavy hadrons are in the recent “ultra precise” muon results that excited the same quibbles.
    Is there some technical correlation (as opposed to the general feeling of concern I have)? (E.g. the same error would push each away from the previous concensus?)

  4. Dear Matt, final question on the subject of quarks existence. You say that down quark and upper quark have a stable lifetime. But both of them are decaying. How it is possible, that a particle that has stable lifetime is decaying? This puzzle I think is not solvable. Do you have a different view?

    1. Let’s start with the following question. Why is it that a neutron on its own is unstable, but a neutron in helium is stable (for far longer than the age of the universe)? Why is it that a proton on its own is stable (for far longer than the age of the universe), but a proton in oxygen-14 is unstable?

      The answer is that the stability of a neutron or proton depends on context. A proton on its own is stable, while a neutron on its own is unstable; but in the presence of other protons and neutrons, the stability and the lifetime can change. (Look at all the different lifetimes of neutrons and protons inside oxygen nuclei, https://en.wikipedia.org/wiki/Isotopes_of_oxygen.)

      The same is true of all particles. Even more for an up quark and a down quark, ***which are never on their own***. The point? The lifetime of up and down quarks is not even defined. Their lifetimes depend on what particles they are inside.

      For instance, inside a neutron, a down quark’s lifetime is 15 minutes, while inside a proton a down quark’s lifetime is far longer than the age of the universe.

      1. Dear Prof.
        Matt, after 35 years of physics, it is the first time I read that proton is unstable. Please send us reference. Neutron is not stable because neutron is not an “elementary particle”, it is made out of “elementary particles”.

        1. (A) I did not say the proton is unstable. (B) The proton’s life is not known to be infinite. It is known only to be ***at least*** 10^33 years or so, far longer than the lifetime of the universe. (C) Searches for proton decay have been going on for more than 35 years; are you sure you’ve been doing physics for 35 years? For instance, https://arxiv.org/abs/0903.0676 . (D) Your understanding of why particles are or not stable is wrong. The proton is not an elementary particle, but it is (so far) stable. The muon is an elementary particle, but it is not stable. Being elementary or not has nothing whatsoever to do with being stable or not.

          1. Dear Matt,
            Proton is an elementary particle and has no elements. Proton is stable. Quarks are artificially made in cyclotrons and dissolve immediately back into superfluid space – ether. Quarks have no existence in the universe. Proton is a vortex of superfluid space. See work of Dr. Sbitnev [unscientific link removed by editor]

            1. Ah, I see — I thought you wanted to understand *science*. But no, you’re just wasting my time. You are welcome to join Dr. Sbitnev in a universe that doesn’t exist, but data going back to 1957 shows he’s completely wrong, and if you don’t understand that after 35 years, you won’t understand it in year 36 either. Good luck to you… all further posts here will be deleted.

                1. John, particle physics is kind of “magic” I do not understand. Unstable particles, that are decaying, are building proton. I do not get this irrationality, and I’m happy. This is not for me.

                2. You yourself are made from atoms, whose nuclei mostly contain neutrons. And yet neutrons are unstable, lasting 15 minutes on their own. How is this “magic” possible, whereby all ordinary material is made of objects that don’t even last an hour? Clearly there is no hope for you to understand quarks if you do not understand nuclei.

                3. It isn’t magic, Amrit. Actually, I now think it’s simpler than you realise. But IMHO you have to look beyond the Standard Model to appreciate it, taking note of the experimental evidence, and reading the old papers.

  5. I have a question about uncertainty principle. Intuitively I think about uncertainty principle in this way: If I take a picture of a car running on a racetrack using a slow shutter camera speed, the photo will not show a car, but rather an elongated, blurred object that kind of reminds one of a car. I this case, if I ask “Where is the car on the track?” I cannot answer that because it’s everywhere between the two points occupied by the blurred object. But I can calculate its speed. I know where that blurred object starts and ends, and I know my camera shutter speed. On the other hand, if I use a fast shutter speed, then the photo will show the car in a definite position on the racetrack. But now I cannot tell anything about its speed. How does this intuition fail compared to reality? In what ways is it wrong? Thanks.

    1. It’s a good question. Your intuition is quite reasonable, but in fact it’s not accurate.

      What you’re missing is that when quantum physics is involved, **the very fact of observation has an effect on the object being observed**. It is as though when you took the photo with the fast shutter, your camera actually caused the car to move off in all directions. Or if, in carefully trying to measure the car’s velocity as well as possible, you caused the car to spread out.

      Better intuition comes from thinking about waves. Consider ocean waves in a storm; they are going all over the place and all spread out. You can work to dampen some of the waves so that what you are left with is a train of ocean waves all going the same way, such as we often see when waves approach a beach with a fixed speed and direction. But then these waves will be spread out all over the ocean, so there’d be no sense in which you know where they are. Or you could force the water waves together into a very high spike, and then you’d know, for an instant, where they are; but immediately the spike of water would ripple out in all directions and in a wide range of speeds.

      In other words, the decision to measure the speed and direction of the waves requires an active intervention to make sure they actually have well-defined speed and direction. Conversely, the decision to measure the location of the waves requires a different active intervention. Those interventions are mutually exclusive; there is no intervention you can make that both localizes the waves and makes their speed and direction evident.

      Does that intuition make sense to you?

  6. This post, and the responses to it, have made me think about the future of fundamental physics. Here we have an expert in theoretical particle physics, wanting to help interested members of the public understand what’s going on in his discipline… But what he writes about is yet another case of how a claim of new physics may be just a false alarm, and meanwhile the comments are dominated by amateurs who don’t even believe in quarks.

    It looks like particle theory is the victim of its own success. It’s one thing to seek support for Big Science when there’s a profusion of unexplained particles and relations between them – I’m thinking mostly of the hadrons, as they looked before QCD. But now… we have one fine-tuned effective field theory, the standard model, valid up to every energy we can reach, plus a few hints from beyond, like neutrino masses and the dark sector, regarding which there may be no further empirical discoveries for the foreseeable future.

    It is imaginable that there won’t be a renewed serious interplay between experiment and fundamental theory, until e.g. string theorists learn how to calculate the mass of the electron in a given “standard model” vacuum. But that might take decades.

    1. If progress in the field depends on string theorists calculating the mass of the electron, rather than on experimental insights, then we’d be in a even sorrier state than I fear. String theorists can’t even figure out how to understand a toy universe that looks even vaguely like ours; the problems are extremely difficult. Yes, we are a victim of a sort of qualified success — we have a working mathematical/conceptual framework with few discrepancies of note, but we are not short on unanswered questions. What we lack is a plethora of inexpensive experiments with which to address them.

  7. Matt, Hi. I would like to add my 2 cents to your argument, which, from my point of view, is correct. The fact that the NNPDF group is using Neural Networks is interesting, but also problematic at a certain level.

    So far, there is no real theory of Neural Networks and Deep Learning, even though there is some good progress in the theoretical field, like for instance, what the book The Principles of Deep Learning Theory presents (BTW, it is interesting that this theoretical work uses renormalization as part of its theory).

    In short, the field of Deep Learning is at a point like Thermodynamics was at the beginning of the XIX century: it was basically an experimental science with not much theoretical background to support it.

    Just like way back then, people understood empirically how to build new machines out of steam engines, turbines and the like, out of trial and error, but there was no much of a theoretical background besides the Carnot theory of heat, to do real engineering like we do today.

    There is some general understanding about some of the inner workings in Deep Learning, but still there is no way to do theoretical work to predict a priori which type of architecture of Neural Network could be proper to solve a certain family of problems, given the characteristics of said family.

    So far, teams use some conceptual educated guesses, and then try architectures and compare results on a certain type of problem, and then see which structure works better.

    Data Scientists just use was is already proven to work better for a certain family of problems.

    The bottom line is clearly stated and summarized by the No Free Lunch Theorem: “all optimization algorithms perform equally well when their performance is averaged over all possible objective functions.”

    If you think about it, it sounds a lot like the Central Limit Theorem.

    The field will eventually evolve to the point when there will be a sound and complete mathematically-based theory of Deep Learning, and it is clearly moving in strides towards that goal, but still there is a lot of work to be done to get there.

    Kind regards, GEN

    1. Gen:

      > The bottom line is clearly stated and summarized by the No Free Lunch Theorem: “all optimization algorithms perform equally well when their performance is averaged over all possible objective functions.”

      Is it an actual theorem that was proved?

      1. Never mind, I found
        D. H. Wolpert and W. G. Macready, “No free lunch theorems for optimization,” IEEE
        Transactions on Evolutionary Computation 1 no. 1, (1997) 67–82.

        Thanks for an interesting comment!

  8. /… Otherwise it will be a very long time before we know whether or not the W boson’s mass is actually above the Standard Model prediction, or whether there really are charm quark/anti-quark pairs playing a role in the proton… /

    Quantum shifting towards more metastable?

    1. Quantum shifting from metastable to stable state?:
      A self-organized non-equilibrium matter that emerges after pulsed laser excitation evolves in a sequence of processes that eventually cause it to reach the ground state.
      Sabine #Hossenfelder is correct, the subtlenesses of ‘Quantum Von Neumann entropy’ take the phase change a long time (10^-12 to 10^12 s?), the inbetween time give some technological Innovations?

  9. Can you refer us to the best (w.r.t. the latest physics) depiction (CGI) of the proton possible structure?

    The latest I have seen is here: https://www.quantamagazine.org/inside-the-proton-the-most-complicated-thing-imaginable-20221019/

    Is it valid to say that in order to meet the conservation of energy AND momentum AND Pauli’s uncertainty principle, that the proton’s wave function (resultant) must be composed of 6 orthogonal vortices of “free energy”. I asked, respectfully, because this mechanism of 6 vortices with all 6 angular momentum vectors pointing to the center could explain the strong force and confinement.

    As for Pauli’s principle, taking just one vortex, the tangential velocity must be at or near c, hence as you go deeper the radius reduces and the angular velocity tends to infinity, hence creating a huge energy density, dense enough to prevent refraction and transition to reflection (transitioning from a bosonic to a fermion field). So, from this layman’s hypothesis, the center of the proton is practically a micro black hole.


    1. Complex quantum mechanical systems *cannot* be fully depicted (using CGI or anything else). This is already true for an atom such as Helium, which has to be depicted in 4 dimensional space, or an Oxygen atom, which requires 34 dimensional space. Objects for which field theory is important are completely beyond reach. For this reason, all depictions of the proton involve different types of compromise. The compromises used in the Quanta Magazine article are completely different from those used by NNPDF when determining parton distribution functions, and there are many others one could choose, always understanding that large amounts of information are being thrown away. So — which compromises do you want or need? The answer to whether I can give you a reference depends on which question you want an answer to.

      1. “… always understanding that large amounts of information are being thrown away.”

        I guess you’re saying it’s easy to get lost by over simplifying the problem with graphical interpretations, and simplification in general.

        As a retire mechanical engineer, what I was trying to above it visualize a possible “free body diagram”, the six orthogonal vortices to try and understand the possible dynamics in the proton.

        So, the list of variable, I understand there could many more than anybody has yet to even think about. My assumption was that every particle is made of “free energy” and the Big Bang started the expansion of space and the rapid drop of energy density, which in turn created forms, oscillations, waves, and particles. There are all vortices, right from t=0.

        So, I guess the question I want answered is, is/are there theories that use vortices as mechanisms to formulate the proton inner structure?

        Thank you for replying. Much respect.

        1. The problem is that data contradicts your assumptions. In the Big Bang, what happens is interactions of particles via the forces of the Standard Model, as described by quantum field theory. It’s not free energy and vortices. We know this because quantum field theory allows detailed calculations for the amount of Hydrogen, Helium, Deuterium and Lithium that should be present in primordial clouds of gas leftover from early in the universe, with one free parameter (the initial total density of protons). That gives 3 predictions. These predictions work. https://w.astro.berkeley.edu/~mwhite/darkmatter/bbn.html

          The proton and its innards are studied in great detail using numerical simulations of quarks and gluons. This is not the best reference because it is too advanced, but it should give you an idea of how sophisticated things were already in 2004.
          https://physicstoday.scitation.org/doi/10.1063/1.1688069 Of course much more has been done in the nearly 20 years since then.

          1. Yes, indeed, the second reference is very advance, but I will try anyway. A lot better reading than the garbage in the news lately, smiley face.

            BTW: In the first reference, this:

            “At high temperature, the matter in the Big Bang consisted only of its most elementary constituents. When the temperature dropped below a few hundred MeV, ordinary nucleons (or baryons) could form: these are protons and neutrons since no heavier nuclei would have survived the high temperatures.”

            “most elementary constituents”, differentiating from the baryons that formed at lower temperatures. What are these elementary constituents?

            You see professor, I just cannot get my mind around it that if you rule out vortices, then doesn’t that imply infinities, i.e. discontinuities that defy the conservation of momentum?

            Also, just skimming through the first few pages of the second reference, are field theories using predominately conservation of energy and less momentum? I guess the question would be how does the Standard Model deal with infinities?

            Thank you for the references and your time.

            1. Conservation of energy and momentum are built into the equations for quantum field theory from the ground floor.

              The Standard Model itself has no infinities. Certain calculations will seem to have infinities if you don’t do them correctly.

    1. The correct statement is that all particles produced at CERN do exist in the universe on their own, and are made in natural particle collisions (such as collisions of cosmic ray particles with the Sun or the Earth’s atmosphere), but they are extremely short-lived, disintegrating within a fraction of a second. That’s why, if and when we want to learn more about these particles, we need our own particle accelerators; we can’t just go find these particles lying around on the ground. Nevertheless, these particles are all natural — all a part of the universe — not artificial. The only thing that’s artificial is the particle accelerator we use to make them collide; but the collision process, and the process by which they form and disintegrate, are all 100% natural.

      1. Dear Prof. Strassler, how quarks that have a lifetime about 10E-23 can build proton that has infinite lifetime? This is the big puzzle of Standard model. In my view, only stable elements can build a stable system. Proton is a vortex of superfluid quantum space, it has no constitutive parts [unscientific link removed by editor]

        1. There’s no problem here, because the lifetimes of up and down quarks, in the context of a proton, are at least 10^34 years. The strange quark, charm quark and down quark all decay faster than a 1 second, but much slower than 10^{-23) seconds; we see particles made from strange quarks pass through macroscopic detectors, and can just barely do so for bottom and charm quarks. Only the top quark has a lifetime that’s extremely short.

          Because up and down quarks are found always in bound states, their lifetimes are not strictly defined. For example, in a neutron, the lifetime of a down quark is about 15 minutes. But in a proton it is 10^34 years. That’s because lifetimes depend on which decay channels are available, and those are different for different bound states.

          Or perhaps you are confusing the lifetimes of excited states of protons (e.g. the Delta resonance) with the lifetime of the quarks that they contain? A similar mistake would be to confuse the lifetime of the first excited state of hydrogen (10^(-8) seconds) with the lifetime of the electron (infinite.)

          1. I cannot get the point how instable elements (quarks) can build a stable element (proton). In my view, also neutron is not “particle” it is composed of proton and electron and antineutrino. For me, “particle” means part of something bigger. The particle must be stable in order to build something bigger.

            1. I am not sure why you are not hearing what I am saying, but I will say it again: up and down quarks are as stable as the proton is.

              And if you believe that a neutrons are composed of a proton, electron, and a neutrino, then you have only yourself to blame for your confusions, since this belief is nonsensical; neutrino interactions are far too weak for them to bind the protons and electrons.

              You will definitely find if difficult to get the point of how physics works if you insist on ignoring data.

              1. What bothers me about all this is that protons are, barring nonperturbative processes (tunneling) violating conservation of baryon and lepton number, stable. That is, they are the composite ground state of their “partons”. As such, they are a single state and have no time dependance. So the “sea” quarks and gluons (and of course photons too) simply can’t come and go. The description of the proton in terms of its constituents is that it is a linear superposition of amplitudes containing small amounts of strange quarks and even much smaller amounts of charm quarks (and antiquarks). To get strange and charm quarks popping in and out you would need linear combinations of a proton and a uus baryon and a udc baryon. That linear combination would indeed have a time dependence (outside that caused by quark decay) which would be exceedingly rapid. This is just like the actually observed neutrino oscillations. I got tenure by actually observing such fluctuations in the spin state of a molecule called biacetyl, the fake “buttery” flavor in movie theater popcorn.

                It that not correct?

                1. The press reports were extremely confusing, and it’s no surprise that you are bothered, since the impression you have as to what’s going on isn’t quite right. You may want to read what I wrote about this in https://profmattstrassler.com/2022/09/09/protons-and-charm-quarks-a-lesson-from-virtual-particles/ .

                  Essentially, the point is that the wave function of a proton naively has various pieces of the form

                  | u u d (g)^n (u ubar)^x (d dbar)^y (s sbar)^z > ,

                  where (n,x,y,z) are integers, g stands for gluon, u,d,s for up,down, strange quarks, and ubar etc for their anti-quarks. By “u” I naively mean a real up quark — a resonant solution to the equations of motion for the up quark field. This is naive because that would be a free up quark, but since there are strong interactions inside the proton, and the up quarks aren’t like free particles at all.

                  Now the question is whether we can also have (c cbar) appearing in the proton wave function, where c are charm quarks. [Notice we are *not* replacing uud with ucd. We are, if anything, replacing (uud) with (u u d c cbar), which has the same quantum numbers.] Clearly we could not have naive free charm quarks in the proton, as they are far too heavy. But we could have disturbances in the charm quark field, with net charm = 0, large enough that we need to account for them in the proton wave function.

                  The way particle physicists make this precise is in the context of high-energy proton collisions. In that limit, where the proton is taken to travel at nearly the speed of light, the problem somewhat simplifies, and one can state more clearly what it means to have (c cbar) in the proton; there are specific effects in electron-proton or proton-proton collisions which depend on how common it is to have effective c and cbar in the proton.

                  One way in which this *could* happen, speaking logically but without experimental evidence, is through a quantum fluctuation in which

                  [Typo corrected] (u u d) –> (u u c) + (cbar d) [or (u d c) + (cbar u)

                  i.e. a virtual fluctuation of a proton into an off-shell charm baryon plus an anti-charm meson; i.e., the proton wave function would then contain |(udc) (cbar d)> (dropping all gluons and other quark-anti-quark pairs for simplicity) as a term in its wave function.

                  But notice we are *not* saying the proton is A| u u d > + B | u c d> . That would violate flavor conservation laws and is impossible; an up quark cannot transform into a charm quark, in the Standard Model.

                  I realize this was long and probably quite confusing; you might want to start with my blog post and then come back to this. The issue raised there is that even positronium contains muons and anti-muons; for the same reason, the proton definitely contains charm and anti-charm. But the question of interest in all these recent discussions is whether it contains more than you’d naively expect, and whether its momentum distribution is different from what you’d expect.

                2. I see what you mean about (u u d) –> (u d c) + (cbar d). Or is that in fact (u u d) -> (u c d) + (cbar u) ? Yours does not preserve charge nor u-ness. [The mass of (u c d) (cbar u) pentaquarks can be guessed from calculated and measured properties of known pentaquarks.]

                  But that was not my point. My point is about the time dependence.
                  (u u d) –> (u d c) + (cbar d) is the same as (u u d) –> (u d c) as far
                  as existance of time dependence goes. You and lots of people talk about “fluctuations”. To me “fluctuations” imply a time dependence that
                  can actually be observed. When a d -> u inside a neutron one gets
                  emission of an actual electron which is both 100% “electron flavor”
                  and 100% “electron mass” and has not time dependence. But you also get an antineutrino which is a pure “electron” flavor but is a
                  mix of mass eigenstates which are “mostly electron” and “mostly muon” and thus one sees the famous real oscillations between electronness and muonness. In any case, there are the molecule experiments where by turning knobs I could make various combinations of “mass” eigenstates (speaking relativistically, Schrodinger molecular eigenstates nonrelavistically) or “photon coupling eigenstates” or “spin eigenstates” and got the expected time dependence if measured in time, or photon energy if measured with long-time spectral measurements) (Three different kinds of states.)
                  The experiments showing time dependence involve superpositions of molecular (mass) eigenstates. All this eventually became completely noncontroversial.

                  If protons are mass eigenstates, how can they have “fluctuations” as
                  opposed to superpositions of amplitudes? A proton is a linear superposition of all possible path amplitudes in the limit of t goes to infinity if there are no external couplings.

                3. It’s indeed not an issue of time dependence; it is an issue of superposition of states. I didn’t say anything about time. I just said something about off-diagonal terms in a Hamiltonian. That’s what “(u u d) –> (u d c) + (cbar d)” [Editor’s note: UGH, I repeated the mistake; it should be (uud) –> (uuc) + (cbar d) ] means, as always in quantum mechanics; it’s an off-diagonal matrix element in a Hamiltonian, which in classical physics would give time-dependence but in quantum mechanics, when one solves for the ground state, gives a superposition of states.

                  Let’s not confusion notation for physics.

                  Fluctuations do *not* imply observable time-dependence in quantum physics unless you make a measurement, which by construction leads to time-dependence.. When I say that the ground state of a hydrogen atom can contain a (far off-shell) muon/anti-muon pair in its wave function, due to quantum fluctuations in the electromagnetic field inside the atom, I am stating the truth. Nevertheless, it is a time-independent statement about the wave function and about off-diagonal terms in the Hamiltonian, not a statement about time-dependence.

                  Because the previous sentence is incomprehensible to any reader who has not taken Quantum Mechanics, the word “fluctuations”, which *suggest* but do not actually *mean* time-dependence, are often used. They represent a compromise, and an imperfect one, but I don’t know of a better approach that can be understood without much more detail. You’ll see on this blog that I am always running into the same problem trying to explain how a proton works to someone who doesn’t understand what eigenstates are.

                  Your neutron example is quite confused, though. Even if there were no neutrino mixing, there is nevertheless time dependence in the decay, because there is (in the long-time limit) no overlap between a 1-particle state and a 3-particle state. It is true that a neutron can fluctuate into a proton, an electron and a neutrino — i.e., the state of a neutron contains the particle eigenstate | p e nu > as part of its wave function. But the decay of a neutron is not a fluctuation, and has a “before” and an “after” (T–> – infinity vs T –> + infinity) — that’s because the proton, electron and antineutrino escape to spatial infinity. [In finite volume there are no true decays.]

                  So we agree, time-dependence arises whenever a state is considered that is not an energy eigenstate. But a neutron is *not* an energy eigenstate of the full Hamiltonian. An electron, by contrast, is an eigenstate. A proton may or may not be, but it if it isn’t, the time dependence is extremely slow, since the proton lives at least 10^{34} years.

                  I hope this clarifies both the terminology and the physics. Let me know if you are still confused about neutrons, but you might want to try thinking about how de-excitation of the first excited state of hydrogen works when it emits a photon, or about how positronium annihilation works.

                4. The only thing I was confused about was the use of the word “fluctuation” when referring to a (stable) composite particle ground state. I do understand free neutron decay as well as hydrogen atoms (I didn’t teach this for 42 years for nothing!. I was always bothered by the fake treatment used by chemists for spontaneous emission but I held my nose when talking to undergrads but not grad students. )

                  Oh yes, there is (u u d) –> (u c d) + (cbar d) versus (u u d) -> (u c d) + (cbar u) …. all four baryons are charge +1 but cbar d is +1/3 and cbar u is zero. That’s bothersome. (And I know that the wave function of a molecular pentaquark is probably different from that of (u c d) + (cbar u) as one of your “fluctuations” in a proton. )

                5. [Palm against forehead] thanks for pointing out the typo — twice! You know, I forgot in my first reply to acknowledge you’d identified a typo, but fixed the quark assignments in the original comment, and then copied the mistake into the second comment. Some days I wonder how I ever got a Ph.D. Not every day, fortunately.

                  Meanwhile, you’ve identified a clear problem with our explanatory language, which I’m running into repeatedly. The question is how to fix it. That is:; in the ground state of the harmonic oscillator, what are the options in terms of how to explain the origin of zero-point energy? Uncertainty, sure… but that’s not so helpful either, and doesn’t easily generalize to the case of, say, electron-positron pair “fluctuations” in a photon, or “fluctuations” of an electron into an electron-photon pair. I’m open to suggestions as to how to explain this both more accurately and clearly.

                1. Well, your request is indeed a fair one. The problem is somewhat more subtle than you imagine, which is why I didn’t just send you to some references to start with. We’ll have to take our time and follow the following steps. (1) Let me convince you that the bottom quark, charm quark and strange quark have easily measurable lifetimes — though already there are subtleties, especially with the strange quark — and that they are much longer than 10^{-23} seconds. Will you accept that? Then (2) we will see that the up and down quark lifetimes must be longer than those of the bottom, charm and strange quarks. Then (3) to go further and define the up and down quarks’ lifetimes leads to many ambiguities, for reasons that have to do with the subtleties of quantum physics and the binding energies of protons, neutrons and atomic nuclei, but they are not short, and in a proton they last for eons. Along the way I will provide all the relevant references, which are given (but somewhat hidden) in the Particle Data Group information repository, https://pdg.lbl.gov, which has not only all the knowledge of particle physics but all the sources of that knowledge archived.

                2. Dear Matt, thank you. Sincerely, I never read quarks have a stable lifetime. Seeing a peer article on this will be for me a big surprise. Yours sincerely, amrit

                3. Well, let’s start with the bottom quark: here are a list of the four ground-state mesons that contain bottom quarks, and you see they all have roughly the same lifetime: 1 trillionth of a second. https://en.wikipedia.org/wiki/B_meson#List_of_B_mesons If you similarly look at a list of baryons, https://en.wikipedia.org/wiki/List_of_baryons , you will see that those that contain a bottom quark come in two classes: (1) lifetimes much shorter than 1 trillionth of a second ***but decaying to another bottom-containing baryon*** [i.e. the bottom quark does ***not*** decay in this step], or (2) lifetimes about 1 trillionth of a second. The fact that *all* of the particles that have a bottom quark before the decay, and have none after the decay, decay in about a trillionth of a second is strong evidence that the bottom quark itself has a lifetime of 1 trillionth of a second.

                  Here is a plot (look at the upper right) from a proton-proton collision at the LHCb experiment, https://www.researchgate.net/profile/Yutaro-Sato-3/publication/314258058/figure/fig1/AS:786385879453696@1564500412740/Belle-a-and-LHCb-b-single-event-displays-illustrating-the-reconstruction-of.jpg, which shows a bottom meson traveling about 1.5 cm (from the proton-proton collision where it was created) before decaying; its decay position is inferred from careful measurement of the tracks of particles that emerge from its decay. (It travels 1 cm, longer than 1 trillionth of a second, because its lifetime is extended significantly by relativistic time dilation; this particle is traveling at near-light-speed.) A similar image of a rare decay of a B_s meson (bottom anti-quark and strange quark) is shown at the end of this article, https://lhcb-outreach.web.cern.ch/2017/02/14/first-single-experiment-observation-of-the-decay-bs0%E2%86%92-%CE%BC%CE%BC/ , in which a B_s turns into a muon and an anti-muon; tracing back the paths of the muon and antimuon show they appeared in the B_s decay at, again, 1.7 cm from the proton-proton collision point. (The precisely measured energy and momentum of the muon and antimuon can be used to show they came from a B_s, whose mass is precisely known by other measurements.) Again, this travel distance is lengthened by relativistic time dilation, expected from the high speed of the B_s (also measurable from the muon and anti-muon.)

                  Now, as for references: https://pdg.lbl.gov/2022/tables/contents_tables_mesons.html gives all the summary information that you would want for lifetimes and decay modes, but without the references; meanwhile, in huge detail, all the references are to be found in https://pdg.lbl.gov/2022/listings/contents_listings.html, and in particular you can find under MESONS a set of pdfs for BOTTOM MESONS, including for example https://pdg.lbl.gov/2022/listings/rpp2022-list-B-plus-minus.pdf , which lists several dozen measurements of the B+ meson lifetime, and a reference for each one (the reference is indicated by the name of the first author and a alphanumeric code, and the actual references appear as a long list at the end of the pdf.) Why don’t you see if you can understand this information first, and then if you want I can try to help you through other cases.

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