# W boson and weak decay

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• GeorgeBaxter
GeorgeBaxter
TL;DR Summary
The W boson is involved in the weak decay. That happens when the mass of the W boson is very low.
Hello everyone

I have been following Fermilab presentations by Dr Don Lincoln for some years. Recently he did a deeper review into the four fundamental forces. He explained why the weak force is relatively weak. The explanation given was that the “normal” mass of the W boson is relatively high. However, the mass of the boson has a wide range, and there is a very small probability that the W has a very low mass. The “normal” mass was given arbitrarily as 100,000 but the weak force only actually occurs when the mass is of the order of 1.

The question is doesn’t that large variation in the mass imply that the W boson is somehow composite? Could that be considered as evidence for preons, a postulated more fundamental particle. If it isn’t preons, then why is there a very large range of mass?

The link to the Fermilab video is below. Around 8 minutes into the video is the W boson discussion.

Thanks
Fermilab W boson and weak decay

That is highly popularised. Do not take the statement that the W-mass varies too literally. In general, never try to extrapolate statements made in popular scientific expositions.

What he seems to be actually referring to is that the mediator W is a virtual off-shell particle. This means that the four-momentum squared of the corresponding virtual particle is not equal to the particle's mass squared.

pines-demon, GeorgeBaxter, dextercioby and 4 others
GeorgeBaxter said:
TL;DR Summary: The W boson is involved in the weak decay. That happens when the mass of the W boson is very low.

Hello everyone

I have been following Fermilab presentations by Dr Don Lincoln for some years. Recently he did a deeper review into the four fundamental forces. He explained why the weak force is relatively weak. The explanation given was that the “normal” mass of the W boson is relatively high. However, the mass of the boson has a wide range, and there is a very small probability that the W has a very low mass. The “normal” mass was given arbitrarily as 100,000 but the weak force only actually occurs when the mass is of the order of 1.

The question is doesn’t that large variation in the mass imply that the W boson is somehow composite? Could that be considered as evidence for preons, a postulated more fundamental particle. If it isn’t preons, then why is there a very large range of mass?

The link to the Fermilab video is below. Around 8 minutes into the video is the W boson discussion.

Thanks
Fermilab W boson and weak decay
Even if a popular video like this is educational as far as possible, it does not allow you to do two things:

a) Solve actual scattering or decay problems as a homework exercise.

b) Think for yourself, in terms of extrapolating from the material presented.

Ah yes, DOCTOR Don Lincoln. When he first started doing this, a bunch of us did the Spies Like Us "Doctor...Doctor..." schtick at the Fermilab cafeteria.

I agree with @Orodruin and @PeroK. His explanation is good for what it is, a popularization, but you can't extend it beyond what he said, and you certainly can't use it to do any calculations.

Think of it like the solar system model of the atom: its less wrong than the ball-and-stick model, but you can't run with it.

ohwilleke
Orodruin said:
That is highly popularised. Do not take the statement that the W-mass varies too literally. In general, never try to extrapolate statements made in popular scientific expositions.

What he seems to be actually referring to is that the mediator W is a virtual off-shell particle. This means that the four-momentum squared of the corresponding virtual particle is not equal to the particle's mass squared.
Thanks for your reply. I am puzzled why Fermilab would have a channel to inform, but somehow make statements which may not be valid. There will always be limits to how far analogies can be pushed. In this case, he did say it was a real mass. I will contact him for an explanation. Thanks for your time,

GeorgeBaxter said:
he did say it was a real mass
He did not. He just talked about "masses".
GeorgeBaxter said:
but somehow make statements which may not be valid.
But they were valid, to the degree that any popularisation may be considered "valid". It was your extrapolated conclusion that was not valid.

Forget my extrapolation. Quoting Dr Don, "While the mass of the weak force particles are, on average, about 100,000 eV, those particles actually have a range of masses. You can see the range here. Where the curve is high, lots of those particles exist. Where the curve is low, very few do. And see that while that the number that exist at one are very small, they are not zero."

What is the explanation for the very low masses?

Again, you are reading too much into this. It is an oversimplified explanation, suitable for people who did not spend years studying quantum field theory.

A popularization is like a mistress. Either it is beautiful and unfaithful, or faithful but not beautiful. (With apologies to whoever said it first)

dextercioby
GeorgeBaxter said:
Forget my extrapolation. Quoting Dr Don, "While the mass of the weak force particles are, on average, about 100,000 eV, those particles actually have a range of masses. You can see the range here. Where the curve is high, lots of those particles exist. Where the curve is low, very few do. And see that while that the number that exist at one are very small, they are not zero."

What is the explanation for the very low masses?
For what it is worth, I would never explain it this way and this is the first time that I've seen someone explain it this way.

It is far more common to talk about virtual particles and to put it into the context of somewhat similar phenomena like quantum tunneling.

The explanation given is a pretty confusing way to explain it. It is not entirely without any foundation or strictly speaking an incorrect way to simplify it. But this approach is more prone to leading to incorrect assumptions about how it works than many alternative simplified explanations. Thumbs down as pedagogy.

I detect a certain level of discomfort. All the comments so far talk around the question, without giving an actual explanation for a very low mass of the W boson.

One response was the 4 momentum squared does not equal the mass squared for a virtual particle. That doesn’t actually explain anything.

Virtual particles were not referred to in the explanation. Virtual particles have real existence, Hawking radiation depending on them being real particles, albeit with a fleeting existence within the Heisenberg uncertainty principle. Even if the particle is virtual, it does not explain why there could be five orders of magnitude difference.

“It is not entirely without any foundation or strictly speaking an incorrect way to simplify it.”

That seems to confirm that very low masses are correct, but still does not explain anything.

The standard model has the W boson as a fundamental particle. How can the mass actually vary over such a large range? All I am asking for now is the simple explanation for the very low mass. Thanks

PeroK
GeorgeBaxter said:
I detect a certain level of discomfort. All the comments so far talk around the question, without giving an actual explanation for a very low mass of the W boson.
If there is any discomfort here, it is created by being forced to use words rather than actual math to describe the physics. As is invariably the case when doing popular science at the expense of accurcy.

GeorgeBaxter said:
One response was the 4 momentum squared does not equal the mass squared for a virtual particle. That doesn’t actually explain anything.
Yes it does, it explains how the statement in the video fits together with actual physics as well as can be expected from a popular description.

GeorgeBaxter said:
Virtual particles were not referred to in the explanation.
Not directly, another pop sci choice.

GeorgeBaxter said:
Virtual particles have real existence, Hawking radiation depending on them being real particles,

No, it doesn’t. It also has never been actually observed. You have unfortunately fallen into the same trap of extrapolating popular scientific descriptions here as you have when interpreting the video.

GeorgeBaxter said:
albeit with a fleeting existence within the Heisenberg uncertainty principle.

Popular science at work again.

GeorgeBaxter said:
Even if the particle is virtual, it does not explain why there could be five orders of magnitude difference.

Yes, it does. If you know the actual physics rather than just make up yoyr own head canon.

GeorgeBaxter said:
The standard model has the W boson as a fundamental particle. How can the mass actually vary over such a large range? All I am asking for now is the simple explanation for the very low mass
If you want to know the actual description, I suggest a 5-year university program focusing on theoretical particle physics. Until then, you are unfortunately stuck with popular descriptions that may never be fully satisfactory because they will never properly reflect the actual theory.

PeroK
Orodruin said:
Yes, it does. If you know the actual physics rather than just make up yoyr own head canon.
Ok, then explain the physics. I have not asked for the Lagrangian. I am asking for the physics. Please explain the physics of how a fundamental particle's mass can vary by five orders of magnitude from the measured, most probable mass. Thanks

GeorgeBaxter said:
Ok, then explain the physics. I have not asked for the Lagrangian. I am asking for the physics.
Why do you think some people go to university and study physics for 3-10 years if it can all be explained in a five-minute video?
GeorgeBaxter said:
Please explain the physics of how a fundamental particle's mass can vary by five orders of magnitude from the measured, most probable mass. Thanks
Define "mass" in the context of a W Boson? What do you think mass is? How do you measure it?

GeorgeBaxter said:
Ok, then explain the physics.
The physics is explained by the math. The physics is the math. To take you from the level of popular science to actually understanding the physics would take 5 years of university studies specialising in theoretical particle physics, likely followed by some 4-7 years of a PhD to cement the knowledge. I would have to write numerous textbooks, but luckily others have already done so. We can refer you to them if you like.

The fact remains that unless you are willing to undertake this endeavour, you will not be in a position to understand the actual physics. Until such time, we can make do with popular descriptions but you must be aware of its limitations and purpose, which is to tell you a story about physics - not to teach you physics.

George: With the right explanation, it wouldn't take five years, or even five days, to arrive at a clearer picture. But a lot depends on what you already understand. Which of these have you already heard about: the uncertainty principle, the superposition principle, path integrals, field-particle duality?

If you want to dive in right away, this is PF's major explanatory essay on virtual particles.

PeroK
mitchell porter said:
George: With the right explanation, it wouldn't take five years, or even five days, to arrive at a clearer picture.
I disagree with this. The OP is not looking to understand from a superficial standpoint. They are attempting to draw own conclusions based on their ”understanding”. Perhaps it took you five days to learn QFT from scratch, but that is definitely shorter than it would take for most people.

mitchell porter said:
George: With the right explanation, it wouldn't take five years, or even five days, to arrive at a clearer picture. But a lot depends on what you already understand. Which of these have you already heard about: the uncertainty principle, the superposition principle, path integrals, field-particle duality?
Thanks Mitchell, for asking the right questions.

I have a degree in mathematical physics from Sussex university. All of the concepts that you mentioned were in the courses. Fields seem to by the dominant concept these days, especially in QED, QFT, QCD. The quantisation of gravity is problematic due to the uncontrollable infinities that are generally tamed by normalisation methods in the Standard Model.

Newtonian mechanics is equivalent to Lagrangian mechanics ( using the path integrals ) and Hamiltonian mechanics. One of my professors showed have Newtonian formalism could transformed, via Lagrangian and Hamitonians, to produce the Schrodinger equations.

Hopefully I have convinced you that I am not child reading comics, I will now explain further.

The Standard model provides explanations about fundamental particles that make up protons, etc. The model suggests that a proton is composed of three quarks, and held together via the strong force, mediated by gluons. However, the mass is the proton is not merely the quark masses and the binding energy. The possibility of a more complex involving a Charmed quark fleetingly appearing.

The mass of the three neutrino flavours is extremely convoluted. A mass that is not clearly, and uniquely defined, shows a deeper complexity, or need for a better model.

The Muon g-2 anomaly has been suggested as hinting the need for new physics

Given that the proton's mass is not simply defined, and has a range, then Dr Lincolns description that a W boson's mass is also rather more complex, then it opens the possibility that the W boson is somehow composite.

I am well aware of the need for advancement mathematics to underpin the theories and observations. However, as this is a physics forum, I have been asking for a physics explanation to explain Dr Lincoln's observation that the W boson can have a large range of masses, spanning five orders of magnitude.

I hope someone can now provide a physics explanation for the wide range on masses.

GeorgeBaxter said:
I have a degree in mathematical physics from Sussex university.
Then why are you watching popularisations that inevitably lead to misconceptions rather than looking into what the theory actually says?

GeorgeBaxter said:
The mass of the three neutrino flavours is extremely convoluted. A mass that is not clearly, and uniquely defined, shows a deeper complexity, or need for a better model.
The neutrino mass in the typical Standard Model is zero. The Standard Model simply lacks the right-handed neutrino required to produce a Yukawa coupling. From that alone it is clear that we need a better model.

Neutrino mass models are not necessarily extremely convoluted, but it is difficult to experimentally establish which of the many existing models is correct as they either involve extremely heavy particles or extremely small couplings (or both). The simplest kind of model for neutrino masses is to just introduce the right-handed neutrinos into the SM, but this is a SM singlet and therefore comes with a lot of phenomenology that is not available for other particles - such as the possibility of a Majorana mass.

GeorgeBaxter said:
The Muon g-2 anomaly has been suggested as hinting the need for new physics
Yes, this is well known.

GeorgeBaxter said:
Given that the proton's mass is not simply defined, and has a range, then Dr Lincolns description that a W boson's mass is also rather more complex, then it opens the possibility that the W boson is somehow composite.
No, here is where the pop sci induced misconception sets in. What he is talking about is simply the W width. The width of an elementary unstable particle is described in any basic textbook on QFT and relates to the optical theorem. There is nothing in that that suggest that the W would be composite.

The Feynman diagram for producing a weak decay includes the W as an internal line and therefore there is a resonance about the W mass, but that resonance has a width. The required energy to hit the top of the resonance is not available in nuclear decays and so we are far out in the lower tail of the resonance peak, thereby suppressing the decay to be "weak".

ohwilleke, dextercioby, Vanadium 50 and 1 other person
Orodruin said:
Then why are you watching popularisations that inevitably lead to misconceptions rather than looking into what the theory actually says?
Firstly, thank complete for a more complete and constructive reply.

I think that we have a vastly different opinion as to what is “popularist” is. To me, it is someone making wild or exaggerated claims, with no reference to academia. Fermilab, and CERN, are world class leading laboratories. Don Lincoln is described as a senior scientist with Fermilab. Hardly mickey mouse. Clearly he is not some wacko describing his own theories. One of his recent videos was an explanation of the full Lagrangian used to describe the Standard Model. Doesn’t sound very populist to me.

When I first studied physics in earnest, I bought a book about Special and General relativity. It was written in 1920 by Albert Einstein. He used everyday references and objects. Measuring rods, trains, lightning strikes, clocks. I wouldn’t class him as a popularist, but he could see the merit of providing good material in an accessible way. Rather as Feynman and Sagan did.

Do you have recommendation for a “not popularist” channel?

I accept your explanation of the W boson in terms of the width of the resonance, and the long tail. It isn’t clear ( to me ) why there is a such long. Indeed, the long tail was evident from the video. There isn’t an explanation for the long tail, but I will leave it there.

This has gone on longer than I anticipated. I will finish with some thoughts as to why it may be important.

The observable Universe is 46 billion light years, or ~ 4 x 10^23 meters. The Planck length is ~ 10^-35 meters. There are changes of physics from the rather fuzzy width of the proton is ~ 10^-15, every few orders of magnitude, subatomic, nuclear, chemistry, biology, planetary, stellar, galactic, even structures billions of light years across. It seems reasonable to think that there is a lot more going on between the Planck length and the scale of the proton. Twenty orders of magnitude.

General Relativity could explain the small but real anomalies in the orbit of Mercury. It is by looking out for anomalies that advances are made. The muon g-2 anomaly may lead to new physics. That could be new particles, as in the postulated supersymmetric particle, or down at a lower size, and potentially preons. Of course, that will come when there is an experimental discovery, or some theoretical advance.

Motore
GeorgeBaxter said:
I think that we have a vastly different opinion as to what is “popularist” is.
Not popularist. Popular science. It is one of the three pillar stones of academia: Teaching, research, and outreach. That does not (necessarily) mean they are not respectable scientist. However, the fact remains that you cannot make material for popular consumption that is also accurate to the degree of the actual theories. No matter how hard one tries, the actual formulation of the theory is so advanced that there would be zero chance of anyone not trained getting anything from it - and so one has to make do with what there is at hand.

GeorgeBaxter said:
It isn’t clear ( to me ) why there is a such long.
Because you have not studied Quantum Field Theory. The distribution function is non-zero all the way down to zero. This drops right out of the theory.

Because you have not studied Quantum Field Theory. The distribution function is non-zero all the way down to zero. This drops right out of the theory.
In a literal sense, yes, I have not studied and solved equations of QFT. However fields generally have the form of inverse square law, or some exponential decay with distance. The fall off of the function will depend upon constants associated with field. Eg. G is the Newtonian law of gravity. In principle, an atom at the edge of the observable universe has a non-zero field. Saying "The distribution function is non-zero all the way down to zero." does not really explain anything. Without the detailed equations, and the constants, I cannot make definitive statements about precise distribution with mass.

Do you have a link to the actual distribution?

GeorgeBaxter said:
However fields generally have the form of inverse square law, or some exponential decay with distance.
In space, yes. Here we are not talking about the spatial dependence and the spatial dependence is not as relevant to the understanding.

The spatial dependence, particularly when the width is small relative to the mass, is a Yukawa potential. This follows directly from the propagator of the Klein-Gordon equation of which the Yukawa potential is the Fourier transform.

GeorgeBaxter

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