If we could slowly vary the strength of the strong force.

[Spinnor]

Say we could slowly vary the strength of the strong force. What would happen to the "size" of proton if the strength of the strong force tended to zero and infinity?

Thanks for any help!

 

[Simon Bridge]

If this is part of a course, then you'll have an equation supplied which relates the strength of the strong force to the "size" (as you put it) of the proton. Without that context, any answer here is likely speculation also.

Think about what "size" means in this context.
Try to define "size", and describe it in terms of the strong nuclear interaction.
Then you will have your answer.

 

[Spinnor]

If this is part of a course, then you'll have an equation supplied which relates the strength of the strong force to the "size" (as you put it) of the proton. Without that context, any answer here is likely speculation also.

Think about what "size" means in this context.
Try to define "size", and describe it in terms of the strong nuclear interaction.
Then you will have your answer.

Size in the sense that a proton is not a point like particle at short enough scales such as when high energy electrons are scattered off them. If the strong force were stronger then I'm guessing that the "size" of the proton is reduced, you would need higher energy electrons to prob the smaller structure? I guess what I'm wondering is if the strength is increased without limit would the size just keep getting smaller and smaller or would there be a sort of phase transition where the proton would no longer be stable and would turn into a positron?

Thanks for any help!

 

[Vanadium 50]

A proton is not a "fat positron", so the answer to your question is "never".

 

[kurros]

I think it is an interesting question. Is confinement dependent on the size of the QCD coupling constant? I mean of course the confinement scale is, but if we reduce the coupling enough is there a point that confinement no longer occurs at all, at any energy? I expect the answer must also be yes, just because it seems ridiculous for gigantic bound states to occur, but then what is special about the value of the coupling where the transition occurs? Perhaps in fact confinement WOULD occur always, except that the confinement energy drops to something ridiculously tiny so that everyday interactions would destroy such states. I.e. you would need to create some kind of BEC-style super-cooled cloud of quarks in order to drop the energy sufficiently for a proton to become bound.

 

[Vanadium 50]

I expect the answer must also be yes, just because it seems ridiculous for gigantic bound states to occur,

The universe does not care what humans find ridiculous, I am afraid.

See, for example, Kang and Luty, JHEP 0911 (2009) 065.

 

[fzero]

I think it is an interesting question. Is confinement dependent on the size of the QCD coupling constant? I mean of course the confinement scale is, but if we reduce the coupling enough is there a point that confinement no longer occurs at all, at any energy? I expect the answer must also be yes, just because it seems ridiculous for gigantic bound states to occur, but then what is special about the value of the coupling where the transition occurs?

The theoretical motivation for confinement is the beta function and asymptotic freedom. Confinement will always occur at low energies, independent of whatever the QCD scale happens to be.

Perhaps in fact confinement WOULD occur always, except that the confinement energy drops to something ridiculously tiny so that everyday interactions would destroy such states. I.e. you would need to create some kind of BEC-style super-cooled cloud of quarks in order to drop the energy sufficiently for a proton to become bound.

Yes, if the QCD scale were 1 eV instead of 250 MeV, then the properties of the proton would be vastly different. One would not need a BEC to form hadrons, though it would take much longer for hadrons to form in the early universe.

 

[Simon Bridge]

I once saw a demo where the lecturer had a bunch of objects and asked us to rank them in order of size - there were balls, a pyramid, and a really long rod. Once we'd all ranked them, he said that the object is "small" if it fits through the holes in the garden sieve he had ... and only the real long one would fit. There are lots of ways to describe "size".

You seem to be thinking in terms of the force that "holds the sides in"... so a strong force pulling an object together makes it smaller.

Strong nuclear force holds nucleons together - if it got stronger then nuclei would get "smaller". The size of a hydrogen nucleus is about 1.75fm ... but that is almost unchanged for the helium nucleus, 4x more massive. In which case we may think of a stronger nuclear force, in making the nuclei of helium smaller, would make the nucleons smaller too. But would this affect the hydrogen nucleus - just one proton?

The force internal to the proton is the color force - holding the quarks together to form the proton... which is also the strong nuclear force. So quarks would be more tightly held together... making the proton smaller.

We can also describe size in terms of interaction crossection; in which case, a stronger force makes nuclear interactions more likely - and so, the crossection is bigger.

Though here's a wrinkle - the question concerns changing the strength of the interaction, not it's range. Intuitively we'd link the two but the strong nuclear force is short-range
Does that change things?

So how you argue depends on the model you are using at the time.

One of the things that draws my attention is the stipulation that the nuclear force be varied slowly ... why not quickly? What difference would that make? I'm thinking there is something specific you are supposed to realize by this which will be worth marks if you can work it into your answer.

Though the transition-metaled one is correct - protons and positrons are very different beasties - you may be wondering if there is a minimum size for a proton or maybe it can just keep collapsing into a proton-mass black hole?

Since we are already talking about a magical process for varying the strong nuclear force ... making gluons much stronger ... why not? It's http://theresonanceproject.org/pdf/schwarzschild_proton_a4.pdf . xD But it's probably not worth losing sleep over.

 

[Spinnor]

A proton is not a "fat positron", so the answer to your question is "never".

Using lattice QCD one could make the strong force stronger? Has anyone done this? If so do you know what results?

 

[Vanadium 50]

Using lattice QCD doesn't make a proton a fat positron. The answer is still 'never'.