Mass of a top quark

[Ekpyrotic]

I have a certain problem that has been bugging me. I'll try to set up the problem at straightforward as possible.

 

(1) It is accepted that a top quark has the mass of 174.3 +/- 5.1 GeV, which in analogical terms is about the mass of a gold nuclei.

 

(2) A top quark is much smaller (in size) than a gold nuclei.

 

(3) A top quark can't possibly be more dense than a gold nuclei because it is made of only itself. (disregarding any bizarre fringe physics)

 

(4) So a top quark is the same mass as a gold nuclei, but it smaller, yet not more dense. How is this possible?

 

Thanks,

 

Jordan (Ekpyrotic)

[w=f[z]]

Hi Jordan,

The mass I think you mean to be [math]GeV/c^2[/math]. (Unless you defined c to be 1....)

 

Can you shed some more light on this problem for us? By density, do you mean mass density (there is also number density, etc.)?

 

 

For starters, where does this information/problem come from?

 

Cheers,

w=f[z]

[Ekpyrotic]

Thanks for the answer w=f[z],

 

The mass I think you mean to be GeV/c^2. (Unless you defined c to be 1....)

 

Indeed that is what I meant, I'm prone to stupid-error-blindness when proof reading my posts.

 

For starters, where does this information/problem come from?

 

The problem came from my head, and the information quoted is accessible from a wide range of resources. [1].

 

By density, do you mean mass density (there is also number density, etc.)?

 

I used mass in the previous post because it is the most logical solution. But, in any form it breaks down because density essentially boils down to: amount of stuff in a particular stuff. When we're talking about a top quark the former amount of stuff doesn't exist because it is pointlike.

 

Hope I have articulated myself,

 

Jordan (Ekpyrotic)

[w=f[z]]

If the top quark is indeed pointlike, then wouldn't the density go to infinity? Afterall, if we're talking about mass density, we'd use the formula [math]\rho=m/V[/math].

 

Cheers

[insane_alien]

I have a certain problem that has been bugging me. I'll try to set up the problem at straightforward as possible.

 

(1) It is accepted that a top quark has the mass of 174.3 +/- 5.1 GeV, which in analogical terms is about the mass of a gold nuclei.

 

(2) A top quark is much smaller (in size) than a gold nuclei.

 

(3) A top quark can't possibly be more dense than a gold nuclei because it is made of only itself. (disregarding any bizarre fringe physics)

 

(4) So a top quark is the same mass as a gold nuclei, but it smaller, yet not more dense. How is this possible?

 

Thanks,

 

Jordan (Ekpyrotic)

 

1/ right

 

2/ right

 

3/ why can't it be more dense? a gold nuclei is made of several hundred quarks with space in between. a top quark is a single particle

 

4/ if it is the same mass in a smaller volume then it IS more dense by the definition of density.

[Klaynos]

With fundamental particles volume is a bit of a dodgy concept anyway.... but IA's points are good...

[insane_alien]

I was going to mention that but i don't know enough about it to make a decent stab of explaining it.

[BenTheMan]

Ekpyrotic---

 

This is a question I had once. Here's how I finally got back to sleeping at night:)

 

The thing is, the top quark is fundamental (as you pointed out), so---if you don't believe string theory---zero dimensional! But what is mass, really? In high energy physics, mass is just some arbitrary parameter---the mass comes from the coupling of the particle to the higgs field. So, whereas a gold neucleus is made up of a bunch of up and down quarks which couple very weakly to the higgs field, the top quark couples very strongly to the higgs field.

 

Think of it like this---suppose you have two (metal) blocks and a huge magnet. Now you know that some materials are attracted more strongly to a magnet, so you wouldn't be surprised if you found that one of the blocks was very easy to move around in the magnetic field, and one of the blocks were very difficult to move around in the magnetic field. You would think ``Oh, well, one of these blocks just has a bigger magnetizaion''.

 

The same is true for the top quark and the up/down quarks. The top quark couples more strongly to the higgs field.

 

Hope this helps.

[Ekpyrotic]

Thanks everyone for your swift answers,

 

The thing is, the top quark is fundamental (as you pointed out), so---if you don't believe string theory---zero dimensional! But what is mass, really? In high energy physics, mass is just some arbitrary parameter---the mass comes from the coupling of the particle to the Higg's field. So, whereas a gold nucleus is made up of a bunch of up and down quarks which couple very weakly to the Higg's field, the top quark couples very strongly to the Higg's field.

 

Think of it like this---suppose you have two (metal) blocks and a huge magnet. Now you know that some materials are attracted more strongly to a magnet, so you wouldn't be surprised if you found that one of the blocks was very easy to move around in the magnetic field, and one of the blocks were very difficult to move around in the magnetic field. You would think "Oh, well, one of these blocks just has a bigger magnetization''.

 

The same is true for the top quark and the up/down quarks. The top quark couples more strongly to the Higg's field.

 

BenTheMan that is a great answer/explanation. Thanks for taking the time to write it. I suppose the next question that the topic is begging for is why does a top quark interact so much more in the Higg's field than an of the other quarks/leptons.

 

But I don't suppose particle physics has the answer to that yet.

[swansont]

Two notes:

 

Referring to mass in terms of energy is a common shorthand in physics; the c^2 is inferred.

 

Neutrons and protons that comprise nuclei are made up of up and down quarks, so the comparison with the top quark mass with a gold nucleus isn't really apt. I'm not sure in what mesons the top quark appears, if any.

[Ekpyrotic]

Hi swansont,

 

Neutrons and protons that comprise nuclei are made up of up and down quarks, so the comparison with the top quark mass with a gold nucleus isn't really apt. I'm not sure in what mesons the top quark appears, if any.

 

I'd hate to question your scientific prowess, but isn't this equivalent to saying you can't compare the mass of a chair and a human because they are made of different materials.

[insane_alien]

i think he means the energies involved, with a gold nuclei you have a binding energy that is accountable for a bit of the mass. with a top quark on its own(we don't know if this is even possible) there would be no binding energy. this throws comparisons off.

[BenTheMan]

BenTheMan that is a great answer/explanation. Thanks for taking the time to write it. I suppose the next question that the topic is begging for is why does a top quark interact so much more in the Higg's field than an of the other quarks/leptons.

 

But I don't suppose particle physics has the answer to that yet.

 

This is the same as asking ``Why is gravity weaker than electromagnetism?'', or, more directly ``Why is an electron's mass 511 keV?''. There may not even BE an answer. This is more of a philosophical question, in some sense.

 

Suppose that there are an infinite string of universes (like the Ekpyrotic scenario, which I think you are familiar). Now, suppose each time a universe is created, the coupling constants and such are random values. Well, with an infinite string of universes, it should be no surprise to find values SOMEwhere that are similar to the values of things like masses that we observe here in our universe.

 

This is bordering on something called the anthropic principle. One can note that, without very specific values for fundamental constants in our universe, intelligent life would be impossible. (For example, if the cosmological constant were not small and positive, then the universe would expand too quickly for life to evolve, or it would collapse back on itself.) But because there is intelligent life, the fundamental constants have to be exactly as they are.

 

It is a circular argument, to be sure. And some people really hate it. I'm not such a huge fan myself.

 

Either way, you can either accept the anthropic principle, or accept the fact that there is some deeper theory which predicts things like masses of top quarks, like string theory.

[swansont]

Hi swansont,

 

 

 

I'd hate to question your scientific prowess, but isn't this equivalent to saying you can't compare the mass of a chair and a human because they are made of different materials.

 

 

If you questioned how it was somehow odd or contradictory that a chair could be more massive and dense than a person, then, yes. The implication (to me) was that there was some conundrum in having the top quark be as massive as a gold nucleus, but a gold nucleus contains no top quarks.

[Ekpyrotic]

BenTheMan:

 

This is bordering on something called the anthropic principle. One can note that, without very specific values for fundamental constants in our universe, intelligent life would be impossible. (For example, if the cosmological constant were not small and positive, then the universe would expand too quickly for life to evolve, or it would collapse back on itself.) But because there is intelligent life, the fundamental constants have to be exactly as they are.

 

This makes a lot of sense, I've been subject to the narrative fallacy. (have you read 'Black Swans' by Nassim?) Thanks for the clarification.

 

Swansont:

 

If you questioned how it was somehow odd or contradictory that a chair could be more massive and dense than a person, then, yes. The implication (to me) was that there was some conundrum in having the top quark be as massive as a gold nucleus, but a gold nucleus contains no top quarks.

 

I must have worded my question badly. The problem was in having the top quark as massive as a gold nucleus, yet much smaller in size. However we couldn't say it was more dense.

 

Hope that has cleared up the issue, thanks,

 

Jordan (Ekpyrotic)

[BenTheMan]

Ekpyrotic:

 

About ``Black Swand''---I've seen it in the book store but haven't read it. Is it worth the money?

 

And, again, it doesn't much make sense to talk about ``densities'' of fundamental particles.

[Ekpyrotic]

About "Black Swan"---I've seen it in the book store but haven't read it. Is it worth the money?

 

It depends on what you like, it's a pretty vigorous analysis of the world (particulary economics) from a mathmatical slant. Although it's very easy reading. Worth reading the blurb and seeing whether it piquets your interest, very well written.

 

And, again, it doesn't much make sense to talk about "densities" of fundamental particles.

 

It's a matter of habit, I'll try and stop.

[foodchain]

Ekpyrotic---

 

This is a question I had once. Here's how I finally got back to sleeping at night:)

 

The thing is, the top quark is fundamental (as you pointed out), so---if you don't believe string theory---zero dimensional! But what is mass, really? In high energy physics, mass is just some arbitrary parameter---the mass comes from the coupling of the particle to the higgs field. So, whereas a gold neucleus is made up of a bunch of up and down quarks which couple very weakly to the higgs field, the top quark couples very strongly to the higgs field.

 

Think of it like this---suppose you have two (metal) blocks and a huge magnet. Now you know that some materials are attracted more strongly to a magnet, so you wouldn't be surprised if you found that one of the blocks was very easy to move around in the magnetic field, and one of the blocks were very difficult to move around in the magnetic field. You would think ``Oh, well, one of these blocks just has a bigger magnetizaion''.

 

The same is true for the top quark and the up/down quarks. The top quark couples more strongly to the higgs field.

 

Hope this helps.

 

Pardon me if this is off topic, but what mediates the higgs field?

[BenTheMan]

Pardon me if this is off topic, but what mediates the higgs field?

 

Why, the higgs boson, of course!

[Severian]

Let me try and answer a few of the things in this thread.

 

1. If you collapse the top-quark wavefunction to a point, then it is indeed infinitely dense (much more than a gold nuclei).

 

2. Since you cannot measure position infinitely accurately, you can never collapse it to a point, so the density is finite but very large (still larger than a gold nuclei).

 

3. The question 'what mediates the Higgs field' is ill-posed, since what is being mediated? One normally uses the word 'mediate' in the context of a force, and even though the Higgs boson does transfer momentum, it is usually not thought of as mediating a force. Indeed, the 'Higgs field' and the 'Higgs boson' are not the same thing. The Higgs boson is a quantum of oscillation of the Higgs field about the vacuum state.