Beta Decay, how can baryons produce Leptons ?

[JPC]

Hey

I know :
n = p+ + e- + (Ve)

meaning that :
p+ = n - e- - (Ve) = n + e+ + Ve ??

But, how does a Baryon like a proton or a neutron produce leptons ?
and how this change can occur :

n = p+ + e- + (Ve)
u d d = u u d + e- + (Ve)

How can a down quark become a Up quark ?
and where do the leptons come from ?

 

[malawi_glenn]

No you do totally wrong.

1. Protons don't decay, they are stable.

And IF protons decayed, this is the process:

p -> n + e- + anti(electron-neutrino)

You have to conserve electron-lepton number.

I don't think any of us has time to teach you all properties of elementary particle reactions, but I am sure we can give you good places to start reading about them.

But to answer your question how an up-quark can become a down-quark, it has to do with exchange of a W-gauge boson, i.e the weak interaction.

 

[JPC]

No you do totally wrong.

1.
And IF protons decayed, this is the process:

p -> n + e- + anti(electron-neutrino)

You have to conserve electron-lepton number.

but, a lot of sources on Internet say proton decay would emmit a positron and not an electron like a neutron decay
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/proton.html

 

[malawi_glenn]

yeah i did the sign wrong, but you must have an ANTI-electronNEUTRINO, in order to conserve letpon number.

http://www.revisionworld.com/files/betadecay.jpg

There you see how the W-boson comes in.

 

[JPC]

Oh ok, but now how does the Quark produce a W-Bosson, with what energy, and how ?

///////////////

But what is wrong with saying this :

n = p+ + e- + (Ve)
p+ = n - e- - (Ve) = n + e+ + Ve ??

I don't know much about nuclear physics yet, but to me would sound logic if
-e- = e+
-e+ = e-

-Ve = (Ve)
-(Ve) = Ve

About notations, if i am using the right one, for particules with no charge, puting a ( ) around means anti right ?

 

[malawi_glenn]

produces? It has to do with the weak interaction, it is a gauge boson.. force carrier of the weak interaction. Quarks have "weak charge".

Ok, you did not clarify your notation, sorry, next time I'll use latex.

 

[blechman]

hold it, guys! If you're looking for proton decay on the internet, you'll be very confused.

Malawi_glenn is right in that the proton cannot decay in the standard model, simply because it is the lightest baryon, and baryon number must be conserved. HOWEVER, people are looking for proton decay because it is a typical prediction of physics beyond the standard model. Such decays violate baryon AND lepton number, so that the final decay is

p\rightarrow\pi^0 e^+

This violates both lepton and baryon number. When you see searches for proton decay, this is the kind of decay people are talking about. It is predicted in models of supersymmetry, grand unification, etc.

 

[malawi_glenn]

Yes, but if nothing else is mentioned, the standard model is assumed.

And also JPC, how does electrons emit photons in QED? How does quarks emit gluons in QCD ?

Those quesions are much diffucult to answer, first one has to accept that this is how it works. Maybe in a PhD course, you'll learn "how" these interactions are derived.

 

[blechman]

Yes, but if nothing else is mentioned, the standard model is assumed.

but JPC was talking about proton decay to a positron on the web, and the only such decay is the one that I was referring to. And it is the decay that people are looking for in proton decay searches.

 

[JPC]

Ok

and why cannot there be a proton decay ?
you say its because it is the lightest baryon, but since u quarks are lighter, wouldn't it mean that uuu is lighter than a proton ?

does this mean that a uuu baryon is not stable, or cannot exist ?

////

and what is the 'baryon number must be conserved' you are talking about ?

 

[malawi_glenn]

it is a differnce between the constituent quark masses and the total baryon mass. In the baryon you also have a sea of gluons and quark-antiquark pairs due to the strong interaction. The up/down quarks has mass of about 4MeV/c^2. the protons mass is 938.27 Mev/c^2 .. now solve that equation ;)


So the lightes baryon is the proton, and second lighest is the neutron. The uuu system is called:

\Delta ^{++} has mass of approx 1232MeV/c^2 (there is also excited states with higher mass etc)

 

[JPC]

so u mean that in a proton there is only like 12 Mev / c² mass for he 3 quarks
and that 926.27 Mev / c² mass is gluons, quark-antiquark pairs ?

 

[malawi_glenn]

Yes, that is correct. Most of the baryon mass comes from the gluon-quark-antiquark sea. Same holds for the mesons of course.
The \pi ^0 meson has mass about 139MeV/c^2 and so on. Welcome to the wonderful world of particle physics =D

 

[MaWM]

Actually, that mass comes from the confinement of the quarks. The uncertainty principle requires that there is a relationship between uncertainty in position and in momentum. Confining a quark to something as small as a proton means it must have an extremely high momentum. It is this extra kinetic energy that gives the proton most of its mass.

 

[malawi_glenn]

Actually, that mass comes from the confinement of the quarks. The uncertainty principle requires that there is a relationship between uncertainty in position and in momentum. Confining a quark to something as small as a proton means it must have an extremely high momentum. It is this extra kinetic energy that gives the proton most of its mass.

I can quote like 10 books in particle physics that confirm my post. have you been taught this in your particle physics courses?

 

[MaWM]

Yes, actually. I'm trying to find a reference online. If you do the calculations using the uncertainty principle, the numbers are pretty good.

 

[malawi_glenn]

Pretty cool so what forces is holding the proton together?

And i want textbook references, what course book did you have?

I can tell you: Read "Particles and Nuclei" by Povh, great intro.

The HUP can explain "why", but don't "how". The momentum distribution of the valence quarks are not fitting here. And as my first sentance implies: The force is mediated by gluons, and gluons are constantly producing quark - antiquark pairs.


If the answer was just "HUP" , then one of the main focuses on todays research in hadron physics would be solved..

 

[blechman]

malawi_glenn and MaWM are saying the same thing!

It is true that most of the energy that goes into the proton (and other hadron) mass comes from the virtual sea quarks and gluons.

Putting it a different way, the HUP says that you can create a bunch of particles from the vacuum carrying a lot of energy (\sim\frac{\hbar c}{1 {\rm fm}}). So you both are in agreement!

 

[malawi_glenn]

I know we are saying the "same" thing,

I just tried to point out that saying that it is the momentum of the three quarks that give rise to higher kinetic energy and hence higher mass (of those 3q) due to fundamentals of special relativity is a quite naive picture.

 

[JPC]

What i don't understand , is that if around the 3 quarks there is a cloud of pions, wouldn't they anhilate each other, like if in this cloud there is a (u)d and a (d)u, these 2 would become energy ? forming gluons too ?

i don't know much about gluons, appart from the fact that baryons send flavored gluons to each other, and that we can list 9 flavors, but that there are actually only 8 (never really understood that yet)

 

[malawi_glenn]

no not pions, now you are mixing up baryons and nucleis. The gluons are constantly beeing producing quark-and antiquark (of same kind), beeing annihilated again after a small small time.

g \rightleftharpoons u + \bar{u}

Quarks "emitts" gluons, gluons are the force mediator of the colur force (QCD). How baryons interact strongly is a bit more complicated, see for example the strong nuclear force thread that was created a few days ago.

There are only 8 gluons, they comes from group properties of QCD gauge theory. I have not reached that level were you derive all this yet, so a more educated person in gauge theories of QCD can tell you a bit more how this result is done :)

And also, glouns carries colour, not flavor; and there are 6 colours. Red, blue, green and their anti.

 

[blechman]

i don't know much about gluons, appart from the fact that baryons send flavored gluons to each other, and that we can list 9 flavors, but that there are actually only 8 (never really understood that yet)

As Malawi_glenn points out, there are gluons that mediate the QCD force. One way to see that there are 8 gluons is as follows: the gluons have a color and an anticolor. Since there are three of each, there are a total of 9 possible pairings. But if you look carefully, one of the 9 gluons turns out to have no net color at all (r\bar{r}+g\bar{g}+b\bar{b}). This last gluon is therefore color-neutral and therefore does not feel the color force (just like electrically neutral objects don't feel the electromagnetic force). So if there were a ninth gluon (called a "color singlet gluon") then we should see a gluon flying around free. We don't, so we conclude that it isn't there.

For the more technically minded: what this is saying is that the gauge group of QCD is SU(3) and not U(3). That this is true is empirical fact. I don't know of any convincing argument from first principles. As an added bonus: in the early days of QCD (mid-to-late 1970's) experiments were done that "counted" the number of gluon-types. The answer was in wonderful agreement with 8.

 

[JPC]

One way to see that there are 8 gluons is as follows: the gluons have a color and an anticolor. Since there are three of each, there are a total of 9 possible pairings. But if you look carefully, one of the 9 gluons turns out to have no net color at all (r\bar{r}+g\bar{g}+b\bar{b}).

oh , so u mean a red-antired, a green-antigreen , and a blue-antiblue cannot exist together ? ?

meaning that one of those (red-antired, green-antigreen, blue-antiblue) cannot exist ?

 

[malawi_glenn]

You can, only get totally 8 glouns that carry coluor. For each interaction, coulor of a quark is destroyed and it gets new colour.

For example:

g_{g\bar{b}}

Changes coluor from blue to green.
So a colourless gluon has no meaning, also the total system of quarks must have net colour zero. And you can not have a colourless gluon.

I hope blechman or some other will explain this in its fully details ;)

 

[JPC]

but what do u mean by colorless ??
these should be colorless then : green-antigreen, blue-antiblue, red-antired ??
meaning that there would only be 6 gluons ??
but since there are 8, i know there's something i haven't understood

///

For example:
g_{g\bar{b}}

what does the 'g' represent ? green ? but of what ?
and the {g\bar{b}} represents a green-antiblue gluon right ?

 

[malawi_glenn]

Colorless is of course when the total color is white; green + red + blue = white. Green + anti green = white; etc.

the big small g is GLUON, and the subscripts are of course: g is green, blue is b etc, and a bar means anti in particle phyiscs language.

So g_{g\bar{b}} is a gluon carrying green and anti-blue colour.

The gluons you have are the following:

g_{b\bar{r}}, g_{b\bar{g}}, g_{g\bar{r}}, g_{g\bar{b}}, g_{r\bar{g}}, g_{r\bar{b}}, g_{01}, g_{02}

Where g_{01}, g_{02} are linear combinations of g_{b\bar{b}}, g_{g\bar{g}}, g_{r\bar{r}} These things might seem very odd, science we told you that gluons must carry net colur, but I found an article about this, that seems to be at a level you can understand.
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/gluons.html

WHY the r\bar{r}+g\bar{g}+b\bar{b} is colorless, but not r\bar{r}-g\bar{g} . i leave to blechman, was a time since i studied particle phyisc;)

 

[blechman]

The fact that r\bar{r}+g\bar{g}+b\bar{b} is color-neutral, while r\bar{r}-g\bar{g} and r\bar{r}+g\bar{g}-2b\bar{b} are not follows if you think about what's happening in a Feynman diagram. In particular, you always sum over all the colors (since you don't actually observe color, you have to sum over it since this is quantum mechanics!). The two "good" gluons change the quantum amplitude; for example: a red quark goes to a red quark, and a green quark goes to MINUS a green quark. The minus sign makes all the difference in the sum.

The color neutral gluon, however, does absolutely nothing to the amplitude - it doesn't change anything, so it really is a "color-neutral" gluon. I will augment Malawi_glenn's response a little by just mentioning that there is no reason, a priori, why there shouldn't be a color singlet gluon (people used to think it might be the photon, but it turns out this doesn't work). It is just empirical fact that there is no such beast.

Finally, you might be wondering why we chose these particular linear combinations? Unfortunately, I don't have a very good answer to that, except that it follows from group theory that these are the right linear combinations to use; that is, they have all the correct transformation properties.

 

[arivero]

The fact that r\bar{r}+g\bar{g}+b\bar{b} is color-neutral, while r\bar{r}-g\bar{g} and r\bar{r}+g\bar{g}-2b\bar{b} are ...

Finally, you might be wondering why we chose these particular linear combinations? Unfortunately, I don't have a very good answer to that, except that it follows from group theory that these are the right linear combinations to use; that is, they have all the correct transformation properties.

Well, at least he can notice they are orthogonal (1,1,1), (1, -1, 0), (1,1,-2).

 

[JPC]

r\bar{r}-g\bar{g} and r\bar{r}+g\bar{g}-2b\bar{b}

But these are groups of gluons
i mean, what's the color combination of the 2 special gluons ?

 

[malawi_glenn]

as Blechman said, you must put this into a Feynman diagram and see.

"In particular, you always sum over all the colors (since you don't actually observe color, you have to sum over it since this is quantum mechanics!). The two "good" gluons change the quantum amplitude; for example: a red quark goes to a red quark, and a green quark goes to MINUS a green quark. The minus sign makes all the difference in the sum."