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 totaly 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 totaly 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."

 

[JPC]

this :
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/imgpar/feynm5.gif ??

 

[malawi_glenn]

well, more detalied ones.. I thought you know how to draw Feynman diagrams for QCD...

personally I don't have time to find or draw them for you (Dont think Blechman have the time too), trust Blechman =)

 

[JPC]

But when you have time can you send me the url where i can find the specific one please ?

 

[malawi_glenn]

why not just wait til you take particle physics course?

 

[JPC]

because in france if i want to do a such program i need to first be accepted in the top engineering schools (in France you we also call schools the sort of good universities).

And to be accepted into these, i must do 2 years of what we call here ' scientific prepa', its like you study maths and physics, with loads of exercises, loads of revisions, a very tough program.
And then at the end you can pass a contest, and the schools will look at the your score, and they will all try to take the best elements (like for the top one 'Polytechnique', out of 40 persons who do scientific prepa, only 1 is accepted) (for second rate ones, something like 15) (and the 24 ones left have to end up in medium schools)

And its just after, if you at least end up in second rate schools, that you can actually start to study things like particule physics, ect

And, right now, I am in 'Terminale ' (12th grade), so if i ever get to learn all of this, its in 2.5 years.

But if i manage to do all those studies, i would like to work in USA, be able to use more modern equipment, NASA sounds interesting, but its hard for a non-american person to work in NASA, unless if you are a universal genius.

 

[malawi_glenn]

Ok.

If you want, we can give you things to do self studies. You need quite much for studiyng particle physics. I can recommend getting a copy of "Introduction to Quantum Mechanics (2nd Edition) by David J. Griffiths " And when you have worked it through and done problems in it and so on, you get "Introduction to Elementary Particles " by same author, 2nd edition comess in march, so hold on, it is regarded as the best intro book in particle physics.

 

[jtbell]

If you want to work in particle physics, NASA is not the place to go. They don't do particle physics (at least not much of it). Particle physics researchers in the USA are mostly hired by universities. Some also work for the laboratories where the accelerators and detectors are actually located (Fermilab, Stanford, Brookhaven).

 

[vanesch]

And its just after, if you at least end up in second rate schools, that you can actually start to study things like particule physics, ect

And, right now, I am in 'Terminale ' (12th grade), so if i ever get to learn all of this, its in 2.5 years.

Although "polytechnique" is probably a good place to go to make a lot of money, it is probably not the best place in the world to do particle physics! I'd say, if you want to do particle physics, try to go to "normale" (just as hard to get into as poly probably). They'll turn you into a true nerd You'll be way smarter, but you'll make less money

And then, there are of course the universities where you can go to, to learn the stuff. I think there are some good courses around... but of course, coming from a university, the chances of really getting a job in particle physics will be remote, as compared to a "normalien".

However, you should really seriously think about what you want to do with your life. I for one, left particle physics because I was disappointed in the day-to-day work. It doesn't have much to do with what you read in the scientific journals, and the things I really did was second-rate computer science, electronic engineering and a little bit of physics. I did more sophisticated things outside the field actually.
Also, the timing might be not right. LHC will start taking data soon, and by the time you'll get in (in 4-5 years), the hottest pieces will be taken already (Higgs, supersymmetry, new stuff ?). It's my experience that smaller scale science and engineering is actually much more rewarding (unless you're really a hot shot), because you can tackle a much broader range of problems and challenges, and you can take responsability for a bigger chunk of a project. But ok, that's my opinion.

 

[JPC]

no but what you don't see , is that in France, universities are not at all the same as in USA.
A university in france is not of a very good level, and a lot of people who do universities don't get a job.

And my parents are not rich enough to pay me a University In USA. Well they could if France seriously decreased its taxes.

But if i cannot do particule Physics, i am also considering working on Space ingeneering (here i think the best would be NASA) (example : working on the reactors of the new shuttles)

Anyways, i still have 2.5 years to choose what i want to do.

Right now i am just getting informed about both options.
And maybe i'll be interesting by another option in 2.5 years, who knows, but it will be scientific that's for sure

 

[blechman]

Alright, JPC, I can't give you advice on what to do with your life (I'm having enough trouble of that myself!), nor do I know much about the status of physics research in France. But I can tell you what is involved in studying particle physics. Of course, this is STRICTLY my humble opinion and personal experience, so don't take my suggestions too literally - everyone's different, after all. This is how things would go in a perfect world:

(1) The first step is to get a good grounding in general physics, including classical mechanics, E&M, Quantum mechanics and stat mech. This is the core of the field, and if you have any desire to contribute to *any* subfield of physics, you must have a firm grip on these things. They permeate all the fields of "modern physics". Not to mention, that if you get a solid background in these things, you can probably go on to do almost anything (engineering, space science, etc).

(2) While you're studying these things, read a bunch of popular science books. Get hold of "Scientific American" or "Physics Today" or your favorite science magazine. As you read more of these books/articles along with your studies in (1), you will begin to understand more and more of how to think correctly, and the kind of research that is done in the field. If you can go to public lectures or seminars, you should do that too. If wherever you go has opportunities for research projects, try to get one.

(3) Once you have a solid background in these things, get an introductory book on particle physics. Zee's "QFT in a Nutshell" is good; so is Griffiths "Intro to Particle Physics". I emphasize that these books will be of limited use to you if you do not take my advice in (1)!

(4) Now begin to study the subject in earnest, with Peskin & Schroder's text, or an equivalent. Usually, this doesn't happen until you get to grad school.

This is the long-term program that you would follow if you want to become a good particle physicist. It's not an easy road, taking typically something like 10 years of school work past secondary school.

As far as affordability: you should check out financial aid opportunities at US universities. Sometimes they can offer you fellowships. I don't know much about how to proceed as a foreign student, but do some reseach, call (or email, it's cheaper!) the financial aid offices of a bunch of places, and see what you can do. That's what I did when I was looking for undergrad schools.

Good luck!

 

[vanesch]

no but what you don't see , is that in France, universities are not at all the same as in USA.
A university in france is not of a very good level, and a lot of people who do universities don't get a job.

But then polytechnique and normale are very good, and even others like arts et metiers, or mines. If I were you, I'd try to do everything to get into a "prepa". In France, it is the way to go. I would even be picky in *which* prepa, because not all are the same. Apply at different places. The first years of university are not very good I've heard. Give yourself all the chances you can, because the French system is such, that about all decisions are taken in the 18-21 year span. So full throttle ahead from now on! Put all other aspects of your life aside for a few years.

In 2 years, if you're successful, you will have several options open, and you'll be more informed by then.

 

[JPC]

Zee's "QFT in a Nutshell" is good; so is Griffiths "Intro to Particle Physics".

But which explains better ? I mean which is less made of long sentences, but more scientific sentences, and better illustrated ?

But then polytechnique and normale are very good, and even others like arts et metiers, or mines. If I were you, I'd try to do everything to get into a "prepa". In France, it is the way to go. I would even be picky in *which* prepa, because not all are the same. Apply at different places. The first years of university are not very good I've heard. Give yourself all the chances you can, because the French system is such, that about all decisions are taken in the 18-21 year span. So full throttle ahead from now on! Put all other aspects of your life aside for a few years.

In 2 years, if you're successful, you will have several options open, and you'll be more informed by then.

I know, that's what i am aiming at doing. I am looking to PCSI in one prepa in the top 15 in France for PCSI//////////////PS : sorry for late reply, but i had lots of work this week

 

[malawi_glenn]

Both are good intro books on QFT / particle physics. But just because they are intro books, they are not easy.

Griffiths is well know for his pedagocical skills.

 

[JPC]

then i should choose 'intro to particle physics' then ?
btw, i can't find it on google book search beta
got a url or a ISBN ?

 

[malawi_glenn]

then i should choose 'intro to particle physics' then ?

It is probably more suited for you, if you want to know fenomenological particle physics.

 

[jtbell]

got a url or a ISBN ?

Search for it on amazon.com. It will tell you the ISBN.

The title is actually "Introduction to Elementary Particles," by the way. But I found it easily with a search for "Griffiths particle physics."

 

[JPC]

Ok found it , thx
I'll buy it during the summer holidays, after i graduate
but didnt know a book could be worth 100 USD

 

[malawi_glenn]

wait til march -08 when the new edition comes. this book is from middle of the 80's. So it is quite expensive so you also want the newst stuff in particle physics right? ;)

 

[JPC]

Yeah ok
but do you have an idea of the mean average price ?

 

[malawi_glenn]

Just search the major book shops on the web.

www.alibris.com
www.amazon.com

etc.