Exploring Lepton Annihilation and Hadron Formation in the Standard Model

[snapback]

Imagine you have electron and positron (leptons) falling towards each other. The interaction between these two is electromagnetic at long distances. It is well established that this reaction eventually leads to annihilation of these two particles. Now consider electron and proton(hadron) falling towards each other. Now, the interaction between these two is again electromagnetic at long distances. However, this process does not lead to annhilation, but a stable compound is formed instead (Hydrogen).

Which force (in the framework of the standard model) is responsible for the difference between these two cases ?

thanks

 

[malawi_glenn]

The electron and the positron are each others antiparticles, whereas the protons antiparticle partner is the antiproton.

In the interaction, all quantum numbers must be conserved, and a proton, which is build up by quarks, have more quantum numbers such as flavour and colour, so in the final state you can't get a photon which is an elementary particle with just spin as quantum number.

So it is a conservation law consideration.

 

[snapback]

So it is a conservation law consideration.

thanks.

to me, a conservation law, is the expression of some underlying symmetry of the governing equations (e.g. in classical physics, the consevation of the angular momentum corresponds
to invariance of the Hamiltonian wrt to rotations, compare Noether theorem).

Now you state that the necessity of conservation of the "special" proton quantum numbers as "flavour and colour" forbids the creation of a photon out of the interaction between electron and proton (this would be annihilation) . To me, positron/electron is a compatible pair of particles (being antiparticlea) whereas the system proton/electron obviously is less symmetric. Why there are then more conservation laws ?

 

[malawi_glenn]

conservation of flavour and colour, on the quark level. And strong isopsin on the nucleon level.

Why there are more conservation laws? Well you have more symmetries than U(1) - gauge symmetry, that is the obvious answer.

 

[snapback]

if you look at the nucleon alone , then I agree, it has on its own additional symmetries. But I prefer to look at the compound system, which contains two particles: for this you gain additional (nucleus) symmetries but of course you lose the particle/antiparticle symmetry when you go from positron/electron to proton/electron. To me , it sounds like a trade-off ;-).

But actually I would like to repeat my original question: Which force (in the framework of the standard model) is responsible for the difference between these two cases ? Naively speaking: if it is the electromagnetic interaction which is responsible that opposite charges are falling against each other, which force (or if you prefer interaction) counteracts the falling and prohibits annihilation in case of proton/electron.

 

[jtbell]

which force (or if you prefer interaction) counteracts the falling and prohibits annihilation in case of proton/electron.

Protons aren't fundamental. Quarks are. How do you annihilate a charge -1 electron with a charge +1/3 or -2/3 quark?

 

[malawi_glenn]

The proton has isospin symmetry quantum number, so since the proton also interact with the strong force, you can't get e^- + p -> Gamma

Also you need to forget about the picture that particles are tiny balls which "falls into each other". There is no force that acts as something "repulsive" in the e^- + proton system. In the analogous way, there is no force acting repulsive in the Pauli exclusion principle in degenerate matter. The thing is simply that there are no available states to go into. In the same way, the electron can't annithilate with a proton to make a photn since in that interaction symmetry of isospin will be violated. (however this invokes the z-component of isospin. The total isospin can be violated, e.g in decay pion0 -> gamma gamma )

An electron and a proton can interact with the Weak force, which CAN violate isospin and other symmetries, that is the peculiarity of the weak interaction.
electron + proton -> Neutron + neutrino
That is an ok interaction.

But I have to stress again that you have to forget about the picture of particles as tiny balls and the interaction as a physical collision of such.

 

[snapback]

But I have to stress again that you have to forget about the picture of particles as tiny balls and the interaction as a physical collision of such.

I never mentioned that I consider the particles as tiny balls.
I used the picture of "falling things" because the idea of electromagnetic interaction
was developed from macroscopic observations, where you always observe that opposite charges are attracting each other
via a certain force (simply consider the case of electrostatic discharge or any electric circuit). This idea of interaction was then extrapolated to the
microscopical world, and it is still used in any QM/QFT calculations (this is at least my impression, please correct me if I'm wrong)

Of course, you can argue that there is makes no sense to use classical notions in microscopic world, but then you might allow the question, whether it is the "same" electromagnetic interaction which we observe at macroscopic or microscopic scales.

The thing is simply that there are no available states to go into

Do you suggest to consider this sentence as a basic postulate ? Or can it be derived
from some more fundamental ?

 

[snapback]

Protons aren't fundamental. Quarks are. How do you annihilate a charge -1 electron with a charge +1/3 or -2/3 quark?

I let the electron collide with a suitable number of quarks, which might need to be in a specially prepared state.

 

[malawi_glenn]

Since you used that language, I argued against it - I read what I read.

You are asking about the Pauli Principle now? Since that sentence was connected to my excursion to the P principle that there are no "force" that prevents things to happen, and in the case of the pauli principle it is from the postulate that identical fermions can not occupy the same quantum state.

 

[malawi_glenn]

I let the electron collide with a suitable number of quarks, which might need to be in a specially prepared state.

So what you need is a many body interaction, or an effective interaction.

If you want reading tips, we are more than helpful to assist. This is quite often asked question.

 

[snapback]

I read what I read.

this is sometimes the drawback of written communication ;-)

You are asking about the Pauli Principle now?

No, I guess this is something for another thread, many topics inside one thread too easily lead to a kind of divergence (at least without moderator)

If you want reading tips, we are more than helpful to assist.

Yes, a good readable, not too formal review article covering both theoretical and experimental aspects of this "many body interaction" would be surely helpful. In addition, are you aware of any good reference to experimental data on "spectral lines" of positronium ?

 

[malawi_glenn]

That statement was done for the pauli principle, so that's why I aksed. You asked about a sentence for the pauli principle, but now you didn't wanted an answer.. strange :P

The statement "if there is no state to

I think Griffiths book on elementary particle physics will suite you well, check out the newest edition. The thing is simple, there is no such coupling between the electron and the proton to make an electron and a proton make a photon.

In the same way, an electron and a positive muon can't combine to make a photon. Then we have an interaction of 2 leptons, so we can totally forget about that "many body problem" of the proton. The leptons carry lepton family number, which would be violated in that interaction.

And speak about divergences, why asking about positronium levels now? :S

 

[snapback]

You asked about a sentence for the pauli principle, but now you didn't wanted an answer.. strange :P

This is not strange, actually, when I posed my question about positronium, I was expecting some discussion about positronium. You brought PP into play, we could discuss this too but not in this thread.

And speak about divergences, why asking about positronium levels now? :S

Why not, when speaking about positronium all aspects need to be considered, stereotyped thinking too often results in missing important points,

Finally, after about 50 posts I realized, that I obviously chose the wrong forum for debating about advanced topics in physics. At least I do not have the impression, that my questions are taken seriously here.

Nevertheless, thank you for your efforts and good luck

Regards

Snapback

 

[malawi_glenn]

Well the thing is that I brought up the Pauli principle was to discuss the general feature of forbibben processes - that there is no "force" involved - since you seemed to have an impression that there is a "force" that prevails proton and electron to form a photon.

When you later commented on a statement I did about the Pauli Principle, and asked for an elaboration, I was suprised, since that was just a side remark done by me. Therefore I asked if you really wanted an answer on that, and you said "no". That was strange I think.

Your question was why eletctron + proton is stable and does not annihilate.

I don't think this is an advanved question, we have quite more advanced things going on. The thing is perhaps that this question is asked by a person who does not have a strong background in particle phy

 

[snapback_]

The thing is perhaps that this question is asked by a person who does not have a strong background in particle phy

You are, perhaps, making too many assumptions but this is always easy when one is sitting in an ivory tower. If you are not willing to answer my question in a polite and assumptionless way, you do not need to. I will survive this.

 

[malawi_glenn]

It is hard to help a person who does not explicit state his background and current status.

When one make statements such as particles falling into each other and asking "which force is responsible within the standard model to prevent the particles to falling into each other" it is hard to judge if the person asking have understood even the basic concepts of the standard model.

As I said, I read what I read.

I want to answer your questions, but it is hard since I don't know where you are.

regarding positronium energy levels, I have a theoretical paper which is quite recent who has a lot of references to experimental studies. Asking that question in a new thread would be more fruitful however.

So, you came back, why?

 

[snapback_]

I don't know where you are.

For me it does not matter (at least in a forum) what the background of a person is. If somebody is asking me a question in his "language", I first try to answer him in the same "language". Otherwise, he might get the impression, that his question is not taken seriously. I consider answering in a different "language" as bad style (but this is of course everyones free choice, how he answers).

I used the provocative formulation with this "things falling against each other" to check the general reaction. I'm often surprised how dogmatic physics became: if one is trying to describe microscopic things and uses classical terminology for this purpose, he is too often immediately labelled (in best case) as "antiquated". Where there is written which language I shall use to describe something ? If I would work mainly with macroscopic things, say, length scale 28nm and above, I would maybe say (the following is not to be taken personally) : "what is all that advanced particle physics stuff about ? If you ask the particle guys to explain in their "language" how "Ohmic law works", they say, oh no, you need to use another formalism". But does it not mean, that the particle formalism is also somehow limited ? So why give that particle formalism a preference when discussing positronium ? Just because you can better calculate at the expense of understanding ?

regarding positronium energy levels, I have a theoretical paper which is quite recent who has a lot of references to experimental studies. Asking that question in a new thread would be more fruitful however.

I'll give that some thought.

So, you came back, why?

Maybe I simply want to have the final say in this thread ;)

 

[malawi_glenn]

I more concerned to teach "the real deal" then by invoking false analogies. If someone thinks that there is some kind of repulsive force or similar that prevents electron and proton going into a photon, I must respond. The question was "which force within the standard model", and since the question tells quite much about the person who asked it one might easy suggest that there is a misunderstanding going one. The question is related to "which women is the president of the United states of America?". The answer is "none".

If one knows basic quantum physics and something about the standard model of elementary particle physics want to know why a certain reaction is not possible, why not saying so? If I want to understand something at the level I am now, I don't use language so the guys I am asking think that I am a totally newbie and first needs to be taught the basics...

If you ask particle physicists about particle physics, you should not be too surprised if you get particle physics answers and descriptions of physical processes. Since you seemed to have some disbeliefs in particle physics, we (I) tried to sort things up for you.Understanding and calculation abilities goes hand in hand. Believing that one understands something is not the same as actually understanding it. I can think that I understand what supersymmetry is since I know that it is a symmetry between bosons and fermions, but when I consult the Weinbergs QFT part 3, I am lost already on page 17.. so do I understand it or not?

The experimental results are from the early 80's, but the paper I have is from 2008. Why are you interested in knowing these energy levels?

 

[DeShark]

electron + proton -> Neutron + neutrino
That is an ok interaction.

Can I hijack this thread a little (since I don't see where it's going other than to argument and dispute over petty things like ego and pride) and ask, "Why, if this is a valid interaction, does this not take place on a daily basis?"

I understand this interaction is due to the weak interaction, which is 10^-11 times as strong as the electomagnetic force. Is this what it means to be 10^-11 times as strong? That the interactions are 10^-11 times as likely to take place? Does anyone know why or is that just like asking why the fine structure constant is approx. 1/137?

Does it make any sense to ask "how many virtual particles are exchanged between the proton and electron in one second of interaction in the hydrogen atom?"? Or is that just nonsense?

 

[malawi_glenn]

It is a valid interaction and it takes place on daily basis, see for instance electron capture process.

The process H+H -> D + e^+ + neutrino

is also allowed, but occurs only on daily basis in very hot places, like the core of the sun for instance. So there is no correlation between a valid allowed subatomic process and "daily basis" (whatever that might be..)

Ok, the "weak fine structure constant" is about half the value of the electromagnetic one, it is about 1/400. So the strength of the interaction is about the same. BUT the RANGE of the weak interaction is very very very small. The exchange quanta of EM force is by massless particles, photons, but the weak interaction have particles of mass about 100times the proton mass. The interaction will depend on the mass ^(-4) of these particles.

(The matrix element is proportional to 1/(|q|^2 + M^2), where q is momentum transfer, and a process depends on the matrix element squared. When the mass is zero, you don't get infinity, that is a quite usual question one get's "if the photon then is massless, why is not that strength infinite if it depends on 1/(M^4)?")

So, this means that a process has about 10^-11 times smaller cross sections -> i.e probability to occur. So, you were correct! :-)

No we don't know why it has that value, we does not know why any constant at all has its value (the electron mass etc). These questions are asked in the grand unified theories and theories for everything (such as String Theory)

That question is nonsense, for the first, the virtual particles is not really exchanged, they are mathematical "tools/terms" which arises when you do a perturbation expansion of the interaction.

Secondly, when you calculate that, you will have an infinite number of such terms (Feynman diagrams which I assume you have heard of and seen). So there is an infinite number of virtual particles being exchange (in each instant). The nice thing about perturbation theory is that since each vertex of the particle lines in a feynman diagram depends on the coupling. (in electromagnetism, the coupling is the fine structure constant).

So, the first order diagram, where one particle is exchanged, contributes to the sum 137 times more than the second order diagram (where two particles are exchanged). And so on. So the value of the process (the cross section, the likelihood to occur) is often very very good approximated by just calculating the first order term. But the total process IS the ENTIRE sum of all such sub-processes.

Third, not even in theory you can calculate how many is exchanged within a time interval since they occur in one instant.

 

[malawi_glenn]

Also. please, next time, start a new thread :-)

 

[snapback_]

since I don't see where it's going other than to argument and dispute over petty things like ego and pride

It has nothing to do with ego and pride: each of us has his own point of view and is defending it strongly. This is normal, and I'm sure you would this too, if someone is challenging your ideas. Anyway, this is a normal learning process: you confront others with your ideas and see what you can learn (in whichever way) from the reaction. But sure "ego and pride" are maybe topics for another thread, in another forum ;-).

 

[snapback_]

If you ask particle physicists about particle physics, you should not be too surprised if you get particle physics answers and descriptions of physical processes. Since you seemed to have some disbeliefs in particle physics, we (I) tried to sort things up for you.

I asked this question about positronium in the atomic physics thread (this seemed to be the appropriate place, since there is not a such big gap between macro and micro description of world) but was there asked to go the high energy/particle physics forum.

Understanding and calculation abilities goes hand in hand. Believing that one understands something is not the same as actually understanding it. I can think that I understand what supersymmetry is since I know that it is a symmetry between bosons and fermions, but when I consult the Weinbergs QFT part 3, I am lost already on page 17.. so do I understand it or not?

I differentiate between understanding and operational understanding. If you "understand", there is an image in your head, enabling you to predict you what will (probably) happen in the future, and enable you to describe things to others. The "operational understanding" is the ability to calculate things, but you can always calculate without having any idea what's going on there (if you know the mathematical tricks). Since I'm a physicist, maths is simply a (powerful) working tool, in no way different to a pure Ge-Detector or a SMU.

But it isn't that understanding necessarily means an operational understanding: so, applying my notions to your Weinberg example I would say: you understand (in your "language" of course) but your operational understanding's lagging behind.

Damn, we are pretty far away from the original topic, but why not ?

The experimental results are from the early 80's, but the paper I have is from 2008. Why are you interested in knowing these energy levels?

I would like to see a comparison between calculated and measured transitions between levels in positronium. Kind of "Lyman-like" emission or absorption lines observed in positronium.

YOu see, my question is really more something for atomic physics.

 

[malawi_glenn]

I did not see your post in the Atomic Physics forum, and there was not such reference in your first post. Neither did you mention what your goal was. You asked what force within the standard model was responsible for the difference for the interaction of electron + positron and electron + proton. But there is no such force, in the similar way that there is not 'force' responsible for the degenerate matter pressure upheld by the Pauli Principle. That was my ultimate answer, since that was your question. Then I wanted to explain why the process electron + proton is forbidden.

I don't know, but you seemed to be pissed off when I asked why you started to ask a question about positronium and that I reacted that you asked a question about my statement on the pauli principle...

I would say that I understand what supersymmetry is about, but I would not say that I have an understanding on what it IS. I have a stronger 'belief' in math than you I would say, I would argue that physics MUST be described by math, since it is the language appropriate for describing the physical world. I probably don't have to mention that philosophy of physics and science is my hobby...

Ok, then the article I have would probably be suited for you. You could probably find something nice and easy to read in American Journal of Physics. To particle physicsits, positronium is valuable for test of Quantum Electrodynamics (one of the greatest achievements of QED IS the precision of energy levels prediction of positronium) and also matter-antimatter symmetry/asymmetry.

Here are some nice articles on positronium,

http://arxiv.org/PS_cache/hep-ph/pdf/9911/9911410v1.pdf

http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000067000010000880000001&idtype=cvips

http://arxiv.org/PS_cache/hep-ph/pdf/0402/0402151v1.pdf

http://arxiv.org/PS_cache/hep-ph/pdf/0310/0310099v1.pdf

I have to admit that some are the references in the wiki-article, and I have not read them all myself in 100% detail

 

[malawi_glenn]

This book might interest you I think: http://www.alibris.co.uk/booksearch?qwork=5250807&wquery=positron+Physics&qsort=p&matches=32&cm_sp=works*listing*buyused

 

[snapback_]

. You asked what force within the standard model was responsible for the difference for the interaction of electron + positron and electron + proton. But there is no such force, in the similar way that there is not 'force' responsible for the degenerate matter pressure upheld by the Pauli Principle. That was my ultimate answer, since that was your question. Then I wanted to explain why the process electron + proton is forbidden.

I will try to summarize the result of the discussion so far (in my own "language"):

my original Gedankenexperiment of this thread was as follows: two charges of opposite polarity start to move against each other (case A: e-/e+ or case B: e-/p+). Since the charges attract each other, there is an interaction. Now, in the end A) and B) leads to a different final state: annihilation or hydrogen. I asked, which interaction (or force) within standard model is responsible for the different ending of this falling. You said, there is "no such force", it is a conservation law consideration". Thus, not a force from the standard model is responsible for the different ending but it is, to say it simple, the fact, that p+ is a different particle then e+ and thus different quantum numbers are in play, I got your point?

Please allow me on final point: is it a valid question in standard model framework, to ask "how the electron realizes that it is interacting with either a positron or a proton" ?

I have a stronger 'belief' in math than you I would say, I would argue that physics MUST be described by math, since it is the language appropriate for describing the physical world..

This different weighting of maths could be precisely the point, why I'm not glad when I face an answer that "there is no such force".

I will check the positronium experimental data (that one form the 80's) which is referenced in the linked articles, and maybe open then a new thread then.

 

[malawi_glenn]

The electron does not "know" anything, it is not an animate entity...

The symmetry and the laws of physics prevents the electron to annihilate with the proton but allows it to annihilate with the positron.

It is a question related to "how does a stone released from a height realize that it must fall due to influence of gravity?"

It is not even a question valid to ask in any circumstance.

 

[snapback_]

The electron does not "know" anything, it is not an animate entity...

The symmetry and the laws of physics prevents the electron to annihilate with the proton but allows it to annihilate with the positron.

It is a question related to "how does a stone released from a height realize that it must fall due to influence of gravity?"

It is not even a question valid to ask in any circumstance.

I do not understand why you are so stricly rejecting to use other notions to describe phenomena. this strict rejection of other formulations is quite fascinating and typical for rather young people. Is it possible that you are a rather young person, maybe max. 30 years old ?

you stated that "philosophy of physics and science is my hobby.." well, if it is not just a blatancy, then, maybe you can read the article "The Speakable and Unspeakable in Quantum Mechanics" by J.S. Bell. It is just 4 pages and is contained in the book "The Speakable and Unspeakable in Quantum Mechanics", by J.S. Bell which was published by Cambridge UP.

It is available at http://disaweb.ub.uu.se/cgi-bin/chameleon?sessionid=2009022121093513563&skin=default&lng=en&inst=consortium&conf=.%2fchameleon.conf&host=disa.ub.uu.se%2b8044%2bDEFAULT&search=KEYWORD&function=CARDSCR&SourceScreen=INITREQ&elementcount=3&t1=j.s.%20bell&u1=1016&op1=0&pos=2&itempos=1&rootsearch=KEYWORD"

Maybe you will get some insight, what are "allowed questions", and if you like we can continue our discussion later on.

 

[malawi_glenn]

Asking such questions is not valid in a scientific discussion, asking how particles know things is a metaphysical question and is therefore asserted to philosophical discussion.

I should have added "in any SCIENTIFIC circumstance" ;-)

In physics, the question is not about if entities 'knows something' but about symmetries.

I've heard of that book, a friend of mine has read it. I have not specialized into quantum philosophy yet. I will actually attend a class on that this summer ;-)

This book seems quite interesting: https://www.amazon.com/dp/0198242891/?tag=pfamazon01-20