Talk:Isospin

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1 Paragraph on SU(6) and symmetry breaking
2 So... is it still "used"?
3 strong theoretical reasons
4 GA Re-Review and In-line citations
5 Corrections to wave functions

[edit] Paragraph on SU(6) and symmetry breaking

I disagree with removing my paragraph on SU(6) and symmetry breaking. It's an extra paragraph (and one I thought was decently written) and isospin always confused me until I knew that information (I'm a physicist). It's important to also consider the readers of the page, high-school kids are not going to be learning about isospin. This is a page most likely visited by undergraduate physics majors, who are looking for the connections to the big picture. Jason Quinn 00:51, 9 Jul 2004 (UTC)

Hello, Jason. Here's is some kind of justification for removing that paragraph

Connections to the big picture are already available as wikilinks to articles on flavor and strong interaction etc. And while it definitely helps to connect it to the big picture more explicitly, the content of that paragraph more rightly belonged to the article on flavor, or quark.
Secondly, it isn't too clear what you mean by adjectives like "good symmetry", "the Eightfold Way is okay" and "badly broken". While I am sure they are part of the jargon which you use as a practising physicist, they are IMHO not the sort of sentences that should live in an encyclopaedic article.
Thirdly, and IMextremelyHO again, sentences like "a results of just the up and down quarks", and "flavor includes all known quarks" are both obfuscatory in meaning, and also physically incorrect (of course, based on what little physics I know).
Incidentally, but no less importantly, it isn't "your" paragraph anymore - you sort of gave it away to be beaten up and kicked around around by everyone on Wikipedia when you pressed that submit button
And, very incidentally, there is no reason why high school kids should not be interested in reading about isospin - I did, when I was in that category.

Regards, [[User:AmarChandra|Amar | Talk]] 05:56, Jul 9, 2004 (UTC)

Exorcised paragraph reproduced below for convenience

In high-energy physics, isospin is considered a subgroup of a larger symmetry group, the Eightfold Way, which is itself a subgroup of SU(6) flavor. Every new quark introduces a larger symmetry group. Isospin was a results of just the up and down quarks (u and d), which are nearly the same mass. The Eightfold Way includes the strange quark (s), which is somewhat heavier. Flavor includes all known quarks, adding charm, bottom, and top (c, b, and t). However the masses of the other quarks are significantly different than the up and down quarks so the strong force is not symmetric with respect to interchange of particles. The symmetry is said to be more and more broken the more the masses differ. Isospin is a good symmetry, the Eightfold Way is okay, and flavor is badly broken.

[edit] So... is it still "used"?

If I'm reading the article correctly -- and I should point out this is the first math/physics article I've come across that I consider even remotely readable -- it seems that isospin is not "real" under a modern treatment, but considered to be a consequence of other physics -- specifically the parton/quark model. Is this correct? If so, I think I/we should add another paragraph at the end, noting this.

Maury 22:37, 28 November 2005 (UTC)

Not true, since quarks carry isospin. Up quark is isospin +1/2 and down quark is isospin -1/2. Pairs of half-integer isospin quarks in a meson sum up to integer isospin values, and so on, according to the representations of SU(2). linas 04:17, 29 November 2005 (UTC)

Ok, but is it the _spin_ of the quarks, or _iso_spin? The article makes it seem that the conservation law in question is not "real", and simply a consequence of the quarks other properties. IE, do quarks carry "isospin charge", or display it in groups. Is there an actual isospin conservation/symmetry at the quark level, or is this a side effect of the dynamics of the strong force (containment)?

There are lots of conservation laws that we no longer consider fundamental, but a side effect of other physics. My question is whether this is one of those examples.

Maury 13:03, 29 November 2005 (UTC)

Yes, quarks carry isospin charge. Its called "iso"spin because its mathematically similar to spin, in that its an SU(2) symmetry. Isospin is the simplest flavour symmetry, and its the closest to being "conserved" in that the mass of the up quark is nearly identical to the mass of the down quark (both of which are believed to have small masses, on the order of half-a-dozen MeV). Isospin is "still" a fundamental symmetry, as there is no other viable explanation at this time. For example, the preon theory has bitten the dust, and there is no experimentally workable string theory.

If you look for mesons made out of u or d and the next-heavier quark, the strange quark, you find that you can arrange them on the corners of a hexagon, called the Eightfold way, which corresponds to the adjoint representation of SU(3). Although the quarks can be arranged in this table (think of it as being a kind of "periodic table"), the mass symmetry is less exact, since the strange quark is much heavier. However, the fact that there is a table, and the fact that the table resembles the adjoint rep of su(3), is one of the ways in which physicists "discovered" quarks: The table makes a strong prediction: namely "all" particles must fit into the table (and to a point, they do). Since the octet is the adjoint rep, which is reducible, the search was on for particles that belong to the fundamental representation, and these turned out to be the quarks.

The table in fact makes much much stronger predictions than just mass symmetries: it also states which particle decays are allowed, and which are forbidden. This is actually the true strength of the table, and the whole notion of flavour symmetry.

The first particle that failed to fit into the su(3) flavour symmetry table was j/psi, which lead to the charmed quark and a Nobel prize. The table was extended to su(4). We now have top and botton, which make up an su(6) flavour symmetry. There are strong theoretical reasons to understand that things stop there; there won't be a 7th or 8th quark.

As mass symmetries, the su(3) flavour symmetry is worse than sub-space that is su(2) isospin symmetry, because the mass of the strange quark is not so small. The mass symmetry gets worse when the charmed quark is included to make su(4). In short, mas flavour symmetry is "badly broken". however, the actual prediction that "all mesons must fit into the adjoint (or higher) representation of su(6)" still stands. This prediction makes strong statements about which particles can decay into what, so in that sense, there really is a real, honest-to-goodness su(6) something in there (with isospin su(2) symmetry being and important, low energy subpiece of it all). Isospin, and more generally flavour symmetry will remain "fundamental" until something is found to replace the Standard Model. linas 15:38, 29 November 2005 (UTC)

Ok, so I understand this. But in the article on hypercharge it says the flavors are strangeness, charm, bottomness and topness. Are the later two really isospin? If so, should that article be changed? Or is hypercharge simply a mathematical construct of some utility that doesn't really have a physical reality?

One interesting comment in the weak isospin article is that it seems to be implying it is the presense of isospin that stops a quark decaying into itself. It is not clear in that article why this is, and it is not mentioned in "this" article at all. Perhaps this is something to add, if it is the case?

I also gather, from your notes above, that the reason they thought their was an isospin was due to the fact that the proton and neutron are otherwise so similar. Normally this would make them degenerate in some sense? Only by introducing the isospin, and having different values, did they "become" separate particles. If I understand this correctly, it would seem a sentance to that effect would be useful as well.

Maury 22:10, 29 November 2005 (UTC)

Don't confuse up and down with top and bottom. In order of increasing mass, the six quarks are: d,u,s,c,b,t. Isospin refers to u,d only, not t,b.

Just a minor correction, the order of increasing mass is u,d,s,c,b,t, as the d is more massive than the u.

When dealing with physics, there is damned litle difference between "mathematical construct" and "physical reality", one cannot perceive the second without employing the first. Isopsin is a construct that mirrors reality.

This article is about "strong" isospin, the isospin that applies to the mass eigenstates for the strong interactions. Unfortunately, these are not eigenstates of the weak interaction, and no one knows why, and there is no convincing theory that talks about this. The mixing between these is given by the CKM matrix. I'll add a sentence to this effect shortly.

Yes, the proton and neutron are (almost) degenerate; they have nearly the same mass. The "only" difference between them is that one is charged. I'll add a sentence emphasizing this. linas 00:12, 30 November 2005 (UTC)

OK, so this article basically sucked. I completely re-wrote it and expanded it, and I hope that now your questions are clearly addressed. linas 02:28, 30 November 2005 (UTC)

If you have any other comments, questions, criticisms, etc. please do state them, as now would be a good time to polish this article and make it as clear as I can make it.linas 04:08, 30 November 2005 (UTC)

[edit] strong theoretical reasons

What are the "strong theoretical reasons" to expect that things stop at flavour SU(6)? As far as I know, there is no theoretical input on the number of generations in the standard model, only experiemental reasons like Z-decay, which only rules out light extra generations. -lethe ^talk 13:32, 19 December 2005 (UTC)

Not sure. The argument I remember was indeed the one-loop amplitude for Z-decay, which was explictly proportional to N_f, the number of flavour generations. The argument, as I remember it, was that, even for large multi-loop corrections, there was no way to fit the experimental data with N_f greater than 3. But I don't remember it well; presumably it said something like "with extra generations whose mass was below the GUT scale". It would be nice to have a wiki aricle that stated the one-loop Z decay amplitude, and clarified this. Hmm. The wiki article on flavour doesn't even mention this (that N_f is almost certainly 3). linas 18:48, 10 January 2006 (UTC)

[edit] GA Re-Review and In-line citations

Members of the Wikipedia:WikiProject Good articles are in the process of doing a re-review of current Good Article listings to ensure compliance with the standards of the Good Article Criteria. (Discussion of the changes and re-review can be found here). A significant change to the GA criteria is the mandatory use of some sort of in-line citation (In accordance to WP:CITE) to be used in order for an article to pass the verification and reference criteria. Currently this article does not include in-line citations. It is recommended that the article's editors take a look at the inclusion of in-line citations as well as how the article stacks up against the rest of the Good Article criteria. GA reviewers will give you at least a week's time from the date of this notice to work on the in-line citations before doing a full re-review and deciding if the article still merits being considered a Good Article or would need to be de-listed. If you have any questions, please don't hesitate to contact us on the Good Article project talk page or you may contact me personally. On behalf of the Good Articles Project, I want to thank you for all the time and effort that you have put into working on this article and improving the overall quality of the Wikipedia project. Agne 00:17, 26 September 2006 (UTC)

[edit] Corrections to wave functions

I recived the following email, which I replied to:

Hi Quilbert,

On Sat, Jan 13, 2007 at 04:20:48PM +0000, Quilbert wrote:
> Hi!
> To me, the proton and neutron wave functions in the article "Isospin" 
> don't make sense. What you state (for the proton) would just be 
> (|duu>  + |udu> + |uud>)/sqrt(3), wouldn't it? But that, in my eyes, 
> is the Delta+ wave function. I wanted to change the article but then 
> saw you're a PhD and seem to be expert on the field. So maybe I am wrong.
> Why do you think that is the correct state? Just apply the I+ operator, 
> it doesn't yield zero, and thus N wouldn't be an isospin doublet.
> With kind regards,
> Quilbert

The right place to ask this question would be on the talk page
associated with the article.

I suppose what is written there is confusing, or at least
misleading. -- where it says "+ perms", I did not mean to imply
that a + sign should be taken for all permutations. Yes, the all-plusses 
case would be a Delta. A minus sign is needed, one would need  
something like (|uud> - |udu> + |duu>) or something
like that; I'm too lazy to check and verify that this gives
all the right quantum numbers for all the different cases.
(And matches the sign conventions used by popular textbooks).

If you are a grad student, and you are studying this, then
please do compare this to what the textbooks say, and make
the needed corrections.

--linas

linas 21:13, 15 January 2007 (UTC)

Hi, yes that was my email, and now I have changed the wave functions in the way I think they are correct. Does everyone agree? At least now, if you apply $I +$ or $S +$ , you get zero, since the sum of all entries is zero for all rows and columns. The other possibility for this would be the matrix $\left(\begin{array}{ccc} 0& -1& 1\\ 1& 0& -1\\ -1& 1& 0\end{array}\right)$ , but I think that is another doublet state, maybe the N(1440)? From what I've read in different places I'm pretty sure the matrix I put into the article is the correct one.