# Good ref for SU(5) GUT basics?

1. Sep 12, 2007

### mjsd

Can anyone suggest a textbook/paper or two that serves as a good intro/reference to reps of SU(5), SU(5) GUTs and embedding the SM?

I am looking for something that is beginner-ish to medium technicality. A reference of some sort that summaries all basic results and properties.

2. Sep 12, 2007

### BenTheMan

Hmmm. The textbook by Georgi (Lie Algebras in Particle Physics) is pretty good---there is a chapter on SU(5) somewhere towards the back. But he presupposes that you have read his book.

SU(5) stuff is tricky. I don't know how beginner-ish'' you want:)

http://pdg.lbl.gov/2007/reviews/gutsrpp.pdf

If oyu ask questions, I could answer them. I know some of this stuff pretty well, but no promises:)

3. Sep 12, 2007

### arivero

The first volume of the collection of articles by Zee. Also, his textbook has a pretty introduction.

4. Sep 13, 2007

### mjsd

thanks guys,... when I said beginner-ish.. I meant for someone who has good knowledge in the SM but not much on properties of SU(5) and GUTs.

thanks BenTheMan, I would ask questions if I know what I can ask! but I guess it is important for me to sit down and go through it semi-thoroughly once first. I have been studying neutrino flavor symmetries and now also trying to study that with a bit of GUT, so need to learn GUT first and foremorst. And starting with SU(5) because that's the simplest ....

5. Sep 13, 2007

### arivero

mjsd, for beginner-ish and isolated study, I'd bet for Zee textbook.

6. Sep 13, 2007

### mjsd

thanks.
but Zee has so many books ... I guess you were referring to Unity of forces in the universe

7. Sep 13, 2007

### arivero

Hmm no, I refer to Unity as "Zee's book" or better "Zee's collection". For "Zee's textbook" I refer to his "QFT in a nutshell". It has introductory level chapters about SU(5) and SO(10)

I apologise I am somehow cryptic in my references.

8. Sep 13, 2007

### mjsd

cool... that's fine. I have a copy of QFT in a nutshell on my shelf.. and yes I forgot it has an entire part on Grand unification. Maybe that will serve as a good intro/revision for me before tackling some hardcore books on GUTs and group embeddings (i did attended some 1-week course on GUT before... but the lecturer didn't have good notes and besides, as usual, if you don't work on the topics,.. you tend to forget after a while...)

anyway, it is always good to know more than a few references on topics like this.

9. Sep 13, 2007

### arivero

About hardcore group theory, I heard that Veltman/tHoft lecture notes have been recently translated into english.

10. Sep 13, 2007

### BenTheMan

msjd---

If you're just interested in GUT phenomenology, I wouldn't worry about hardcore group theory''. Most of the stuff you need is pretty basic, and you can pick it up as you go along. Georgi's book is pretty good, but most of what you need can be found in chapter 15 of Peskin's book.

If you want more advanced books on GUTs, Graham Ross has a good book (Grand Unification) that covers the subject in some detail. Less detailed is Mohapatra's `Unification and Supersymmetry''. This book is very vague in that it presents the results of many calculations, but not the calculations themselves, which are often long and hard. It DOES have extensive references to the literature, though, which is nice.

11. Sep 14, 2007

### mjsd

thank guys. very much appreciated. I guess I wasn't so clear on what I really need at the beginning... so just asked a few general questions. But I think in order to investigate what I am trying to investigate, I shall need to know all the reps of SU(5), tensor/kronecker products of them (and their irreducible pieces) and those pesky Clebsch-Gordan Coeffs, possible quantum number assignments for the scalar fields (neutrino flavor sym models always come with a lot of scalar fields)

So, I guess, perhaps I would like to find a reference that give me a summary of the properties of SU(5): its irreps, tensor products, C-G coeffs or perhaps a book that teaches you how to systematically calculate all these. I remember doing some of these for discrete group like A4, Z3. But perhaps the generalisation to Lie Groups may be a bit harder, and I want to have a good ref so that I know if I have made a mistake; besides I am sure that this has been done millions of times before by the experts... that's all.
cheers.

12. Sep 15, 2007

### BenTheMan

Oh. Just look them up in Slansky. He worked out all the reps and tensor products.

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=find+a+slansky+and+t+group+theory&FORMAT=WWW&SEQUENCE= [Broken]

Be careful. All of his SU(5) Dynkin Indices are off by a factor of a half.

You can derive all of those things using Young's Tableaux, but its easier to look them up. Check out the charts at the end (start page 195ish).

As far as what fields live in what representations, those can be determined by the branchings of SU(5) into the SM, which are also in the tabels of slansky.

Last edited by a moderator: May 3, 2017
13. Sep 15, 2007

### mjsd

thanks a lot. I have to admit that I 've only just realised (after asking ppl in my office) that there is an old copy of Slansky lying around somewhere.... the rumors is that it used to be my/their adviser(s) copy (very much damaged with coffee spills as well).

Last edited by a moderator: May 3, 2017
14. Sep 15, 2007

### BenTheMan

Ha. This pretty puch describes my copy, too.

15. Sep 16, 2007

### arivero

Bless KEK, they scanned it.

16. Sep 17, 2007

### mjsd

ditto. ("bump" into my boss today and the reason he doesn't need the crappy copy from his student days any more is that he now has that electronic copy...)

anyway, thanks for your input arivero and BenTheMan.