Prerequisites for chiral Perturbation theory

Question

I am Ms final year student. Could you pls guide me for the prerequisites of the chiral Perturbation theory? I have studied Quantum Field theory up to large $N$ gauge theory and renormalizations. Now I would like to head towards the chiral perturbation theory.

Also, I would request for the textbook which gives the basics of chiral perturbation theory.

Answer 1

Introduction to Effective Field Theories, Aneesh Manohar

These are his lecture notes from 2017 Les Houches School. He discusses in quite some detail the general features of EFTs, not just chiral PT. In particular there is a good exposition on power counting and regularization.

You can follow it up with

A Primer for Chiral Perturbation Theory, Stefan Scherer & Matthias Schindler

which is based on Scherer's lecture notes, that apt45 mentioned in their answer.

And even though you have learnt renormalization, it might be helpful to take a second look at it as just a mathematical technique, without all the trappings of field theory. For that you can use

A Hint of Renormalization, B. Delamotte.

Answer 2

I think that your basis is good to start studying Chiral Perturbation Theory. Let me give you some references. All standard textbooks cover the basics of Chiral Perturbation theory (CPT), but I suggest you to start from Effective Field Theories(EFTs). Indeed, the CPT is the most famous example of EFT and it's a good starting point to understand all the physics behind EFTs. The review by Georgi is a very good one, you can find it here, read it.

Then, regarding Chiral Perturbation Theory, I suggest you the following references

Matthew D. Schwartz, Quantum Field Theory and the Standard Model

• Chapter 22.3 : You can find a short introduction to the theory of mesons
• Chapter 28 : It treats spontaneous symmetry breaking and then it discuss shortly the Chiral Lagrangian.

Introduction to Chiral Perturbation Theory, Stefan Scherer, 0210398 hep-ph

• This is more a review you can find on arXiv. It covers a lot of interesting topic. Try to read it.

S.Weinberg, The Quantum Theory of Fields: Volume 2, Modern Applications

• Chapert 19: this is absolutely the best treatement about spontanous symmetry breaking and theory of mesons. I suggest you to read it when you will have a bit of familiarity with EFTs and CPT from the resources I gave you before.