DGLAP g-g splitting function?

[Sideways]

Hi -

this is my first post. I'm a recent PhD particle experimentalist; though I'm trying to get a better understanding of underlying theory in my spare time (I hope to contribute more here later).

My question - does anyone know a good source for a derivation of the P_gg (gluon-gluon) splitting function in the Altarelli-Parisi/DGLAP evolution equations? This hasn't been an easy thing to come by. I've worked through solutions for P_qq, P_qg and P_gq ; P_gg is apparently considerably trickier, and explicit solutions seem accordingly more difficult to come by.

I've looked at Altarelli, Parisi's original paper, and I'm having trouble with the notation; I'm wondering if there's a (newer?) textbook out there that works this out explicitly.

Thanks!

 

[Sideways]

Never mind - figured it out! (Sifting through the 1977 paper by Altarelli/Parisi, Peskin & Schroeder's Field Theory, and the 3-gluon vertex Feynman rule eventually confessed the right answer.)

 

[sir-pinski]

Hi there, congratulations on your recent PhD! As a theoretical physicist, I can definitely understand your desire to have a better understanding of the underlying theory. The DGLAP evolution equations are a fundamental tool in understanding the behavior of parton distribution functions (PDFs) in high-energy collisions.

To answer your question, the DGLAP g-g splitting function was first derived by Altarelli and Parisi in their 1977 paper "Asymptotic Freedom in Parton Language." However, as you mentioned, the notation and derivation in this paper can be difficult to follow.

A more accessible resource for the derivation of the P_gg splitting function is the book "An Introduction to Quantum Field Theory" by Michael Peskin and Daniel Schroeder. Chapter 19 specifically covers the DGLAP equations and includes a detailed derivation of the P_gg splitting function.

Additionally, the book "QCD and Collider Physics" by Keith Ellis, John Campbell, and William Stirling also has a clear and concise explanation of the derivation of the P_gg splitting function in Chapter 4.

I hope these resources will be helpful in your understanding of the DGLAP equations and the g-g splitting function. Best of luck in your studies!