Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Matrix elements of four-quark operators

+ 3 like - 0 dislike
506 views

In weak interaction phenomenology, especially in strangeness changing processes, effective four-quark operators are used. Such as $Q_1 = (\bar{s}_\alpha \gamma_\mu (1-\gamma_5) d_\alpha) (\bar{u}_\beta \gamma^\mu (1-\gamma_5) u_\beta)$ kind of operators, for example in this, Eq.22, page no. 21. ($\alpha,\beta = 1,2,3 $ are color indices). I needed help in calculating the matrix elements of these operators, let's say, for the process $ \bar{s} \to \gamma^* d \to e^+ e^-$ through a quark-loop, here I have drawn a $u$-quark loop but it can be any quark $q$.

Figure

The problems that I am facing are:

  1. It involves both spinor and color indices.
  2. It's very different than calculations involving single kind of leptons where trace-technology is much simpler, but here we have different kinds of quarks.

Can anyone please provide answers or link to books or notes where similar calculations are done. For example, explicit cross-section calculations using Fermi's four-fermion operators, even this will be really helpful.

Thank you


This post imported from StackExchange Physics at 2015-07-03 21:53 (UTC), posted by SE-user quanta

asked May 15, 2015 in Theoretical Physics by quanta (15 points) [ revision history ]
edited Jul 3, 2015 by Dilaton

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOv$\varnothing$rflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...