# A Fierz identity

1. Feb 24, 2017

### Luca_Mantani

Hi,
I was calculating some amplitudes and I end up with an expression like this:
$$(\bar{c}\gamma^\mu\gamma^\nu\gamma^\rho P_L b)(\bar{d}\gamma_\mu\gamma_\nu\gamma_\rho P_L u)$$

In the solution of the exercise they say that, from the Fierz identity:
$$(\bar{c}\gamma^\mu\gamma^\nu\gamma^\rho P_L b)(\bar{d}\gamma_\mu\gamma_\nu\gamma_\rho P_Lu)=16(\bar{c}\gamma^\mu P_L b)(\bar{d}\gamma_\mu P_L u)$$

How can I show that?

2. Mar 1, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Mar 21, 2017

### eys_physics

Probably, it is useful for you to read this reference:
https://arxiv.org/pdf/hep-ph/0306087.pdf