content_image/295224.jpg content_image/295223.jpg content_image/295222.jpg content_image/295221.jpg
Therefore 

<img src='content_image/295224.jpg'>

## E.2.3 Soft Photon Approximation, Massless Dijet 

Compute electron (mass m = 0) beta decay starting with Eq. (F.84), 

<img src='content_image/295223.jpg'>

We will want to exploit the replacement $^{∑}$ϵ$_{µ}$ ϵ ∗ ν → − g$_{µν}$ so we will have to preserve the Ward identity (charge conservation), 

<img src='content_image/295222.jpg'>

To do so we will have to keep the second term explicitly with P$_{M}$ ≃ [ M, M, 0 , 0] being the momentum of the “proton” after (as well as before) beta emission. Then (essentially Eq. (F.86)), 

<img src='content_image/295221.jpg'>

