# I Fermion self energy

1. Nov 8, 2016

### Safinaz

Hi all,

In Peskin's book, Chapter 7, the self energy of electron has been calculated. In Equation (7. 28) $p\!\!\!/$ set to equal the mass of the electron $m_0$. What if I calculate the self energy of a massless fermion mediated by a loop of another massless fermion and a scalar, like the following diagram:

I got at the end this formula for the mass matrix:

$\Sigma_{ij}(k) = \frac{ y_{jm} y_{im} \Gamma(2)^{-1}}{(16\pi^2)} P_R^2 ~ p\!\!\!/ \int^1_0~ dx~ (1-x) ~ \log\Big( \frac{x\mu^2}{(1-x)m^2-xp^2} \Big) \\ = \frac{ y_{jm} y_{im} }{(32\pi^2)}~ P_R^2 ~ p\!\!\!/ ~ (-1+\log\frac{\mu^2}{m^2})$

Now what will be the value of $p\!\!\!/$ ? also what can be the renormalization scale $\mu$ ? or the cut off scale of the theory ..

In addition if I want to evaluate the amplitude of the process, this means I will square the previous formula and get $p^2$ which will equal zero on- shell, which means I have to calculate this process off-shell, but in this case how to find out the value of $p^2$ ?

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2. Nov 13, 2016