I Fermion self energy

  • Thread starter Safinaz
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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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