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I Fermion self energy

  1. Nov 8, 2016 #1
    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 ## ?
     

    Attached Files:

  2. jcsd
  3. Nov 13, 2016 #2
    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.
     
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