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A Computation of anomalous dimension in MS scheme

  1. Feb 22, 2017 #1
    Hi,
    I am computing the anomalous dimension of a mass operator in the MSbar scheme, but i have a doubt. The following is the solution of an exercise given by a professor but i don't understand a passage. I have computed the counterterm ##\delta## and i have the formula
    $$\gamma=-\mu \frac{d\delta}{d\mu}$$

    Substituting my calculation and dropping all the constants (which i need but are not relevant for the question) i have

    $$\gamma\propto \mu \frac{de^2(\mu)}{d\mu}\frac{1}{\epsilon}$$

    Then I use the formula

    $$\mu \frac{de(\mu)}{d\mu}=-\epsilon e + \beta(e)$$

    The solution says that if I substitute and drop the ##\beta(e)## i get the finite result we need, since the ##\epsilon## in the numerator cancels the one in the denominator. But why we drop the ##\beta## term, which is finite? If we keep it, we are not able to cancel the ##1/\epsilon## and we get a divergent term, even if we know that the anomalous dimension is finite. What am i missing in this calculation?

    Thanks in advance for the help!
     
  2. jcsd
  3. Feb 25, 2017 #2

    vanhees71

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