Computation of anomalous dimension in MS scheme

In summary, the conversation is about computing the anomalous dimension of a mass operator in the MSbar scheme. The speaker has a doubt about a passage in an exercise given by a professor. They have computed the counterterm and have a formula for the anomalous dimension. The solution provided says to drop the beta term, but the speaker is unsure why since it is a finite term. They are seeking clarification on this calculation.
  • #1
Luca_Mantani
36
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!
 
Physics news on Phys.org

1. What is the MS scheme?

The MS scheme, also known as the minimal subtraction scheme, is a renormalization scheme used in quantum field theory to remove infinities from calculations.

2. What is the anomalous dimension in the MS scheme?

The anomalous dimension in the MS scheme is a measure of how the coupling constant changes as the energy scale of a physical process is varied. It is a crucial quantity for understanding the behavior of a theory at different energy scales.

3. How is the anomalous dimension computed in the MS scheme?

The anomalous dimension in the MS scheme is computed by calculating the beta function, which describes how the coupling constant changes with energy. The anomalous dimension is then obtained by integrating the beta function with respect to the energy scale.

4. Why is the computation of anomalous dimension important?

The computation of anomalous dimension is important because it allows us to study the behavior of a theory at different energy scales. It also helps us understand the renormalization properties of a theory and how it behaves in the ultraviolet and infrared regimes.

5. What are the applications of computing anomalous dimension in the MS scheme?

The computation of anomalous dimension in the MS scheme has many applications in theoretical physics, such as in the study of quantum chromodynamics (QCD), which describes the strong interactions between particles. It is also used in the development and testing of new theories and models in particle physics.

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