I was trying to learn renormalization in the context of ChPT using momentum-space cut-off regularization procedure at one-loop order using order of p^2 Lagrangian. So,(adsbygoogle = window.adsbygoogle || []).push({});

1. There are counter terms in ChPT of order of [tex] p^4 [/tex] when calculating in one-loop order using Lagrangian of order [tex] p^2 [/tex].

2. Divergences are of polynomial kind and logarithmic kind.

3. The counter terms always take care of polynomial divergences (and [tex] 1/\epsilon [/tex] kind of div. in dimensional method)

4. The logarythmic divergence gets absorbed during coupling constant renormalization.

During my calculation using cut-off method I obtained a result where I have only logarithmic divergence and no other divergent term, then I need to understand what is the use of counter-terms in this case.

In any case, we have to consider the counter-terms in ChPT but here we are not doing dimensional regularization so no [tex] 1/\epsilon [/tex] to get killed by the counter terms, and in my calculation involving cut-off regularization, I have no polynomial divergence either ! Only logarithmic divergence, then what is the use of the counter-terms here ?

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# Cut-off Regularization of Chiral Perturbation Theory

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