Callan-Symanzik equation in dimensionally regularized scheme

[metroplex021]

In every textbook treatment of the CS equation for the bare theory I've seen, the CS equation (and hence the beta-function) is expressed (partly) in terms of variations with respect to the cut-off Lambda, where it is clear that this Lambda refers to a hard momentum cut-off. Can anybody direct me to an expression for the CS equation (for the bare theory) in which the cut-off is modeled by the epsilon of dimensional regularization, where epsilon =4-d, where d is the number of space dimensions? (It seems weird that (as I'm told) particle physicists almost always use dimensional regularization in their day-to-day work, and yet the textbook expos of the CS equation all seems to assume hard cut-off regularization.) Any help or hook-ups gratefully received!

 

[azntoon]

The best reference I can give is a paper by David J. Toms, "The Effective Action and the Renormalization Group" (Phys. Rev. D 21, 2805). In this paper, he considers the CS equation in both hard cutoff and dimensional regularization schemes. He also discusses the relationship between the two regularization schemes and how the CS equation differs in each case. Hope this helps!