Solving RG equations with the Lambert W function

Understand

It has been known for some time that 2-loop renormalization group (RG) equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert W function.

• We apply the method to a generic theory with a Gaussian fixed point to construct RG invariant physical parameters such as a coupling constant and a physical squared mass.
• As a further application, we speculate a possible exact effective potential for the O(N) linear sigma model in four dimensions.