Banks-Zaks fixed point

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In quantum chromodynamics (and also N = 1 superquantum chromodynamics) with massless flavors, if the number of flavors, Nf, is sufficiently small (that is small enough to guarantee asymptotic freedom), the theory can flow to an interacting conformal fixed-point of the renormalization group. If the value of the coupling at that point is less than one, then the fixed point is called a Banks-Zaks fixed point.

More specifically, suppose that we find that the beta function of a theory up to two loops has the form

β(g) = − b0g3 + b1g5

where b0 and b1 are positive constants. Then, there exists a value g=g_\ast such that \beta(g_\ast) =0:
g_\ast^2 = \frac{b_0}{b_1}.
If we can arrange b0 to be smaller than b1, then we have g^2_\ast <1. It follows that the theory in the IR is a conformal, weakly-coupled theory with coupling g_\ast.

For the case of QCD the number of flavors, Nf, should lie just below \tfrac{11}{2}N_c, where Nc is the number of colors, in order for the Banks-Zaks fixed point to appear.