 Three-dimensional quartic Yukawa power-counting identity

ID: three-dimensional-quartic-yukawa-power-counting-identity

b

external bosonic legs,

f

external fermionic legs and

n_{4}

scalar quartic vertices, the superficial degree of divergence is the displayed expression. Indeed

ω = 3 L - 2 I_{b} - I_{f}

2 I_{b} + b = 2 n_{Y} + 4 n_{4} + 6 n_{6}

2 I_{f} + f = 2 n_{Y}

and

L = I_{b} + I_{f} - n_{Y} - n_{4} - n_{6} + 1

. Substitution eliminates the counts of the two marginal vertices. The bound concerns overall ultraviolet divergence, before numerator cancellations and subtraction of ultraviolet subdivergences.

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