 One-loop sextic cancellation in quartic Yukawa theory

With zero scalar sextic coupling, the only potentially logarithmically divergent one-loop six-scalar vertex has three quartic Yukawa vertices on a fermion loop. Its leading numerator is $(/k{)}^3=k^2/k$, whose trace vanishes. A mass insertion or external momentum lowers the degree and makes the integral convergent. This is not vanishing of every odd gamma-matrix trace: for ${\gamma }^0={\sigma }_3$, ${\gamma }^1=i{\sigma }_1$, ${\gamma }^2=i{\sigma }_2$, one has $\mathrm{tr}({\gamma }^0{\gamma }^1{\gamma }^2)=-2i$. No one-loop sextic counterterm is needed, although a finite six-point vertex may remain.